Wave Inversion Technology (WIT)

# Annual WIT reports

### 2018

Please note that the Annual WIT report 2018 is available exclusively for our sponsors.

- Download the entire WIT report 2018 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**A. Bauer, B. Schwarz, T. Werner, and D. Gajewski****Unsupervised event indentiﬁcation and tagging for diffraction focusing**

Bauer et al. introduce a fully unsupervised scheme for the global identification and tagging of diffractions with a common origin in depth and outline potential applications of the gained knowledge.

pdf (password required).**L. Diekmann, B. Schwarz, A. Bauer and D. Gajewski****Source localisation and joint velocity model building using wavefront attributes**

Diekmann et al. present a workflow for the localisation of passive seismic sources and simultaneous velocity model building. The method is based on wavefront attributes and uses wavefront tomography to approximate the velocity distribution and obtain consistent source excitation times for the passive events.

pdf (password required).**M. Glöckner, S. Dell., C. Vanelle, and D. Gajewski****Velocity-estimation improvements and migration/demigration using CRS with continuing deconvolution in the time domain**

Glöckner et al. present method to improve time-migration velocities and images. Therefroe, they use the new generated migrated coherence section to obtain a velocity refinement. Furthermore, least-square migration together with demigration is used to improve the migrated image. The suggested process was succesfully applied to field data.

pdf (password required).**M. Glöckner, D. Gajewski, S. Muff, and C. Berndt****Wavefront tomography with diffraction-only 3D P-cable data**

Glöckner et al. present a velocity-model building approach for 3D P-cable data. The special characteristic of P-cable data, short offset and a high frequnecy source, prohibit convetional VMB. Here, we present a diffraction-based processing and using wavefront tomography to obatin a velocity model without offset information.

pdf (password required).**P. Znak, B. Kashtan, and D. Gajewski****Velocity model building by geometrical spreading focusing**

Znak et al. test a novel wavefront attributes based tomographic method based on minimizing of backpropagated geometrical spreading. The authors recall the Fréchet derivatives formulas for computing the gradient of the new functional and also provide a reduced adjoint-state method formulation. Synthetic reflection data inversion was performed.

pdf (password required).

### Full waveform inversion

**N. Athanasopoulos, T. Bohlen****Aquifer characterization using elastic full-waveform inversion**

Athanasopoulos and Bohlen demonstrate the value of using elastic full-waveform inversion of seismic data for improved aquifer characterisation. After retrieving the elastic parameters through FWI they perform a qualitative comparison with GPR data to obtain a better structural characterisation of the aquifer. Combining the results of these two geophysical techniques provides more reliable subsurface models and reduces uncertainties on reconstructing the aquifer architecture.

pdf (password required).**L. Gassner, T. Gerach, T. Hertweck and T. Bohlen****Seismic characterization of submarine gas-hydrate deposits in the Western Black Sea by acoustic full-waveform inversion of OBS data**

Gaßner et al. show an application of full-waveform inversion to ocean-bottom seismic data acquired in the Black Sea for the purpose of gas-hydrate detection. The inverted velocity model for one of the profiles has a clear indication of a bottom-simulating reflector, consistent with a reference towed-streamer seismic data set. The detailed models allow to estimate hydrate and gas saturation directly from the parameters rather than by means of reflectivity analysis.

pdf (password required).**Y. Pan, L. Gao, and T. Bohlen****A review on phase-velocity and full-waveform inversions of shallow-seismic surface waves**

Pan et al. review the multichannel analysis of surface wave (MSAW) and full-waveform inversion (FWI) methods to investigate their ability to reconstruct detailed subsurface models in near-surface applications.

pdf (password required).**N. Thiel, T. Hertweck and T. Bohlen****Comparison of acoustic and elastic full-waveform inversion of 2D towed-streamer data in the presence of salt**

Thiel et al. show acoustic and elastic full-waveform inversion (FWI) results of a marine 2D data set acquired offshore Angola where sediments containing a salt body with significant topology are present. For this particular data set, elastic FWI leads to more consistent and reliable model updates with less artefacts compared to acoustic FWI which, at first glance, might seem unusual for towed-streamer data. Although 2D marine towed-streamer data are least favourable for the application of FWI compared to 3D data or ocean-bottom data, even for such data sets it is recommended to check on the existence of elastic effects before deciding on the final processing and imaging approach.

pdf (password required).

### 2017

Please note that the Annual WIT report 2017 is available exclusively for our sponsors.

- Download the entire WIT report 2017 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**A. Bauer, B. Schwarz, T. Werner, and D. Gajewski****Unsupervised global identiﬁcation of diffractions based on local wavefront measurements**

Bauer et al. introduce a fully unsupervised scheme for the global identification and tagging of diffractions and passive events with a common origin in depth by analyzing the local similarity of zero-offset wavefront attributes.

pdf (password required).**A.W. Camargo and L.T.Santos****Application of an Augmented Lagrangian Method for Constrained Full Waveform Inversion**

Camargo and Santos present a FWI analysis formulated as nonlinear programming with constraints. We used the Algencan optimization package that presents robust methods for such types problems.

pdf (password required).**J.C. Costa, W.E. Medeiros, M. Schimmel, F.L. Santana, and J. Schleicher****Reverse time migration using phase cross-correlation**

Costa et al. discuss new imaging conditions for RTM based on the phase coherence between the forward and backward propagated wavefields. These imaging conditions, which can be calculated simultaneously to conventional conditions at little or no extra cost, make use of the instantaneous phase and envelope of the analytical signals of the source and receiver wavefields. Numerical experiments with synthetic and field data show that these new imaging conditions can highlight weak reflectors by locally improving the resolution of RTM images.

pdf (password required).**M. Glöckner, S. Dell, B. Schwarz, C. Vanelle, and D. Gajewski****Kinematic time migration/demigration: automatic velocity model building and migration deconvolution**

Glöckner et al. generally discuss kinematic time migration/demigration duality and show how to use this in an advanced time imaging.

pdf (password required).**M. Glöckner and D. Gajewski****Diffraction Separation with Migration Apertures**

Glöckner et al. present a diffraction separation based on migration apertures. Apertures in the range of the first Fresnel zone favour reflections whereas large apertures enhance diffractions. Differences are visible in the migrated coherence section and can be used for a masking and final demigration to obtain diffraction only pre stack data. The proposed method is applied to synthetic data. It shows good separation results for simple data but also the limitations when data is more complex.

pdf (password required).**V.M. Gomes, H.B. Santos, J. Schleicher, A. Novais, and M.A.C. Santos****Curvelet denoising for preconditioning of 2D poststack seismic data inversion**

Gomes et al. analyse how seismic denoising using the curvelet transform as a conditioning step affects acoustic poststack seismic inversion. Their experiments involve both white and coloured noise with a standard hard thresholding technique for denoising and a Bayesian approach to constructing the objective function for inversion. Even though the minimum converges to solutions with reduced noise, curvelet filtering helps to reduce the misfit error considerably. However, they find that for high levels of white noise, and even for rather low levels of coloured noise, curvelet filtering by the tested method fails. In these situations, a more robust filtering technique is required.

pdf (password required).**C. Vanelle, I. Abakumov, and D. Gajewski****Wavefront Attributes in Anisotropic Media**

Vanelle et al. present an extension of the Common Reflection Surface operator to account for arbitrary anisotropy in the 3D finite-offset situation. The derivation is based on geometry and ray theory. The resulting expressions have the same shape and number of coefficients as their isotropic counterparts as long as they are expressed by traveltime derivatives. However, the expressions for the coefficients in terms of wavefront attributes differ from the isotropic case and additional parameters need to be introduced to account for the anisotropy, e.g., the zero-offset operator in 2D requires four attributes instead of three in the isotropic case. Numerical examples in 2D and 3D demonstrate the accuracy of the new operator.

pdf (password required).**J. Walda and D. Gajewski****A new implementation of conﬂicting dips in the common-reﬂection-surface method using differential evolution**

Walda and Gajewski introduce an alternative method of detecting intersecting events in the common- reflection-surface method. The CRS method enhances the signal-to-noise ratio of stacked data significantly. Furthermore, its wavefront attributes can be used in appealing subsequent processing steps, in particular diffraction imaging and velocity model building. Increasing computational facilities research in recent years showed, that a simultaneous parameter estimation is nowadays feasible. Furthermore, it leads to more accurate CRS parameters compared to the pragmatic approach, introduced when CRS was published. This also made alternative methods of detecting intersecting events possible. Nevertheless are modern methods still expensive, in particular for 3D acquisitions since the search space was divided into smaller spaces where CRS has to be performed in each of the smaller spaces. In this paper, we use one application of CRS over the full search space and detect clustering at each iteration based on the dip angle or slowness. The application to 2D synthetic and field data shows promising results. The 3D case indicates issues with the acquisition footprint which needs further investigation.

pdf (password required).**P. Znak, B. Kashtan, and D. Gajewski****Wavefront tomography by dynamic focusing**

Znak et al. propose a novel wavefront curvature based post-stack tomography method valid for reflection, diffraction and passive seismic data inversion. The basis of the new approach is minimizing of geometrical spreading at diffractor position, which they call dynamic focusing. The natural parametrization of the inverse problem by velocity model as the only unknown leads to significantly decreased tomographic matrix dimension and higher data-unknowns ratio. Since deriving and coding the conventional wavefront tomography is cumbersome even in the isotropic case, the reduction of the Fréchet derivatives number is an attractive feature if generalization to anisotropy is desired. The authors provide both Fréchet derivatives and adjoint-state method formulae for computing the gradient of the new functional and perform a field data test.

pdf (password required).

### Modelling

**F. Wittkamp, T. Steinweg, and T. Bohlen****Finite-difference seismic modelling on CPUs and GPUs using matrix-vector products**

Wittkamp et al. present a matrix-vector formalism for time-domain finite-difference seimic modelling. Matrix-vector products can be parallelized on multiple computing systems using an HPC library. We implemented the open-source framework LAMA to develop hardware-independent code. Benchmarks of a 3D elastic forward problem show promising scaling results of the code on CPUs as well as GPUs.

pdf (password required).

### Full waveform inversion

**N. Athanasopoulos and T. Bohlen****Sequential full-waveform inversion of refracted and Rayleigh waves**

Athanasopoulos givs an introduction to a modified workflow of applying full-waveform inversion to shallow seismics. He demonstrates how, with a two-stage procedure, the contribution of the P-wave velocity is properly incorporated in the convergence of the FWI algorithm and no longer ignored due to the high-amplitude Rayleigh waves.

pdf (password required).**Y. Pan, L. Gao, and T. Bohlen****Sequential inversions of surface-wave phase velocity and the full waveform for shallow seismic imaging**

Pan et al. give a short introduction on how to sequentially invert surface-wave phase velocity and the full waveform for shallow seismic imaging of near-surface materials. A synthetic case demonstrates the advantages of this strategy, and a real-world case proves its validity.

pdf (password required).**N. Thiel and T. Bohlen****Comparison of acoustic and elastic FWI for complex salt environments**

Thiel et al. compare the results of acoustic and elastic FWI applied to a marine towed-streamer field data set. They show in this report that even for marine data, it is necessary for complex salt environments to use elastic FWI instead of acoustic FWI.

pdf (password required).

### 2016

- Download the entire WIT report 2016 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**I. Abakumov, B. Schwarz, and D. Gajewski****Auxiliary anisotropic medium**

Abakumov et al. propose a new type of auxiliary medium which utilize anisotropy to account for heterogeneity of the subsurface. The new auxiliary anisotropic medium incorporates properties of effective and optical auxiliary media and enables the derivation of the 3D extensions of the existing multidimensional moveout approximations.

pdf**I. Abakumov, B. Schwarz, and D. Gajewski****3D shifted hyperbola**

Abakumov et al. introduce a formulation of the shifted hyperbola that is valid in three dimensions. The new 3D shifted hyperbola, is more accurate than the conventional 3D NMO. Hence, it bears the potential to provide an improved stacked volume and more reliable stacking parameters.

pdf**D.F. Barrera, J. Schleicher, and J. van der Neut****Limitations of correlation-based redatuming methods**

Barrera et al. show the derivation and approximation of the one-sided correlation-based interferometry equation for surface-data redatuming. Their numerical examples demonstrate that in a homogeneous overburden the resulting single-boundary direct-wave redatuming works perfectly. However, if the overburden is inhomogeneous, it suffers from artifacts, which get even worse if the complete wavefield is used instead of the direct wavefield. Therefore, this interferometric redatuming technique should always be applied using direct waves only.

pdf**D.F. Barrera, J. Schleicher, and J. van der Neut****Up- and downgoing Green’s functions retrieved by inverse waveﬁeld extrapolation**

Barrera et al. propose a new methodology to recover the up- and downgoing wavefield components at a new datum in depth from surface seismic data. The procedure is based on the one-way reciprocity theorems of convolution and correlation type and makes use of two wavefield estimates that can be simulated with the knowledge of an overburden model only. Their numerical examples demonstrate that the procedure works as theoretically predicted and that it does not suffer from the kind of non-physical events that are common in correlation-based redatuming.

pdf**A. Bauer, B. Schwarz, and D. Gajewski****Utilizing diffractions in wavefront tomography**

Bauer et al. try to improve the resolution of velocity models obtained from wavefront tomography by systematically incorporating low-amplitude diffractions into the inversion. Simple and complex results suggest that utilizing diffractions for velocity inversion may help to improve the lateral resolution of the obtained velocity models as well as the results of depth migration.

pdf**W.C. Ferreira, F. Hilterman, L.A. Diogo, H.B. Santos, J. Schleicher, and A. Novais****Global optimisation for AVO inversion: a genetic algorithm using a table-based ray-theory algorithm**

Ferreira et al. develop a table-based ray-theory algorithm to be employed in AVO inversion by global optimisation using a genetic algorithm. The forward modelling algorithm has shown excellent performance, because it allows a large number of members in the population of the genetic algorithm. If used with the correct constraints, the algorithm is capable of recovering the original model with accuracy. However, without constraints, the non-uniqueness of the problem can cause the algorithm to converge to alternative, equally well-fitting solutions.

pdf**G.R. Gomes, J. Schleicher, A. Novais, and H. B. Santos****Depth migration velocity analysis by velocity continuation in common-image gathers**

Gomes et al. implement the image continuation technique in the depth CIG domain to develop a rather inexpensive routine for migration velocity analysis starting at an extremely simple initial velocity model. Synthetic data examples demonstrate the method’s potential of generating first migration velocity models in depth.

pdf**L. Li, H. Chen, X. Wang, and D. Gajewski****Comparison of migration-based microseismic location methods**

Li et al. compare three migration-based microseismic source location methods, namely, diffraction stacking, semblance-weighted stacking and cross-correlation stacking. They suggest that the stacking of squared values of waveforms has better imaging resolution than stacking of absolute values for all methods, when there is no polarization corrections. Diffraction stacking and semblance-weighted stacking share the same stacking operator, and the latter can suppress the noise better. Cross-correlation stacking utilizes the interferometric migration operator and exhibits more reliable results when considering velocity uncertainty. The numerical results demonstrate the feasibility and robustness of migration-based methods for locating low signal-to-noise ratio (S/N) microseismic events.

pdf**C. Vanelle, I. Abakumov, and D. Gajewski****The Anisotropic Common Reﬂection Surface Operator**

Vanelle et al. extend the Common Reflection Surface operator to account for arbitrary anisotropy in the zero-offset as well as finite-offset situation. The derivation is based on geometry and ray theory. The resulting expressions have the same shape and number of coefficients as their isotropic counterparts as long as they are expressed by traveltime derivatives. However, the expressions for the coefficients in terms of wavefront attributes differ from the isotropic case and additional parameters need to be introduced to account for the anisotropy, e.g., the zero-offset operator in 2D requires four attributes instead of three in the isotropic case. Numerical examples demonstrate the accuracy of the new operator.

pdf**J. Walda, B. Schwarz, and D. Gajewski****A competitive comparison of multiparameter stacking operators**

Walda et al. compare multiparameter methods that can be parametrized by the same wavefront attributes, which are the common-reflection-surface (CRS), implicit CRS, non-hyperbolic CRS and multi- focusing. CRS-type operators use a velocity shift mechanism to account for heterogeneity. Multifocusing on the other hand uses a different mechanism: a shift of reference time. We formulate multifocusing such, that it uses the same mechanism as the CRS-type operators and compare them on a marine data set. In turn, we investigate the behavior of time-shifted versions of the CRS-type approximations. In order to provide fair comparison, we use a global optimization technique, differential evolution, which allows to accurately estimate a solution without initial bias. Our results show, that the velocity shift mechanism performs, in general, better than the one incorporating time shift. The non-hyperbolic operators are also less sensitive to the choice of aperture and perform better in the case of diffractions than conventional CRS, since diffractions are of higher order. Since the computational cost of non-hyperbolic CRS is almost the same as the one of conventional hyperbolic CRS but generally leads to a superior fit, we recommend its use in future.

pdf**S. Wißmath, C. Vanelle, B. Schwarz, and D. Gajewski****Prestack data enhancement with ﬁnite-offset CRS attributes**

Wißmath et al. present an extension of the prestack data enhancement method with partial CRS stacks, where finite-offset attributes are used instead of zero-offset attributes. In order to reduce the computational costs associated with finite-offset CRS processing, they suggest to obtain the finite-offset attributes by extrapolation from zero-offset attributes and a subsequent local optimisation. They investigate two different approaches to such an attribute prediction, namely a first-order prediction combined with a truncated operator, and a prediction that uses the first- and second-order attributes with the full operator. Application to marine field data confirms that partial stacking with finite-offset attributes using either of the two approaches leads to enhanced quality of the newly-generated prestack data.

pdf**Y. Xie and D. Gajewski****5D interpolation and regularization with wavefront attributes**

Xie and Gajewski extend the partial 3D CRS method into a 5D interpolation and regularization technique, where the CRS wavefront attributes are determined by a global search strategy, e.g., the evolutionary-based DE algorithm. Then an azimuth-based regularization within each 3D CMP gather is presented. With the 3D SEG/EAGE C3WA data as an example, our results indicate that the partial 3D CRS can perform well in the 5D interpolation and regularization if a global search strategy together with the azimuth-based regularization are considered.

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### Full waveform inversion

**L. Gassner and T. Bohlen****Seismic characterization of submarine gas hydrate deposits in the Danube Deep Sea Fan (Black Sea) by acoustic 2D full waveform inversion**

Gassner and Bohlen present the application of 2D acoustic full waveform inversion to an OBS data set recorded in the Black Sea. The aim of the study is to recover elastic parameters, e.g. vP , of the subsurface to characterize sub seafloor gas hydrate deposits. The recovered compressional wave velocity distribution gives hints on the distribution of hydrates and the occurrence of free methane gas.

pdf**N. Thiel and T. Bohlen****2D acoustic full waveform inversion of submarine salt layer using dual sensor streamer data**

Thiel and Bohlen apply the Full Waveform Inversions (FWI) on the problem of reconstructing salt layers. Acoustic FWI was performed for a marine 2D field data profile. They show the successful inversion of a salt layer in the synthetic and field data case. During the inversion process wavefield separation was performed and Flooding Technique used.

pdf**F. Wittkamp and T. Bohlen****Individual and joint 2-D elastic full-waveform inversion of Rayleigh and Love waves**

Wittkamp and Bohlen investigate the performance of the individual 2-D elastic full-waveform inversion (FWI) of Rayleigh and Love waves as well as the feasibility of a simultaneous joint FWI of both wave types. In synthetic reconstruction tests they compare the performance of the individual wave type inversions and explore the benefits of a simultaneous joint inversion. Subsequently, they recorded a near-surface field dataset to verify the results by a realistic example.

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### 2015

- Download the entire WIT report 2015 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**P. Bakhtiari Rad, Y. Xie, C. Vanelle, and D. Gajewski****3D time migration velocity model building using CRS-based prestack diffraction separation**

Bakhtiari Rad et al. propose a 3D data-driven workflow for time-imaging based on an extension of the CRS-based prestack diffraction separation method. The workflow exploits the fact that stacking velocities for diffractions do not depend on reflector dip. Therefore, stacking velocities obtained from diffraction-only data can be directly used for time migration without further need for residual move-out correction. The proposed method combines the weighting function with the partial CRS stacking technique to separate diffractions before stacking. Subsequently, automatic picking is applied to diffraction velocity spectra to determine a time migration velocity model. Application to a complex 3D synthetic data set confirms the potential for diffraction separation as well as time migration velocity model building using diffractions.

pdf**A. Bauer, B. Schwarz, and D. Gajewski****Zero-offset-based prestack diffraction enhancement using a traveltime decomposition approach**

Bauer et al. apply an enhanced version of the previously introduced diffraction traveltime decomposition approach to simple and complex data and show that the method is able to enhance diffractions in the prestack domain even at large offsets entirely based on zero-offset information.

pdf**A. Bauer, B. Schwarz, M. Lotze, T. Werner, and D. Gajewski****NIP tomography revisited – from reﬂections to diffractions**

Bauer et al. revisit the zero-offset-based NIP tomography as a tool to efficiently invert for the sub-surface velocity structure. In contrast to previous investigations, they focus on non-Snell scattering contributions of the wavefield and show, by exploiting their high ray-path redundancy and illumination properties, that diffractions bear the potential of inverting systematically higher-resolved models than reflection-only data.

pdf**E. Borin, H. Cardoso da Silva, J.H. Faccipieri Jr., and M. Tygel****Accelerating semblance computations on heterogeneous devices using OpenCL**

Borin et al. discuss computational performance on processing methods that heavily rely on the evaluation of traveltime and the semblance functions. The use of OpenCL is investigated to accelerate these computations on multicore CPUs, GPUs, and other hardware accelerators. Experiments indicate that the OpenCL code is highly portable among different computing devices. The performance results suggests that GPUs are promising computing devices to accelerate seismic processing methods that rely on semblance computations.

pdf**T.A. Coimbra, A. Novais, and J. Schleicher****Improved conﬂicting-dip treatment in the offset-continuation trajectory stack**

Coimbra et al. discuss a multi-path approach to improving the conflicting-dip problem in multi-parameter stacking techniques and demonstrate its functionality by means of numerical examples with the offset-continuation trajectory (OCT) stack.

pdf**M. Glöckner, Y. Yang, C. Vanelle, and D. Gajewski****Kinematic time demigration: the implicit CRS approach**

Glöckner et al. investigate the possible application of the implicit CRS approach as kinematic time demigration operator. The method is applied to synthetic and field data and shows the feasibility of the approach.

pdf**M. Salcedo, A. Novais, J. Schleicher, and H.B. Santos****Optimisation of the parameters in complex-Padé Fourier ﬁnite-difference migration**

Salcedo et al. optimise the parameters of complex-Padé Fourier finite-difference migrations in order to extend the range of imageable reflector dips. They show that with optimised parameters, a one-term Padé expansion is sufficient to image dips up to 65 degrees. The second term only leads to improvements for small ratios between the reference and model velocities.

pdf**H.B. Santos, J. Schleicher, A. Novais, A. Kurzmann, and T. Bohlen****Robust time-domain migration velocity analysis methods for initial-model building in a full waveform tomography workﬂow**

Santos et al. present a workflow for the construction of initial velocity-models for full-waveform tomography (FWT) methods consisting of automatic time-migration velocity analysis by means of double multi-stack migration, followed by time-to-depth conversion by image-ray wavefront propagation. Evaluation of the converted velocity model as an initial velocity model in an acoustic FWT process indicates the potential to achieve a fully automatic tool for initial-model building in a FWT workflow.

pdf**J. Walda and D. Gajewski****Improvement of the common-reﬂection-surface stack by differential evolution and conﬂicting dip processing**

Walda and Gajewski improve the common-reflection-surface (CRS) stack by incorporation of conflicting dips in combination with a global optimization scheme. First the quality of the estimated attributes is demonstrated. Afterwards the method is applied to partial CRS to regularize and enhance prestack data. To correctly estimate the CRS operator, we use differential evolution where we divide the angle space in several intervals to account for conflicting dips. Previously masked events are now visible as demonstrated by diffraction separation.

pdf**Y. Xie and D. Gajewski****3D CRS attribute search using particle swarm optimization**

Xie and Gajewski introduce the particle swarm optimization (PSO) algorithm to simultaneously search the initial 3D CRS attributes, which is a desired search strategy compared to pragmatic three-step grid search.

pdf**Y. Yang, C. Vanelle, M. Glöckner, and D. Gajewski****Kinematic time demigration: the CSP approach**

Yang et al. suggest a partial time demigration method for enhancing prestack data quality. It is based on a single square root equation in terms of midpoint displacement, half-offset and migration velocity. By applying partial time migration followed by the new partial time demigration, the quality of original data can be improved. The newly-generated prestack data can then be used as input for conventional processing and thus result in better images. Application to a simple and a complex synthetic data set as well as to field data confirms that the signal-to-noise (S/N) ratio of the resulting prestack data is improved. Furthermore, the method can be utilised for prestack data regularisation.

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### Modelling

**T. Bohlen and F. Wittkamp****3-D viscoelastic time-domain Finite-Difference seismic modelling using the staggered Adams-Bashforth time integrator**

Bohlen and Wittkamp investigate the implementation of the staggered Adams-Bashforth method (ABS) to increase the temporal accuracy in FDTD seismic modelling. ABS is a multi-step method that uses previously calculated wavefields to increase the order of accuracy in time. In 1-D and 3-D simulation experiments they verify the convincing improvements of simulation accuracy of the fourth-order ABS method. In a realistic elastic 3-D scenario the computing time reduces by a factor of approximately 2.4, whereas the memory requirements increase by approximately a factor of 2.2. The ABS method thus provides an alternative strategy to increase the simulation accuracy in time by investing computer memory instead of computing time.

pdf**J. Schleicher and J.C. Costa****Aseparable strong-anisotropy approximation for pure qP wave propagation in transversely isotropic media**

Schleicher and Costa derive a separable strong-anisotropy approximation for the dispersion relation of pure qP waves in VTI media. A comparison to results from a low-rank implementation of the full dispersion relation demonstrates that this can provide high-accuracy wavefields even in strongly anisotropic inhomogeneous media.

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### Full waveform inversion

**V. Kazei and E. Tessmer****Efﬁcient deﬂection angle based ﬁltering for FWI**

Kazei and Tessmer introduce a novel regularization algorithm for full-waveform inversion via non-stationary filtering of the misfit functional gradients. The non-stationary filtering is usually computationally intensive, yet the proposed algorithm is very efficient since it requires neither the computation of non-stationary convolutions, nor the model space extension. The filter was tested on the Marmousi model and proved to be helpful to improve FWI convergence.

pdf**M. Kunert, A. Kurzmann, and T. Bohlen****Application of 2D acoustic full waveform inversion to OBC-data**

Kunert et al. apply acoustic full waveform inversion to a marine seismic data set acquired in shallow water. A complex inversion workflow is developed and a satisfactory model of P-wave velocity is recovered from OBC data. Small-scale structures, such as fault zones, were reconstructed. Due to low velocities, we assume gas accumulations in these areas.

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### Other topics

**T.A. Coimbra, J.H. Faccipieri, L.-J. Gelius, and M. Tygel****Enhancement of stacked sections using ZO CRS parameters**

Coimbra et al. propose a noise-reduction algorithm that is applied to a CRS stacked volume. By means of the proposed algorithm, each sample in the CRS stacked volume will be spread out to its neighboring points in the volume along the CRS diffraction traveltime surface that pertains to that sample. The proposed method was applied to synthetic (Sigsbee2b-nfs) and real (Jequitinhonha) datasets with promising results in terms of better signal-to-noise ratio, event enhancement and conflicting-dip corrections.

pdf**T.A. Coimbra, J.H. Faccipieri Junior, and M. Tygel****Time-to-depth conversion using modeling rays**

Coimbra et al. review and advance time-to-depth conversion by means of so-called modeling rays. This approach avoids the construction of image rays, thus avoiding its disadvantages, which include problems of caustics,interpolation and regularization that are characteristic of image ray-tracing techniques. Besides a review of the concept and tracing of modeling rays, we propose a new algorithm for time-to-depth conversion that is simpler and more efficient than the ones available in the literature. Applications to synthetic and real data provide encouraging results.

pdf**J.H. Faccipieri, D. Rueda, T.A. Coimbra, I.L. Rodrigues, A.L. Farias, and M. Tygel****Surgical CRS Stacking**

Faccipieri et al. proposes an iterative process for CRS processing which consists of the following steps: (a) User-selection at a few (picked) points, on an initial (given) CMP stacked section and global exhaustive evaluation of CRS parameters on these points; (b) Interpolation/extrapolation of the obtained CRS parameters to fill out all sample positions that comprise the ZO section or volume to be constructed; (c) Global refinement of CRS parameters using the previously obtained parameter as initial values; (d) Computation of the CRS stack with the refined parameters and finally (e) This process is repeated by adding, subtracting or editing points until a desired result is achieved.

pdf**D.M. Kamioka, A.W. Camargo, A. Novais, J. Schleicher, and L.T. Santos****Minimum semblance: A modiﬁed coherence measure to improve the resolution of semblance sections**

Kamioka et al. introduce Minimum Semblance, a simple modification of conventional semblance. It uses the minimum value of several semblance values within a given time window. Numerical examples show that Minimum Semblance increases resolution of semblance sections with comparable computational cost to the conventional measurement.

pdf**S. Maciel and R. Biloti****A set of descriptors for automatic classiﬁcation of scatterers in seismic sections**

Maciel and Biloti show a new way to construct a set of descriptors for diffraction operators in order to classify scatterers in seismic sections. This is done using statistical attributes from the distribution of amplitudes along a diffraction traveltime path. The approch brings new light into diffraction imaging and Kirchhoff summation. Results show that automatic classification of scatterers might be performed with classic Machine Learning techniques.

pdf**B. Schwarz, A. Bauer, and D. Gajewski****Passive seismic source localization via CRS attributes**

Schwarz et al. introduce a data-driven scheme to simultaneously invert for the spatial location of a passive seismic source and the velocities of the traversed medium. Being based on the attributes of the normal-incidence-point (NIP) wave, the method utilizes two different parameterizations of a geometrically derived stacking operator to estimate the unknown passive source excitation time. Concluding this work, the applicability of the approach is demonstrated with a simple synthetic example.

pdf**M. Vefagh and D. Gajewski****A coherency guided method for pre-stack multiple attenuation**

Vefagh et al. introduce an approach for multiple attenuation, which is applicable to any type of multiple reflection including internal multiples. It includes picking zero-offset traveltimes of multiples in a stacked section which is guided by the coherence, these traveltimes are then used to predict the pre-stack multiples with the help of the stacking velocity. This method performs stable for far offsets and it does not require high computational effort. Both synthetic and field data examples illustrate the potential of the method.

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### 2014

- Download the entire WIT report 2014 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**K.A. Ahmed, B. Schwarz, and D. Gajewski****Application of the 3D CRS workﬂow in a crystalline rock environment**

Ahmed et al. apply a 3-D CRS workflow to data from a hard rock environment, where they emphasise the coherence-based seismic imaging approach. Their studies show that, in comparison to the actual stacks, coherence provides more information on the sub-surface, particularly on the geological structures.

pdf**P. Bakhtiari Rad, B. Schwarz, C. Vanelle, and D. Gajewski****Common reﬂection surface-based prestack diffraction separation**

Bakhtiari Rad et al. suggest a CRS-based workflow for the generation of prestack diffraction-only gathers. The method applies prestack data enhancement by partial stacking after performing a separation of reflected and diffracted events. Results for the complex Sigsbee 2A data as well as for field data not only confirm the applicability of the method, they also demonstrate the potential for time migration velocity analysis using diffraction-only data.

pdf**A. Bauer, B. Schwarz, and D. Gajewski****From ZO to CO with diffractions: Theory**

Bauer et al. introduce a straightforward decomposition principle for diffractions, which establishes a direct connection between zero-offset and common-offset information. This allows the ZO-based prediction of common-offset diffraction wavefield attributes. By fitting traveltimes they show that each common-offset diffraction operator may be decomposed into two independent zero-offset operators. Application to simple waveform data reveals the potential of the new method to reliably image diffractions in the common-offset domain.

pdf**A. Bauer, B. Schwarz and D. Gajewski****From ZO to CO with diffractions: Complex data examples**

Bauer et al. apply the previously introduced decomposition principle for diffractions to complex synthetic and marine field data. Combining the stability of zero-offset processing with the improved illumination in the common-offset configuration, the promising results reveal the potential of the new method to reliably enhance diffractions and attenuate reflections in pre-stack data and thus motivate a reliable pre-stack diffraction separation. High quality common-offset diffraction attributes favor the development of a diffraction-stereotomography.

pdf**M. Bobsin, B. Schwarz, C. Vanelle, and D. Gajewski****Time migration applying the i-CRS operator**

Bobsin et al. derive a prestack time migration operator based on the i-CRS operator. The required time migration velocities are determined as a byproduct of the preceding i-CRS stack. The application to synthetic and field data leads to the promising conclusion that complex features like faults and diffractions are well resolved, as are the reflections.

pdf**J.A.C. Gonzalez, J.J.S. deFigueiredo, T.A. Coimbra, J. Schleicher, and A. Novais****Unconventional velocity seismic processing based on the diffraction ﬁlter and residual diffraction moveout: application to a Viking Graben dataset**

Gonzalez et al. develop a practical approach to construct velocity models in the time and depth domains using seismic diffractions. This methodology applies plane wave destruction (PWD) filters jointly with the residual diffraction moveout (RDM) method. Its only requirements are the presence of identifiable diffraction events after filtering out the reflection events and an arbitrary initial velocity model as input. We compare post-stack migrated images (in the time and depth domains) with images migrated with models obtained from conventional seismic processing. In both cases, we used post-stack Kirchhoff migration. Beyond the need to identify and select the diffraction events in the post-stack migrated sections in the depth domain, the method has a very low computational cost. The processing time to reach an acceptable velocity model was 75% less as compared with conventional processing.

pdf**H.B. Santos, T.A. Coimbra, J. Schleicher, and A. Novais****Remigration-trajectory velocity analysis: Improved derivation and proof of concept**

Santos et al. improve on the derivation of remigration-trajectory velocity analysis presented last year. Moreover, they present a detailed algorithm of the method and carry out additional numerical tests on synthetic datasets from three gradient models and the Marmousoft data. These tests demonstrate the feasibility of the method in more realistic situations with strong velocity variations in different directions.

pdf**H.B. Santos, D.L. Macedo, E.B. Santos, J. Schleicher, and A. Novais****Use of 3D gravity inversion to aid seismic migration-velocity building**

Santos et al. develop a 3D depth-velocity model building based on 3D gravity inversion. Their method consists in determine the density distribution of specific bodies (targets), and replace them by coherent velocity values. This initial velocity model can be used together with migration velocity analysis tools, which in turn, can provide sufficient information to updated the initial geometric parameters for a recent gravity inversion. The main advantage of their technique is that it provide a iterative and robust algorithm that does not require the solution of an equation system. This joint processing and interpretation shows to be a fast alternative to improve the knowledge of complex structures like salt structures and sub-salt sediments.

pdf**B. Schwarz, C. Vanelle, and D. Gajewski****Auxiliary media revisited – new insights and applications**

Schwarz et al. revisit the concept of auxiliary media and provide a unified view on presently used stacking techniques. By introducing the inverse transformation from the optical to the effective domain, the authors emphasize that all higher order stacking operators, like the multifocusing approximation or the hyperbolic common-reflection surface, have two different faces. Synthetic examples indicate that these transformations not only contribute to unification, but that they also, i. e., when used in combination, provide unique opportunities for wavefield characterization and passive source time inversion.

pdf**L.S.S. Valente, H.B. Santos, J.C. Costa, and J. Schleicher****A strategy for time-to-depth conversion and velocity estimation**

Valente et al. present a strategy for time-to-depth conversion and velocity estimation based only on image-wavefront propagation. In particular, it makes use of a geometric manipulation to directly compute both the velocity field and the traveltime, avoiding a previous ray-tracing step. Moreover, it requires only the knowledge of the image-wavefront of the previous time step. It robustness is proved with its application on a simple synthetic example and on the Marmousi model. The quality of the results are evaluated by depth migrated images from the Marmousi data set with the extracted velocity models.

pdf**C. Vanelle, S. Wißmath, and D. Gajewski****Finite-Offset CRS: parametrisation and attribute prediction**

Vanelle et al. suggest an intuitive parametrisation for the CRS offset case. They introduce a new method to obtain the finite offset CRS attributes by extrapolation from either zero offset or another finite offset. These attributes can be used, e.g., as initial values for a global optimisation. Another important application is their incorporation into the partial stacking algorithm for pre-stack data enhancement. That technique currently requires a search for the zero-offset parameters that best describe the traveltime at a given offset, which is not only tedious and potentially non-unique, but also leads to a lower degree of accuracy than the use of the corresponding offset parameters. With the new method, the latter parameters are available. The resulting expressions are exact for planar reflectors. Generic examples with curved reflectors show that the offset parameters can be predicted with good accuracy.

pdf**J. Walda and D. Gajewski****Handling the conﬂicting dip problem in the CRS/i-CRS methods**

Walda and Gajewski recognize that most current implementations of the CRS operator suffer from the occurrence of conflicting dip situations in the acquired data. To address this properly we apply the idea of the CDS to the i-CRS operator and show, that conflicting dips can be resolved well in multi-parameter processing. The results are promising and reveal a lot of potential for further applications. This is shown by a diffraction separation technique applied to field data obtained in the Levantine Basin.

pdf**Y. Yang, C. Vanelle, and D. Gajewski****Prestack data enhancement by partial time migration: a subsalt case study**

Yang et al. suggest a partial time migration method for subsalt imaging. It combines the robustness of time migration with the data enhancement properties of multi-parameter stacking. The presented method is based on the generation of partially time-migrated gathers, i.e., prestack data in the common scatterpoint (CSP) domain, that are used as input for a subsequent multi-parameter stacking procedure. The results are kinematically equivalent to conventional prestack time migration results, but lead to better image quality because of the inherent prestack data enhancement capability. The application to a complex synthetic data set as well as to field data demonstrates a considerable improvement, not only in faults and salt boundaries, but also in the subsalt region.

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### Modelling

**T. Bohlen and F. Wittkamp****Higher order 1-D FDTD seismic modelling using the staggered Adams-Bashforth time integrator**

Bohlen and Wittkamp investigate the implementation of the multi-step Adams-Bashforth method to increase the temporal accuracy in FDTD seismic modelling. They show that the global accuracy of FDTD seismic modelling can be easily increased up to fourth order without significant additional computational costs. The price to pay is an moderate increase of the memory requirement which is feasible on modern parallel High-Performance computers.

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### Full waveform inversion

**R. Shigapov, A. Kurzmann, and T. Bohlen****Viscoacoustic full waveform inversion for spatially correlated and uncorrelated problems in reﬂection seismics**

Shigapov et al. investigate multiparameter viscoacoustic full waveform inversion. Sequential and parallel inversion strategies are applied to inverse problems with both spatially correlated and uncorrelated models. Results are shown for a simple 1D medium as well as the Marmousi model.

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### Other topics

**M. Behzadi, D. Gajewski and C. Vanelle****Seismic event localisation based on cross-correlation stacking**

Behzadi et al. present a passive seismic imaging method based on moveout correction and cross-correlation stacking. The method takes into account and countermands effects due to geometrical spreading and reduces the impact of the acquisition footprint. Application to synthetic and field data examples demonstrates the performance of the method and shows that it succeeds in a reliable localisation not only for impulsive sources but also for microtremors.

pdf**T.A. Coimbra, J.H. Faccipieri, and M. Tygel****CRP time migration**

Coimbra et al. propose a Kirchhoff-type, time migration algorithm that is optimal in two respects. First, the summation is performed along the common-reflection-point (CRP) curve (as opposed to the conventional diffraction-time hyperbola). Second, a small aperture, associated to the projected Fresnel zone (PFZ), is employed that is able to restrict the summation to that part of the CRP curve where constructive interference occurs. First real-data examples confirm that the technique has a good potential for high-quality, time migration imaging.

pdf**J.H. Faccipieri Junior, T.A. Coimbra, L.-J. Gelius, and M. Tygel****Stacking apertures and estimation strategies for reﬂection and diffraction enhancement**

Faccipieri et al. investigate the use of different apertures tailored for reflection and diffraction enhancement events. The use of SSR moveouts with small apertures in midpoint, produced comparable results as the ones of conventional CRS with full-parameter reflection moveouts. In both cases, reflections are enhanced and diffractions attenuated. However, using the DSR moveout with large midpoint apertures produced stacked sections in which diffractions are enhanced and reflections attenuated. The quantification of small and large apertures was defined using an approximation of the PFZ for optimal overall imaging.

pdf**L.-J. Gelius and M. Tygel****Generalized screen propagator revisited**

Gelius and Tygel propose a generalized higher-order screen propagator to be used in modelling and migration in the frequency-wavenumber domain. The new formulation is compared with other known screen propagators and its superior behaviour is demonstrated.

pdf**J. Schleicher and J.C. Costa****Pure qP-wave propagation in VTI media**

Schleicher and Costa discuss the pseudo-S wave in VTI media and show how their occurrence can be avoided. A Padé approximation with slightly unconventional numbers for the Padé coefficients led to the best approximation. An implementation of a low-rank approximation to this equation demonstrated that is can provide high-accuracy wavefields even in strongly anisotropic inhomogeneous media.

pdf**M. Vefagh, D. Gajewski, and S. Dümmong****A zero-offset picking approach for pre-stack multiple attenuation**

Vefagh et al. introduce an approach for multiple attenuation, which is applicable to any type of multiple reflection including internal multiples. It includes picking zero-offset traveltimes in a stacked section, which are then used to predict the pre-stack multiples with the help of the stacking velocity. This method performs stable for dipping reflectors and far offsets. Furthermore, it does not require high computational effort. Both synthetic and field data examples illustrate the potential of the method.

pdf**J. Walda and D. Gajewski****Global optimization of the CRS operator using a genetic algorithm**

Walda and Gajewski suggest the use of a genetic algorithm for the global optimization in the CRS context. The CRS operator improves the signal to noise ratio significantly due to the consideration of neighboring midpoints as well as the offset. The determination of the required attributes for the CRS operator is often done by the pragmatic approach to get initial values that are refined by a local optimization. This approach has limitations. Therefore we propose to use a genetic algorithm based optimization and show that the stack and especially the determined attributes are significantly improved.

pdf**P. Witte and D. Gajewski****Optimization of the semblance in the 2D CRS stack using a coarse line search**

Witte et al. investigate the properties of the semblance function in the two-dimensional CRS stack and propose a modified version of the conjugate direction method for its optimization. Instead of relying on initial guesses from the pragmatic approach, an initial starting guess for the final local optimization is obtained by coarsely sampling the objective function along a one-dimensional direction.

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### 2013

- Download the entire WIT report 2013 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**P. Adetokunbo, D. Gajewski, B. Schwarz, and C. Vanelle****Offset dependence of stacking attributes for CRS and i-CRS operators**

Adetokunbo et al. investigate the influence of the spread length on the determination of stacking attributes with the CRS and i-CRS operator.

pdf**K.A. Ahmed, D. Gajewski, and B. Schwarz****Application of the 3D CRS workﬂow in crystalline rock environment**

Ahmed et al. present an application of the 3D-CRS workflow to hard rock data. The considered data are low fold and the emphasize of the study is on coherence since it provides better images than the stack.

pdf**E. Borin, A. Novo, I. Rodrigues, J. Sacramento, J.H. Faccipieri, and M. Tygel****Enabling large data processing with the 3D ZO CRS Stack software**

Borin et al. provide an overview of the 3D ZO CRS Stack software, including its parallel execution model, and an analysis of the performance of the software when executing large data sets. The authors show that the current implementation of the makeGeometry procedure hinders the processing of large (1TB) data sets and present a solution for the problem.

pdf**T.A. Coimbra, J.J.S. de Figueiredo, A. Novais, J. Schleicher, and S. Arashiro****Migration velocity analysis using residual diffraction moveout in the pre-stack depth domain**

Coimbra et al. extend their diffraction-based migration-velocity-analysis method to the prestack domain. The algorithm uses the focusing of remigration velocity rays from uncollapsed migrated diffraction curves to iteratively update the velocity model. Since the velocity rays are constructed from a ray-tracing like approach, the method has a very low computational cost between migrations. Synthetic data examples demonstrate the method’s feasibility.

pdf**T.A. Coimbra, D.F. Barrera P., J. Schleicher and A. Novais****Interferometric redatuming using direct-waveﬁeld modeling**

Coimbra et al. combine modeling with interferometry and correlate the modeled direct wavefield with seismic surface data to relocate the acquisition system to any datum in the subsurface to which the propagation of direct waves can be modeled with sufficient accuracy. They demonstrate theoretically and numerically that reflections from deeper interfaces are repositioned with satisfactory accuracy.

pdf**T. A. Coimbra, H. B. Santos, J. Schleicher and A. Novais****Prestack migration velocity analysis using time-remigration trajectories**

Coimbra et al. present a prestack time-migration tool for local improvement of the seismic migration-velocity model, based on time-remigration trajectories. Kinematic parameters from local-slope information of seismic reflection events are used to locally correct the velocity model. The main advantage of this technique is that it allows to carry out a residual moveout correction for all offsets of a common image gather (CIG), taking into account the reflection-point displacement in the midpoint direction. Tests on synthetic and SMAART-Sigsbee2B data demonstrated the feasibility of the method.

pdf**L.-J. Gelius and M. Tygel****High-resolution imaging of seismic data: How to combine wave-theory with signal processing techniques**

Gelius and Tygel revisit seismic imaging employing integral-equation type of migration. To further improve the resolution of the reconstruction of both reflections and diffractions, they propose to employ ideas taken from Fresnel-aperture migration which uses low-frequency stationarity to select that part of data that coherently contribute to the final image. The approach offers an efficient way to window the coherent reflection energy which if being aligned, which, together with a window-steered MUSIC approach, has the potential of giving high-resolution seismic images.

pdf**L.-J. Gelius and M. Tygel****On the use of smooth velocities in ray-based stacking and time-migration**

Gelius and Tygel revisit ray-based approaches to stacking and time-migration of seismic data, and investigate the role of the smooth-velocity condition normally attached to such techniques. It is shown that the smooth velocity field plays the role of a replacement medium in such a way that the one-way analogues of the stacking and time-migration operators can be approximated, in a paraxial sense, by its impulse responses. It is shown how stacking and time-migration velocities relate to useful properties along the central or mapping ray of the impulse responses.

pdf**M. Koushesh, B. Schwarz, and D. Gajewski****Interpolation and prestack data enhancement using Partial i-CRS Stack**

Koushesh et al. evaluate the power of CRS and i-CRS methods in interpolating and enhancing of signal to noise ratio in pre-stack data.

pdf**A. Novais, J. Schleicher, and J. C. Costa****A spatial approximation for the Li correction**

Novais et al. investigate the theoretical expression of the Li correction in order to approximate the involved Fourier transforms by means of the method of stationary phase. They find a simple phase-correction factor in space, using the direction of wave propagation as the dominant direction. Numerical experiments with the exact propagation angle show that the so-achieved correction has acceptable quality with considerable reduction in computational cost.

pdf**H.B. Santos, J. Schleicher and A. Novais****Initial-model construction for MVA techniques**

Santos et al. discuss two recent time MVA methods, being common-image-gather image-wave propagation and double multi-stack migration, and compare their potential for the construction of initial models for more sophisticated MVA techniques. At the example of the Marmousoft dataset, they show that both methods can be used in a fully automated procedure to produce a velocity model and a time-migrated image without a-priori information at comparable cost.

pdf**J. Schleicher, J. C. Costa, and A. Novais****Reduction of crosstalk in blended-shot migration**

Schleicher et al. study various ideas of using weights in the imaging condition of blended-shot migration, in order to reduce crosstalk. They combine the ideas of random phase and/or amplitude encoding and random alteration of the sign with additional multiplication with powers of the imaginary unit. The results indicate that with a combination of these weights, the crosstalk can be reduced by a factor of 4. Moreover, they compare random shot grouping with one based on Costas arrays. The objective is to avoid the occurrence of patterns in the distribution, in this way reducing coherent crosstalk energy. Finally, they show that the crosstalk noise can be reduced after migration by image processing.

pdf**B. Schwarz, C. Vanelle, and D. Gajewski****Auxiliary media – a generalized view on stacking**

Schwarz et al. provide a generalized view on current multi-parameter stacking techniques. They indicate that all higher-order traveltime approximations, despite being parameterized with the same set of attributes, are based on the straight ray assumption and can be devided into two main subcategories, which behave fundamentally different when heterogeneity is present. The authors suggest a simple recipe for the transformation from one category to the other and argue that both types of operators have distinct advantages, either accounting well for heterogeneity or leading to an efficient implementation.

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### Modelling

**A.W. Camargo and L.T. Santos****Analysis of a ﬁnite difference scheme with adaptive spatial operator for the acoustic wave equation**

Camargo and Santos analyse a FD scheme for the acoustic wave equation, with an adaptive spatial operator which reduces the computational cost but not the accuracy. The idea is to use long operators in low velocity regions and short operators in high velocity ones.

pdf**L.-J. Gelius and M. Tygel****The cost function used in 3D mCSEM inversion - is the Born approximation valid?**

Gelius and Tygel discuss the validity of the first Born approximation that is used in the inversion of marine Controlled Source Electromagnetic (mCSEM) data. An extended Born approximation is advocated for which provides significantly more accurate results with a modest increase of computational effort.

pdf**M. Voegele, E. Tessmer, and D. Gajewski****Stability tests on a numerical solution of a pseudo-acoustic TTI wave equation**

Voegele et al. point up the well-known stability issues of a pseudo-acoustic wave equation on numerous 2D TTI macro-models. By varying the amount of shear-wave velocity along the symmetry axis they get a better insight in the activation of non-physical solutions for the wave equation. In this way, a common thread between the parameters for anisotropy and the occurring instabilities is derived.

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### Full waveform inversion

**S. Butzer, A. Kurzmann and T. Bohlen****Applying a diagonal Hessian approximation for preconditioning in 3D elastic full waveform inversion**Butzer et al. shows the application of a diagonal Hessian approximation for preconditioning in 3D elastic full waveform inversion.

pdf**S. Heider and T. Bohlen****Full waveform inversion in crystalline host rock: analysis of receiver coupling**Heider et al. show a synthetic example for inverting a random distributed velocity model and prior steps to invert for the field data.

pdf**D. Macedo, I. Vasconcelos and J. Schleicher****Scattering-based sensitivity kernels for time-lapse differential-waveform inversion**Macedo et al. apply scattering theory to the time-lapse problem, considering the time-lapse change as a perturbation of the singular part of the model. They make use of the time-lapse differential-waveform inversion framework, with the linearized scattering-based decomposition of the sensitivity kernel. Their numerical examples demonstrate that the inclusion of the singular part into the model used for back- propagation helps to improve the perturbation estimates from FWI by taking advantage of the additional subsurface illumination provided by multiple-scattering phenomena.

pdf**M. Schäfer, L. Groos, T. Forbriger, and T. Bohlen****Applications of 2D full waveform inversion to recorded shallow seismic Rayleigh waves**Schäfer et al. present two field datasets which they acquired to test their 2D full waveform inversion (FWI) approach. They discuss the main preprocessing steps applied to the field data as well as first FWI results.

pdf**N. Thiel, A. Przebindowska, A. Kurzmann, and T. Bohlen****Subsalt imaging with acoustic and elastic 2D full waveform inversion**Thiel et al. investigate the potential of Full Waveform Inversions (FWI) applied on the subsalt imaging problem. Synthetic acoustic and elastic FWI tests were performed for a marine 2D profile. The Flooding Technique is applied and further developed.

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### Other topics

**A.J.O. Pereira and R. Biloti****Stationary phase analysis for interferometric interpolation applied to dipping reﬂectors**Pereira and Biloti present an stationary phase analysis for the seismic interferometrical interpolation of traces in the presence of dipping reflectors.

pdf**C. Vanelle****Reﬂections from a spherical interface**Vanelle provides an algorithm for the generation of analytical traveltimes for waves reflected by a spherical interface.

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### 2012

- Download the entire WIT report 2012 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**A. Bauer, B. Schwarz, C. Vanelle, and D. Gajewski****Extension of the i-CRS operator to converted waves**

Bauer et al. extend the i-CRS multi-parameter stacking operator to converted waves and investigate it with two different parametrizations. The resulting three and five parameter operators are subject to several numerical studies in simple generic models in order to examine their traveltime accuracy and their ability to estimate the optimization parameters. A comparison that also considers a hyperbolic operator reveals the superiority of the new non-hyperbolic five parameter operator.

pdf**M. Bobsin, D. Gajewski, B. Schwarz, and C. Vanelle****A new stacking operator: i-CRS with 4 parameters**

Bobsin et al. investigate a four parameter extension of the i-CRS formulae. The fourth parameter is the overburden velocity. Accuracy and sensitivity studies show an improved behavior in terms of traveltime accuracy and sensitivity towards the kinematic wave field attributes in comparison with CRS, MF abd i-CRS (three parameter). The application as a stacking operator leads to comparable results with the three parameter i-CRS.

pdf**T.A. Coimbra, J.J.S. de Figueiredo, J. Schleicher, A. Novais, and J.C. Costa****Migration velocity analysis with diffraction events using residual moveout: Application to SIGSBEE-2B data**

Coimbra et al. discuss the use of the focusing of remigration trajectories starting at incompletely migrated diffraction events for seismic diffraction imaging and velocity model improvement. The method uses an approximate velocity model as input. It provides diffraction locations in the depth domain and information about the average velocity model which can be converted to interval velocities. They demonstrate the feasibility of the method using synthetic data examples from three simple constant-gradient models and the Sigsbee2B data.

pdf**T.A. Coimbra, A. Novais, and J. Schleicher****Offset-Continuation stacking**

Coimbra et al. introduce a data-driven stacking technique that transforms 2D/2.5D prestack multi-coverage data into a stacked common-offset (CO) section, referred to as OCO stack. The method combines offset continuation with stacking techniques to allow for the a horizon-based velocity analysis method, where root mean square (RMS) velocities and local event slopes are determined by stacking along event horizons.

pdf**J.H. Faccipieri, D. Rueda, L.J. Gelius and M. Tygel****Recovering diffractions in CRS stacked sections**

Faccipieri et al. propose a combined approach in which the conventional CRS stack is superimposed by a CRS diffraction-enhanced stack in such way that we can recover the diffractions attenuated in CRS stacked sections. Such a combination will ensure, not only a signal-to-noise enhanced stack, but also preservation of finer diffraction details. The proposed approach has been tested with good results employing marine seismic data acquired offshore Brazil.

pdf**L.-J. Gelius, M. Tygel, A.K. Takahata, E.G. Asgedom, and D.R. Serrano****High-resolution imaging of diffractions - a steered MUSIC approach**

Gelius et al. address the question of how to form a high-resolution image of diffracted wave contributions in seismic reflection data. Straightforward use of migration type of reconstruction methods will not be able to preserve the fully resolving power of diffractions, due to the diffraction-limit conditions inherently attached to those approaches. We propose a new high-resolution imaging technique based on a windowed or steered MUSIC implementation. Application of the method on both synthetic and field data demonstrated a resolving power beyond that of standard migration.

pdf**A. Pronevich, S. Dell, B. Kashtan, D. Gajewski****Diffraction traveltime approximation for general anisotropic media**

Pronevich et al. suggested a new traveltime approximation of diffracted waves for general anisotropic media. The traveltime expression formulated as a double-square-root equation that allows to accurately and reliably describe diffraction traveltimes. Numerical examples and application of the method to a synthetic data set demonstrate how the new approximation work.

pdf**A.K. Takahata, L.-J. Gelius, R.R. Lopes, I. Lecomte and M. Tygel****A regularized ﬁltering approach to 2D deconvolution of prestack depth migrated seismic images with the use of resolution functions**

Takahata et al. review key topics associated with deblurring of prestack depth migrated seismic images based on the use of resolution functions and propose an approach based on regularized 2D spiking deconvolution. The potential of this technique is illustrated by the use of synthetic data.

pdf**C. Vanelle and D. Gajewski****True-amplitude Kirchhoff depth migration in anisotropic media: the traveltime-based approach**

Vanelle and Gajewski extend their traveltime-based strategy for amplitude-preserving migration to anisotropic media. The required Greens functions are generated using only traveltimes. This has the advantage that dynamic ray tracing methods with their high demand on model smoothness need not be applied. Examples demonstrate the quality of the high image quality as well as the accuracy of the reconstructed reflection amplitudes.

pdf**C. Vanelle, K. Sager, B. Schwarz, B. Kashtan, and D. Gajewski****Estimation of anisotropy parameters with the i-CRS operator**

Vanelle et al. extend the i-CRS operator to account for the presence of seismic anisotropy. They demonstrate that the new operator leads to a highly accurate traveltime description. Furthermore, they conclude that the estimation of anisotropy parameters with the i-CRS operator has high potential.

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### Modelling

**R. Bloot, J. Schleicher, L.T. Santos, and J.C. Costa****On the Helmholtz decomposition in weakly anisotropic VTI media**

Bloot et al. use the theory of vector-field decomposition with the purpose of solving the VTI elastic wave equation in a homogeneous medium. The result is an elegant generalization of known facts of the classic isotropic case, particularly Helmholtz decomposition into decoupled wave equations for P and S waves.

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### Full waveform inversion

**S. Dunkl, A. Kurzmann and T. Bohlen****3D elastic full waveform inversion of small-scale heterogeneities in transmission geometry**

Dunkl explains the implementation of a 3D elastic full waveform inversion. Random medium model data is inverted with different acquisition geometries, and a comparison to 2D full waveform inversion is shown.

pdf**L. Groos, M. Schäfer, T. Forbriger and T. Bohlen****Can we ignore P-wave velocity in full waveform inversion of shallow seismic Rayleigh waves?**

Groos et al. investigate the influence of the initial P-wave velocity model on the reconstruction of the S-wave velocity model in a full waveform inversion (FWI) of shallow seismic Rayleigh waves.

pdf**S. Heider, S. Jetschny, R. Giese, and T. Bohlen****2-D elastic full waveform inversion for a transmission experiment in crystalline rock – a synthetic study**

Heider et al. show some necessary steps to invert for the fiel data. These steps are tested with a synthetic random distributed velocity model.

pdf**D. Macedo, I. Vasconcelos, and J. Schleicher****Scattering-based decomposition of sensitivity kernels for full waveform inversion – part 2: perturbation estimates with adjoint kernels**

Macedo et al. study a decomposition based on scattering theory that allows to break the acoustic-wavefield sensitivity kernels with respect to model parameters into background and singular parts. Their numerical results show that those subkernels can be used to backproject the scattered residual only into model space and obtain background-model perturbation estimates. In an experiment with restricted acquisition geometry (reflection data, narrow offset), the multiple-scattering subkernels take advantage of medium self-illumination provided by the scattered wavefields.

pdf**A. Przebindowska, A. Kurzmann, D. Köhn, T. Bohlen****A parameterization study for acoustic full waveform inversion**

Przebindowska et al. investigate the influence of the parameter choice describing the medium on the multi-parameter acoustic inversion of marine reflection seismics.

pdf**M.Schäfer, L. Groos, T. Forbriger, T. Bohlen****Testing point source to line source transformations for application of full waveform inversion to shallow seismic surface waves**

Schäfer et al. discuss effects of geometrical spreading corrections towards 2D full waveform inversion of shallow seismic surface waves.

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### Other topics

**P.E.P. Marcondes, J.J.S. Figueiredo, M.E. Far, J. Schleicher, N. Dyaur, and R.R. Stewart****Experimental relations between stress and fracture properties in synthetic anisotropic media**

Marcondes et al. built two physical anisotropic model, acquired ultrasonic measurements under varying stress level, and analysed the results. They show the relationships between seismically derived elastic parameters and fracture parameters. On the basis of this information from rock samples or analogous models, or even cross-well data, it might be possible to characterize the properties of a fractured reservoir or even figure out which regions of a reservoir are more extensively fractured.

pdf**R. Morelatto and R. Biloti****Structure enhancing ﬁltering with the structure tensor**

Morelatto and Biloti make an analysis of the structure tensor ability to estimate local slopes on 2D seismic data, in order to perform structure enhancing filtering. They compare this method to two different methods of slope estimation using plane-wave destruction.

pdf**C. Raub, D. Gajewski, E. Tessmer, and D. Spickermann****Seismic imaging of the dynamic water column**

Raub et al. discuss the influence of the dynamic ocean on the imaging of the water column. The investigation is quantified by a synthetic modeling study considering an ocean model close to the Strait of Cardiz. The images of the water column may show only very little similarities depending on acquisition time. Particularly the lateral extent of imaged structures highly depends on the acquisition direction with respect to the flow of water masses.

pdf**M. Werning and D. Gajewski****Time-lapse seismic of the subsurface underlying a dynamic ocean**

Werning and Gajewski show the effects of a dynamic ocean on time-lapse seismic data of the subsurface. Synthetic data are used for this study. The influence on the repeatability of the data is discussed.

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### 2011

- Download the entire WIT report 2011 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**I. Abakumov, B. Schwarz, C. Vanelle, B. Kashtan, and D. Gajewski****Double-square root traveltime approximation for converted waves**

Abakumov et al. introduce a new non-hyperbolic multiparameter stacking operator based on a double square root expression and a pragmatic search strategy for converted waves. The key step of their method is the simulation of a zero-offset section by the stack of γ-CMP gathers, which may be considered an approximation of common conversion point gathers. Numerical experiments confirm that the new expression is superior to the corresponding hyperbolic operator.

pdf**B. Amaro, J. Schleicher, A. Novais, J. C. Costa, and L. T. Santos****Stabilized least-squares imaging conditions for common-shot wave-equation migration**

Amaro et al. compare a number of imaging conditions based on stabilized least-squares solutions. The conclude that imaging conditions that sum over all sources before deconvolution do not fully preserve amplitudes. As demonstrated on synthetic data of different complexity, the best imaging conditions, both in a true-amplitude sense and regarding migration artifacts are based on total least squares.

pdf**M. Behzadi and D. Gajewski****Microtremor Localizaion**

Behzadi and Gajewski present a new passive seismic imaging method based on move out correction and cross-correlation stacking. The point source and microtremor events related to a known hydrocarbon reservoir in a complex medium are localized. The maximum of image function obtained by this method provides the source location. Both first and most energetic arrivals are considered and the results of most energetic arrivals provided better source location.

pdf**T.A. Coimbra, J.J.S. Figueiredo, A. Novais, and J. Schleicher****Migration velocity analysis with diffraction events using residual moveout**

Coimbra et al. present an approach to seismic diffraction imaging and velocity model improvement. This method that uses an approximate velocity as input requirement, provides a average velocity model and diffraction locations in depth domain as result. Our algorithm is based on focus of remigration trajectories over diffraction curves and velocity continuation. This method has been shown as low computational cost numerical method. Beyond that, the automatic location of diffraction points is achieved after image picking.

pdf**C.A.N. Costa, I.S. Campos, J.C. Costa, F.A. Silva Neto, J. Schleicher, and A. Novais****Iterative methods for 3D implicit ﬁnite-difference migration using the complex Padé approximation**

Costa et al. implement a 3D downward continuation FD migration without splitting in the space coordi- nates using a complex Padé approximation and implicit finite differences, eliminating numerical anisotropy at the expense of a computationally more intensive solution. They show that the use of the complex Padé approximation not only stabilizes the solution, but also acts as an effective preconditioner for the BICGSTAB algorithm, reducing the number of iterations as compared to implementation using the real Padé expansion.

pdf**S. Dell and D. Gajewski****Diffraction imaging in three dimensions with kinematic waveﬁeld attributes**

Dell and Gajewski extended their approach for CRS-attributes based diffraction imaging to 3D geometry. The approach is based on a simultaneous application of the CRS-based diffraction operator and a diffraction filter to separate diffracted events. Also they introduced a technique to build migration velocities in both the depth and time domain. The migration velocities are determined using isolated diffracted events in the poststack domain.

pdf**J.J.S. de Figueiredo, J. Schleicher, F. Oliveira, E. Esmi, L. Freitas, A. Novais, P. Sussner, and S. Green****Automatic detection and imaging of diffraction points using pattern recognition**

de Figueiredo et al. further develop a method for the detection of diffractor points in a common-offset-gather domain. The method is based on pattern recognition using amplitude distribution along the diffraction operator. While the method, in principle, requires knowledge of the migration velocity field, i.e., RMS or interval velocities, it is very robust with respect to an erroneous model. A real GPR data example demonstrates the feasibility of the method.

pdf**D. Mondini, J.C. Costa, J. Schleicher, and A. Novais****Three-dimensional Complex Padé FD Migration: splitting and corrections**

Mondini et al. compare the performance of splitting techniques for 3D complex Padé Finite-Difference (FD) migration techniques in terms of image quality and computational cost. The compared splitting techniques are two and alternating four-way splitting. They also extend the Li correction for use with the complex Padé expansion and diagonal directions. From numerical examples in inhomogeneous media, they conclude that alternate four-way splitting is the most cost-effective strategy to reduce numerical anisotropy in complex Padé 3D FD migration.

pdf**D. Rueda, J.H. Faccipieri, and M. Tygel****Smoothing kinematic waveﬁeld attributes to reduce random noise and enhance signal-to-noise ratio in seismic imaging**

Rueda et al. employ a smoothing procedure on Common-Reflection-Surface (CRS) parameters to eliminate fluctuations and outliers of stack sections. Application of the scheme attenuates random noise in the stacked sections, leading to an increase in signal-to-noise ratio and better continuity of the reflections. Application to a synthetic and real marine data sets provided encouraging results.

pdf**M. Sakamori and R. Biloti****Numerical Moveout Estimation for Migration Velocity Analysis in Super-Gathers**

Sakamori and Biloti present a study on a numerical approach to describe the residual moveout observed in image gathers as a function of the migration-velocity correction factor and the dip of the reflector. The new description allows the incorporation of neighbouring image gather to stabilize and improve the the parameter estimates.

pdf**B. Schwarz, C. Vanelle, and D. Gajewski****The recursive stacking operator (RSO) Part 1: from RSO to CRS parameters**

Schwarz et al. introduce two conceptually different parameterizations of the isotropic recursive stacking operator (RSO) in terms of the three well-known CRS parameters. While the first parameterization is based on the application of a time shift, the second one results from a Taylor series expansion of the squared RSO traveltime. Accuracy studies reveal that the time-shift-based parameterization behaves essentially the same as the planar multifocusing expression. The parameterization based on a Taylor series expansion turns out to provide higher accuracy than CRS and planar multifocusing over the full investigated range of reflector curvatures for constant vertical velocity gradient media of differing gradient strength.

pdf**B. Schwarz, C. Vanelle, and D. Gajewski****The recursive stacking operator (RSO) Part 2: Application to heterogeneous media**

Schwarz et al. apply two different parameterizations of the recursive stacking operator (RSO) in terms of the CRS attributes to different synthetic datasets. For the simple case of a spherical reflector in a con- stant vertical velocity gradient medium, application of RSO leads to higher semblance values and more reliable attribute estimates than CRS and planar multifocusing over the full range of reflector curvatures. This also results in an improved approximate attribute-based poststack time migration. Comparison of the stacking and migration results from application of RSO to those from CRS for the Sigsbee 2a model con- firms the overall superior performance of RSO for a more complex subsurface setting.

pdf**C. Vanelle, M. Bobsin, P. Schemmert, B. Kashtan, and D. Gajewski****RSO: a new multiparameter stacking operator for an/isotropic media**

Vanelle et al. suggest a new stacking operator, the recursive stacking operator (RSO), for curved subsurface structures in the presence of anisotropy. It is derived from evaluating Snell’s law at a locally spherical interface. Examples show that the new operator performs well for a wide range of reflector curvatures from nearly planar reflectors to the diffraction limit.

pdf**C. Vanelle, B. Kashtan, I. Abakumov, and D. Gajewski****A CRS-type stacking operator for converted waves**

Vanelle et al. suggest a new CRS-type hyperbolic stacking operator for converted waves. Although their operator was derived under the assumption of a constant vp/vs ratio, it has the advantage that CRS attributes from a monotypic stack can be used as intial values for the converted wave stack, even when vp/vs is varying, leading to a significant increase in computational efficiency of the optimisation procedure. Furthermore, monotypic and converted wave attributes can be evaluated for shear model building.

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### Modelling

**R. Bloot, J. Schleicher, and L. T. Santos****On the elastic wave equation for weakly anisotropic VTI media**

Bloot et al. present a general elastic wave equation in weakly anisotropic VTI media by linearizing the stiffness tensor. Using zero-order ray theory, they derive the associated eikonal and transport equations for q-P, q-SV and q-SH waves in general and pseudo-acoustic VTI media.

pdf**J.J.S. de Figueiredo, R.R. Stewart, J. Schleicher, N. Dyaur, B. Omoboya, R. Wiley, and A. William****Shear-wave anisotropy by aligned cracked inclusions: Frequency and attenuation properties**

de Figueiredo et al. use ultrasonic surveys to investigate the influence of source frequency on elastic parameters (the Thomsen parameter γ and shear-wave attenuation) of fractured anisotropic media. Un- der controlled conditions, they prepared anisotropic models containing penny-shaped rubber inclusions in a solid epoxy resin matrix with 10 to 17 layers, crack density ranging from 0 to 6.2%, and number of uniform rubber inclusions per layer ranging from 0 to 100. S-wave splitting measurements have shown that scattering effects are more prominent in models where the crack aperture to seismic wavelength ratio ranges from 1.6 to 13.3 than other models where the ratio was varied from 2.3 to 23.

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### Full waveform inversion

**S. Dunkl, A. Kurzmann, and T. Bohlen****3D elastic full waveform inversion of random medium - ﬁrst results**

Dunkl gives an overview about 3D elastic full waveform inversion. She shows the performance of the inversion code for the example of a random medium model in transmission geometry.

pdf**A. Kurzmann, A. Przebindowska, and T. Bohlen****On the importance of attenuation in acoustic waveform tomography of marine seismic data**

Kurzmann investigates the influence of attenuation on acoustic 2D full waveform tomography. Acoustic tomography – with or without involvement of attenuation – is applied to viscoacoustic data. The resulting error in velocity reconstruction is quantified.

pdf**D.L. Macedo, I. Vasconcelos, and J. Schleicher****Scattering-based decomposition of sensitivity kernels for full waveform inversion**

Macedo decomposes the Fréchet-derivative sensitivity kernels for the full wavefield using a scattering-based approach and assuming acoustic-only data. Those results provide for the decomposition of current FWI kernels into different sub-kernels which have explicitly different levels of nonlinearity with respect to data. This capability to discern levels of nonlinearity within FWI kernels is key to understanding model convergence in gradient-based, iterative FWI.

pdf**A. Przebindowska, A. Kurzmann, D. Köhn, and T. Bohlen****The role of density in acoustic full waveform inversion of marine reﬂection seismics**

Przebindowska et al. analyse the role of the density information in the reconstruction of subsurface model by means of full waveform inversion.

pdf**M. Schäfer, L. Groos, T. Forbriger, and T. Bohlen****On the effects of geometrical spreading corrections for a 2D full waveform inversion of recorded shallow seismic surface waves**

Schäfer et al. discuss the effects of geometrical spreading corrections for a 2D full waveform inversion of shallow seismic surface waves. They show synthetic inversion results with line source wavefields and amplitude corrected point source wavefields as observations. They conclude that not only an amplitude correction but also a phase-transformation must be applied to the point source seismograms. Therefore they introduce possible transformations known from literature for body waves and test them for surface waves.

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### Other topics

**E.G. Asgedom, L.-J. Gelius, and M. Tygel****2-D constant-offset diffraction separation**

Asgedom et al. Introduces a new way of diffraction separation in a common-offset section. They utilized a special version of the CRS moveout equation employing a constant-offset central ray and demonstrated the possibility of diffraction separation using both synthetic and real data.

pdf**T. Barros, R. Lopes, J. M. T. Romano, and M. Tygel****Implementation Aspects of Eigenstructure-based Velocity Spectra**

Barros et al. propose an iteratively implementation of MUltiple Signal Classification (MUSIC) algorithm, used for obtainment of high resolution velocity spectra. They also propose a new MUSIC algorithm, based on the spatial covariance matrix of seismic data.

pdf**R. Biloti****GêBR: a free seismic processing interface**

Biloti introduces GêBR, a graphical user interface for seismics processing packages, describing its most appealling features.

pdf**V. Das and D. Gajewski****Comparison between normalized cross-correlation and semblance coherency measures in velocity analysis**

Das and Gajewski make an attempt to understand the dependence of coherency measure for velocity analysis. A comparative study of normalized cross-correlation sum and semblance; which are two different measures of coherency is undertaken. The two coherency measures are applied on a large number of synthetic datasets involving different situations. The results of these applications show that the normalized cross-correlation sum measure is better than semblance method in most of the cases, in terms of resolution and identification of events in complex situations.

pdf**E. Minarto and D. Gajewski****Optimization of Common Reﬂection Surface (CRS) attributes based on a hybrid method**

Minarto and Gajewski discuss the conjugate direction method for the minimization of an objective function. Numerical tests on an analytical example demonstrate the ability of this method to find the global minimum in situations were the Nelder-Mead optimization method gets stuck in a local minimum. The application of the conjugate direction procedure to CRS using the SIGSBEE data revealed that the determination of CRS attributes has a computational advantage of about 4-5 compared to the Nelder-Mead method.

pdf**M. Tygel, H. Perroud, R. Lopes, and R. Krummenauer****Sensitivity analysis of the non-hyperbolic common reﬂection surface**

Perroud et al. investigate a recently proposed moveout, of non-hyperbolic character but depending on the conventional common-reflection-surface (CRS) parameters. Such moveout, valid for 2D and 3D models, is referred to as non-hyperbolic CRS traveltime. The few synthetic experiments, available only for 2D models, show that the new moveout exhibits impressive accuracy in long offsets, which encourages its use in the CRS method. In this ongoing research, still restricted to 2D, the sensitivity of the non-hyperbolic CRS moveout to its parameters is evaluated with the aim of the design of parameter estimation strategies. By means of a controlled parameter perturbation in selected configurations, which extend those used in conventional CRS, the study confirms the high potential of the new moveout as an optimal choice for CRS.

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### 2010

- Download the entire WIT report 2010 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**E.G. Asgedom, M. Tygel, and L.-J. Gelius****Higher-resolution determination of zero-offset Common-Reflection-Surface (CRS) stack parameters**Asgedom et al. propose the use of the MUltiple SIgnal Classification (MUSIC) algorithm as a replacement of semblance to obtain a high-resolution estimation of CRS parameters.

pdf**J.C. Costa, D. Mondini, J. Schleicher, and A. Novais****A comparison of splitting techniques for 3D FFD migration**Costa et al. compare the performance of splitting techniques for stable implementations of 3D Fourier Finite-Difference (FFD) migration. Using numerical examples in homogeneous and inhomogeneous media, they show that alternate four-way splitting into the coordinate directions at one depth and the diagonal directions at the next level yields results of the same quality as full four-way splitting at the cost of two-way splitting.

pdf**J.J.S. Figueiredo, F. Oliveira, E. Esmi, L. Freitas, A. Novais, and J. Schleicher****Diffraction imaging based on the diffraction operator**Figueiredo et al. present two approaches to seismic diffraction imaging based on the diffraction operator, which can be used in both the time and depth domains, in accordance with the complexity of the area. The first method makes applies pattern recognition to the amplitudes along the diffraction operator. The second method relies on a statistical analysis of these amplitudes to design a weight function that suppresses noise and reflections and enhances diffraction events.

pdf**G. Garabito, C.A.S. Ferreira, J.C.R. Cruz****CRS-beam PSDM: Kirchhoff-beam prestack depth migration using the CRS operator**Garabito et al. present a new procedure of prestack depth migration combining the flexibility of the Kirchhoff migration operator with the CRS stacking method. This procedure is mainly based on CRS ability to collect paraxial amplitudes around a reference trace to be migrated over a Huygens surface and positioning the stacked values in its true depth positions.

pdf**G. Garabito, W. Söllner, W. Lima and I.G. Oliveira****Velocity Analysis by Focusing Diffractions Simulated from CRS-attributes**Garabito et al. present a stable and fast poststack procedure to interactively estimate the velocity model by means of coherency and focusing analyses of diffraction events simulated from CRS-attributes. They validate this approach by using a synthetic data from a layered model.

pdf**J.S. Maciel, J.C. Costa, and J. Schleicher****Coherence measures in automatic time migration velocity analysis**Maciel et al. give a short introduction to automatic time migration velocity analysis methods and discuss their parametrization. Numerical examples demonstrate the how the approach works.

pdf**H. Perroud, M. Tygel, A. Mahamat, D. Rousset****A strategy for 3D CRS parameter estimation: the Tournemire site case study**Perroud et al. present here the results of CRS reprocessing of a 3D real dataset. The main objective was to evaluate the ability of the methodology to recognize weak vertical-displacement faults. An original strategy was elaborated to define the best possible 3D CRS parameters. The resulting image shows improved event continuity compared to conventional processing, pointing out to a possible fault zone.

pdf**A. Przebindowska, A. Kurzmann, D. Köhn, T. Bohlen****Acoustic Full Waveform Tomography of marine reﬂection seismic data**Przebindowska et al. present the application of acoustic full waveform tomography to the marine data set from the North Sea. The study discusses some of the problems that concern the field data preprocessing, wavelet estimation, and the choice of different inversion strategies.

pdf**H. Shahsavani and J. Mann****A model-based approach to the Common-Diffraction-Surface Stack**Shahsavani and Mann present a model-based approach to the recently introdced Common-Diffraction-Surface (CDS) stack method. The latter has been specifically developed for situations where the Common-Reflection-Surface stack suffers from numerous conflicting dip situations. Originally implemented in a purely data-driven manner, the CDS approach has now also been implemented in a substantially faster model-based manner to obtain stack sections optimized for poststack migration. This approach is well suited for complex data where prestack migration is unapplicable due to difficulties in building a macro-velocity model of sufficient accuracy.

pdf**O. Zhebel, D. Gajewski, and C. Vanelle****Localization of seismic events in 3D media by diffraction stacking**Zhebel et al. present an extension of the localization of seismic events by diffraction stacking to 3D media. Examples for data with a high noise level in homogeneous media are considered as well as heterogeneous media with triplications. Also effects of the double couple radiation pattern were investigated. Furthermore, a field data example from Southern California is presented where the acquisition footprint is compensated by weights based on Voronoj cells.

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### Modelling

**S. Dell and D. Gajewski****Image-ray tomography**Dell and Gajewski propose a new method for tomographic inversion. The inversion is based on the kinematic wavefield attributes extracted in the time-migrated domain. The method can be seen as an additional tool to provide constraints for kinematic velocity model building. It is particularly useful in areas where diffractions and triplications are located close to reflections generating conflicting dip situations. The method has been successfully tested on a synthetic data example.

pdf**S. Dell and D. Gajewski****Common-Reﬂection-Surface-based workﬂow for diffraction imaging**Dell and Gajewski present an application of the CRS-based diffraction imaging to synthetic and field data. They also show how the separated diffracted events can be used to build time-migration velocity model.

pdf**T. Kaschwich, H. Gjøystdal, I. Lecomte, and E. Iversen****Reﬂection, Diffraction and Resolution**Kaschwich et al. investigate the impact of diffractions on pre-stack depth migration images and discuss some correlated resolution aspects. Furthermore, we present examples where we apply a ray-based approach to compute synthetic seismograms for both reflected and diffracted events. Finally, we document the applicability of the approach to different model types, e.g. isotropic and anisotropic media.

pdf**E. Tessmer****Modelling and prestack reverse-time migration by the Rapid Expansion Method with time-stepping**Tessmer demonstrates that the Rapid Expansion Method (REM) for seismic modelling applied in a time-stepping manner is superior to finite-difference time-stepping. This is important for long propagation times where numerical dispersion might occur. He tests the solutions of REM by comparison with analytic solutions. He also shows how the time derivative of the solution of the wave equation needed, e.g., for the computation of Poynting vectors can be calculated at almost no extra cost.

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### Other topics

**M. Baykulov, S. Dümmong, and D. Gajewski****From Time to Depth with CRS Attributes**Baykulov et al. describe the use of CRS attributes in various modules for reflection seismic data processing. The CRS attribute based modules contribute to multiple suppression, model building, pre-stack data enhancement and depth imaging. The paper demonstrate the interaction of the modules and shows the benefits by combining them in a processing workflow. For example, the prestack data enahncement not only improves the quality of prestack data but also helps to suppress filtering artifacts in multiple removal and allows a better QC of migration velocities.

pdf**J.S. Dramsch and D. Gajewski****Trace interpolation and extrapolation with partial CRS stacks**Dramsch and Gajewski deleted traces from a synthetic data record to interpolate over sparse data and to extrapolate over the end of acquisition. They compare the original traces to the results of the interpolation process using partial CRS stacks. The results are encouraging not just for short offsets but also for intermediate offsets and at the end of the acquisition. This observation concerns arrival times and frequency content of the interpolated traces.

pdf**L.T. Santos, J. Schleicher, J.C. Costa, and A. Novais****Fast estimation of CRS parameters using local slopes in inhomogeneous media**Santos et al. apply the fast extraction of CRS parameters using modern local-slope-extraction techniques to synthetic data from inhomogeneous velocity models. A comparison of the numerical results to a simplified implementation of a conventional CRS procedure demonstrates that the technique lead to meaningful values for the so-determined CRS parameters.

pdf**M. Tygel, B. Ursin, E. Iversen, and M.V. de Hoop****Depth conversion of zero-offset and time-migrated reﬂections**Tygel et al. extend previous expressions for inversion of reflector dip and curvature from CRS coefficients of time-migrated reflections to include (a) A simpler and more direct expression for the reflector curvature and (b) Corresponding expressions for the CRS coefficients for ZO (stacked) reflections. The obtained expressions represent useful constraints for map migration along normal rays or image rays.

pdf**C. Vanelle, B Kashtan, S. Dell, and D. Gajewski****A new stacking operator for curved subsurface structures**Vanelle et al. suggest a new stacking operator for curved subsurface structures. The resulting implicit traveltime expression is derived from evaluating Snell’s law at a locally spherical interface. Examples show that the new operator performs well for a wide range of reflector curvatures from nearly planar reflectors to the diffraction limit.

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### 2009

- Download the entire WIT report 2009 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**M. Baykulov and D. Gajewski****Partial 3D CRS stack**

Baykulov and Gajewski performed partial 3D CRS stacks to enhance the quality and regularity of prestack 3D seismic data. Results of the automatic CRS parameter search are used to perform a simple and robust weighted summation. The method is verified on 2D and 3D synthetic data and applied to field 3D data. Improved prestack gathers have higher S/N ratio and show better coherence of reflections.

pdf**J.C. Costa and J. Schleicher****Double path-integral migration velocity analysis: A real data example**

Costa and Schleicher apply the idea of double path-integral migration velocity analysis to a real data set to show that the method yields quantitative information about the migration velocity model. Migrated images using interpolations with different regularisations of the extracted velocities demonstrate the high quality of the resulting velocity information.

pdf**S. Dell and D. Gajewski****Poststack time migration velocity analysis by CRS diffraction stacking**

Dell and Gajewski demonstrate a new application of the CRS attributes for time migration velocity analysis. They show how the attributes can be used to effectively separate reflected and diffracted energy. Then, they introduce and apply a new technique for poststack time migration velocity analysis on the diffracted wavefield. As a result, they obtain highly-focused time migrated images in addition to the velocities.

pdf**S. Dell, D. Gajewski, and C. Vanelle****Common scatter point data mapping**

Dell et al. propose a new method to map common midpoint (CMP) gathers into common scatterpoint (CSP) gathers. The CSP data mapping is based on the parameterization of the migration operator with the apex time. Then, they apply a migration velocity analysis to CSP gathers and perform an automatic Common Reflection Surface (CRS) stack for this gathers. As a result, they obtain more accurate velocity spectra and highly-focused time migrated images.

pdf**S. Dümmong and D. Gajewski****Geological constrains in the CRS parameter search**

Dümmong and Gajewski add geological constraints into the search procedure of CRS attributes. These constraints are linked to the stacking velocity and the geological dip of the structures under investigation. Field data examples illustrate the effect of the constraints on the determined CRS attributes and the final stack.

pdf**S. Kang****A brief review of 3D NIP wave tomography**

Kang revisits the fundamentals of the normal-incidence point (NIP) wave tomography. Inverting for picked kinematic wavefield attributes otained from the 3D CRS stack, this approach offers an efficient way to generate a kinematically consistent smooth 3D velocity model along with the reconstructed NIPs in the subsurface.

pdf**D. Köhn, D. De Nil, A. Kurzmann, A. Przebindowska, N. Nguyen, and T. Bohlen****On the inﬂuence of model parametrization in elastic full waveform tomography**

Köhn et. al. discuss the influence of parametrization in elastic full waveform tomography of synthetic multicomponent reflection seismic data. Starting from a long wavelength model for the elastic material parameters the waveform tomography result can resolve details below the seismic wavelength. The influence of different parameterizations on resolution and ambiguity are investigated using a simple test problem. Afterwards the resolution for a geological realistic model will be discussed.

pdf**H. Lima, L. Leite, B. Heilmann, and J. Mann****CRS-based seismic imaging in complex marine geology**

Lima et al. present results of a consistent workflow for processing and imaging applied to marine seismic data. The data set was collected in the Southern Atlantic offshore Brazil. Searching for techniques to increase the data resolution, fundamental steps of signal processing together with imaging methods based on the data-driven CRS technology, such as CRS-stack-based residual static correction and pre-stack data enhancement, were applied and proved to be successful. The final aim of the data processing and imaging sequence was to obtain sections ready to be submitted to geological interpretation. The latter was conducted on the final stacked and CRS time-migrated sections.

pdf**D.L. Macedo, J.J.S. Figueiredo, R.S. Portugal, and J. Schleicher****Velocity analysis on CMP sections based on the smearing paradigm**

Macedo et al. propose to use smearing instead of stacking when constructing velocity spectra in CMP velocity analysis. They describe, discuss, and test two methodologies in a very simple model. Smearing the total amplitude leads to conventional velocity spectra, with possible advantages because of its potential for parallel computing. Using the amplitude density gives rise to a slightly different coherency measure. Numerical experiments indicate that this measure might be able to improve the focussing of the velocity peaks in the velocity spectra.

pdf**F. Oliveira, A. Novais, J. Schleicher, and J. Costa****Velocity dependence of 2.5D true-amplitude single-stack redatuming**

Oliveira et al. discuss the dependence of single-stack redatuming constructed from migration-demigration chainging on the velocity model. For this purpose, they demonstrate the application of single-stack redatuming to synthetic seismic data for media with two or many flat layers and in models with lateral velocity variations. Our examples demonstrate the quality of the redatumed data both kinematically and dynamically.

pdf**F.A. da Silva Neto, J.C. Costa, J. Schleicher, and A. Novais****2.5D Reverse time migration**

Silva Neto et al. show that reverse time migration (RTM) in 2.5D offers an alternative to improve resolution and amplitude when imaging 2D seismic data. They implement a truly parallel finite-difference modelling algorithm in the mixed time-space/wavenumber domain. Numerical experiments using synthetic data demonstrate the better resolution and amplitude recovery of 2.5D RTM relative to 2D reverse time migration.

pdf**L. da S. Sadala Valente, J.C. Costa, and J. Schleicher****Evaluation of time to depth conversion algorithms for depth velocity model building**

Valente et al. review three time-to-depth conversion techniques, discuss their algorithmic procedures and show their differences by applying them to a 2D synthetic data set. In particular, they demonstrate that the different procedures react differently to different kinds of regularization. Although the image-ray trajectories and the resulting depth velocity models depend on the regularization employed, the final depth images corresponding to these different models are very similar.

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### Modelling

**L.-J. Gelius, E.G. Asgedom, and M. Tygel****A simple analysis of diffraction-limited imaging and super resolution**

Gelius et al. provide a simple framework of understanding and analyzing both diffraction-limited imaging as well as super-resolution. By utilizing the null-space solutions of the wave problem, super-resolution is apparently obtained since such solutions can give an extremely well localization of the point-source target.

pdf**T. Kaschwich, I. Lecomte, H. Gjøystdal, E. Iversen, and M. Tygel****Advanced ray-based synthetic seismograms**

Kaschwich et al. present a comparison between different ray-based modeling techniques, such as standard ray tracing, Kirchhoff-Helmholtz forward modeling and modeling by demigration. Furthermore, we propose a modified modeling by demigraion approach by using an alternative PSDM simulator.

pdf**E. Tessmer****Instabilities in pseudo-acoustic wave equation modelling of TTI media**

Tessmer discusses that modelling algorithms based on the so-called pseudo-acoustic wave equations for TTI media are unstable if variations of symmetry axes tilt are present. By numerical examples he shows that an algorithm based on the anisotropic equations of motion yields stable results.

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### Other topics

**R. Aleixo, J. Schleicher, and J. Costa****Determination of traveltime parameters in VTI media**

Aleixo et al. extend Alkhalifah’s two-step procedure for extracting the NMO velocity and the nonhyperbolicity from seismic travaltimes. For this purpose, they use a more accurate nonhyperbolicity term in the traveltime approximation, which allows to predict the bias in the NMO velocity estimate, thus providing a means of correcting both the estimated NMO velocity and the resulting anisotropy parameter value. By means of a numerical example, they demonstrate that the estimation of both traveltime parameters is improved considerably.

pdf**T.A. Coimbra, A. Novais, and J. Schleicher****OCO ray tracing using OCO trajectories**

Coimbra et al. relate offset-continuation (OCO) rays to the kinematic properties of OCO image waves that describe the continuous transformation of the common-offset reflection event from one offset to another. By applying the method of characteristics to the OCO image-wave equation, they obtain a ray-tracing-like procedure that allows to construct OCO trajectories describing the position of the OCO output point under varying offset. The endpoints of these OCO trajectories for a single input point and different values of the RMS velocity form then the OCO rays. A numerical example demonstrates that the developed ray-tracing procedure leads to reliable OCO rays, which in turn provide high-quality RMS velocities.

pdf**L. Freitas, R. Ballesteros, A. Caballero, G. Gierse, J. Pruessmann, A. Vazquez, and G. Clemente****Seismic depth processing using the CRS technique - a 3D land data example from Mexico**

Freitas presents a case study for a 3D land data from Mexico illustrating how applications of the CRS attributes may contribute to important steps of the conventional workflow of depth processing.

pdf**G. Garabito, J.C. Cruz, and L.S. Lucena****2D CRS stack: The use of the stacking velocity as an “a priori” information in the optimization of CRS parameters**

Garabito et al. discuss the results of the application of two CRS stack implementations (multi-step and one-step search strategies) in a low-fold real land dataset, without using any constraints in the determination of the CRS parameters and using the stacking velocity model as an information known “a priori” in the optimization process.

pdf**L.W.B. Leite and W.W.S. Vieira****Sensitivity, resolution and ambiguity of the CRS stack operator**

Leite and Vieira investigate the relationship between sensitivity analysis, based on the Miller-Murray model, S, of the CRS operator with respect to the parameters v0, RNIP , RN and α0, and compare with the attributes search strategies that is based on physical-mathematical considerations of the stack operator.

pdf**H. Perroud, M. Tygel, and L. Freitas****Inverse CRS**

Perroud et al. propose an algorithm for an (approximate) Inverse CRS transformation, namely one that (approximately) transforms the CRS attributes back to data space. The CRS transform pair established in this way may find a number of applications in seismic imaging and data processing, in the same way as other well-known transformations, e.g., Fourier, Radon, tau-p, etc.

pdf**L.T. Santos and J. Schleicher****Improving the estimation of CRS parameters using local slopes**

Santos and Schleicher show that the complete set of CRS parameters can be extracted from seismic data by an application of modern local-slope-extraction techniques. The necessary information about the CRS parameters is contained in the slopes of the common-midpoint and common-offset sections. Here, they improve the previous extraction technique, eliminating the need for slope derivatives.

pdf**M. Tygel, B. Ursin, E. Iversen, and M.V. de Hoop****An interpretation of CRS attributes of time-migrated reﬂections**

Tygel et al. provide an interpretation of the CRS coefficients of time-migrated reflections. The interpretation is done in terms of the ability of such coefficients to determine dip and curvature of the reflectors in depth.

pdf

### 2008

- Download the entire WIT report 2008 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**D. Amazonas, R. Aleixo, J. Schleicher and J. Costa****2D anisotropic complex-Padé hybrid finite-difference depth migration**

Amazonas et al. apply the complex Padé approximation to the acoustic wave equation for vertical transversely anisotropic (VTI) media to derive a more stable FD and hybrid FFD/FD migration for such media. Synthetic examples demonstrate the improved stability of the complex migration algorithms as compared to their real counterparts.

pdf**D. Amazonas, R. Aleixo, J. Schleicher and J. Costa****True-amplitude wave-equation migration**

Amazonas et al. implement SSPSPI and complex Padé FFD migrations using the amplitude corrections determined by the true-amplitude one-way wave equations. They demonstrate the amplitude gain using these amplitude corrections on the synthetic SEG/EAGE salt model.

pdf**D. Anikiev, D. Gajewski, B. Kashtan, E. Tessmer, C. Vanelle****Application of a modified diffraction stack for the localization of microtremor data**

Anikiev et al. apply a modified diffraction stack for the localization of microtremors in a complex heterogeneous medium. The study shows that stacking is a suitable tool to localize acoustic emissions in strongly heterogeneous media. However, first arrival traveltimes might not be adequate to localize low frequency microtremor data even if the correct velocity model is assumed.

pdf**M. Baykulov and D. Gajewski****Prestack seismic data enhancement with partial Common Reflection Surface (CRS) stack**

Baykulov and Gajewski performed partial CRS stacking to enhance the quality of sparse low fold seismic data. They describe an algorithm, which allows to generate NMO-uncorrected gathers without the application of inverse NMO/DMO. Gathers obtained by this approach are regularised and have better signal-to-noise ratio compared to original common-midpoint gathers. The method is verified on 2D synthetic data and applied to low fold land data from Northern Germany. Prestack depth migration of the generated partially stacked CRS supergathers produces significantly improved common-image gathers as well as depth migrated section.

pdf**P. Chira-Oliva, J.C.R. Cruz, M. Cardoso****Fourth order CRS stack: synthetic examples**

Chira-Oliva et al. proposed the fourth-order CRS traveltime expansion as a new alternative for the seismic stacking. The fourth-order CRS operator tested on simple synthetic models provide good stacked sections with a higher S/N. Then, the investigated CRS operator simulates better the ZO sections than the conventional CRS operator within larger offsets.

pdf**S. Dümmong, D. Gajewski, and C. Hübscher****A multiple suppression method via CRS attributes, updated**

Dümmong and Gajewski are presenting a continued development of a multiple suppression method using CRS attributes. Multiples are predicted on the CRS stacked section, prediction errors are addressed and prestack seismograms generated with CRS attributes are adaptively subtracted from the original data.

pdf**G. Garabito, W. Söllner and J.C. Cruz****Macro-model independent migration to zero offset (CRS-MZO)**

Garabito et al. propose a new method for migrating two-dimensional (2D) multicoverage seismic data to zero-offset section, i.e., Migration to Zero-Offset (MZO). It is based on the Commom Reflection Surface (CRS) stack formulas that are used to approximate the diffraction stack operator, and to produce a demigration of the zero-offset stacked data. This new approach, so called CRS-MZO, is applied to synthetic and real land datasets.

pdf**D. Köhn, A. Kurzmann, A. Przebindowska, D. De Nil, N. Nguyen and T. Bohlen****Elastic full waveform tomography of synthetic multicomponent reflection seismic data**

Köhn et al. discuss the first results of elastic full waveform tomography of synthetic multicomponent reflection seismic data. Starting from a long wavelength model for the elastic material parameters the waveform tomography result can resolve details below the seismic wavelength. The influence of different parameterizations and preconditioning operators on the tomography result will be discussed.

pdf**A. Kurzmann, D. Köhn, A. Przebindowska, N. Nguyen and T. Bohlen****Performance of acoustic full waveform tomography for different acquisition geometries**

Kurzmann et al. investigate the performance of full waveform tomography (FWT) for a transmission and a reflection geometry. Especially the progress of the FWT for a reflection geometry is very sensitive to the starting model. Additionally we show possibilities to increase the performance of our time-domain implemention, such as step length optimization and shot parallelization.

pdf**J. Schleicher, J.C. Costa, and A. Novais****Time migration velocity analysis by image-wave propagation of common-image gather**

Schleicher et al. show that image-wave propagation in the common-image gather (CIG) domain can be combined with residual-moveout analysis for iterative migration velocity analysis. For this purpose, the CIGs obtained by migration with an inhomogeneous macrovelocity model are continued starting from a constant reference velocity. The interpretation of continued CIGs as obtained from residual migrations leads to a correction formula that translates the residual flattening velocities into absolute time-migration velocities.

pdf**J. Schleicher and J.C. Costa****Migration velocity analysis by double path-integral migration**

Schleicher and Costa demonstrate that information about the migration velocity can be extracted from path-integral migration. The idea of path-integral imaging is to sum over the migrated images obtained for a set of constant migration velocities. By doing so twice, weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images.

pdf**M. Soleimani and J. Mann****Merging aspects of DMO correction and CRS stack to account for conflicting dip situations**

Soleimani and Mann combine concepts of DMO correction and CRS stack to properly handle conflicting dip situations during stacking. Based on the CRS traveltime approximation for diffraction events, coherence analysis and stacking are performed separately for any fixed plausible emergence angle within a given range, followed by a superposition of all contributions. For synthetic data we demonstrate the enhancement of diffraction events in the stacked section and their undisturbed superposition with other events. For real data, the approach leads to an improved imaging of faults in the poststack migration results.

pdf**C. Vanelle and D. Gajewksi****NIP-wave tomography for converted waves**

Vanelle and Gajewski suggest a new method to combine PP and PS data to obtain a shear velocity model. The method is based on the NIP wave tomography and uses wave field attributes determined with common reflection surface stacking of the data in combination with ray tracing.

pdf**I. Veile and J. Mann****Limited-aperture true-amplitude Kirchhoff depth migration – a new concept and preliminary results**

Veile and Mann discuss the double diffraction stack method in the context of limited-aperture Kirchhoff migration. The common-reflection-surface stack method provides useful attributes to estimate the size of the optimum migration aperture for zero-offset and its displacement with increasing offset. In practice, the center of the aperture, the location of the stationary point, has to be associated with the corresponding depth point in the migrated domain, e. g. by numerical calculation of the dip of the migration operator. We investigate whether the double diffraction stack is a reliable alternative for that purpose and present first preliminary results.

pdf

### Modelling

**T. Kaschwich and H. Bolin****Simulated Migration Amplitudes: Theory and Applications**

KaschwichandBolin: IlluminationmapsareausefultoolforsurveyplanningandforQCofamplitudes picked on selected target horizons. The Simulated Migration Amplitude technique (SMA) is a ray-based un-weighted Kirchhoff migration of synthetic data around seismic reflectors. In order to enhance illumination mapping for hydrocarbon exploration and reservoir imaging in complex subsurface structures, we present the extension of the SMA to converted waves and in anisotropic media and incorporate noise and attenuation effects.

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### Other topics

**D. Gajewski, K. Sommer, C. Vanelle, and R. Patzig****Seismic Event Localization in an Anisotropic Environment**

Gajewski et al. present a passive seismic real data case study of a hydraulic injection experiment at the German continental deep drilling site KTB and show the influence of anisotropy on the localization of events. For this data the location of events and the shape of the event cloud are substantially altered if the anisotropy is neglected.

pdf**W. Lima, G. Garabito, I.G. Oliveira and J.C.R. Cruz****BOTOSEIS: A new Seismic Unix based interactive platform for seismic data processing**

Lima et al.: presents a new interactive platform, called BOTOSEIS, that is used to facilitate the application of the Seismic Unix (SU) package, which was developed by the Center of Wave Phenomena (CWP) of the Colorado School of Mines. The BOTOSEIS is built for applying the SU programs by means of graphical user interface. It is developed in Java programming language. The BOTOSEIS platform deserves for creating and managing projects, lines and flowcharts from only one interactive environment. By using the BOTOSEIS the user can run and control several process at one time, and also easily include new SU based applications.

pdf**L.T. Santos, J. Schleicher, J.C. Costa, and A. Novais****Fast estimation of CRS parameters using local slopes**

Santos et al. show that the complete set of CRS parameters can be extracted from seismic data by an application of modern local-slope-extraction techniques. The necessary information about the CRS parameters is contained in the slopes of the common-midpoint and common-offset sections at the central point. In this way, the CRS parameter extraction can be sped up by several orders of magnitude.

pdf**B. Ursin, M. Tygel and E. Iversen****SS traveltime parameters and geometric spreading from PP and PS reflections**

Ursin et al. extend the kinematical approach of the PP + PS = SS method to second-order traveltimes of the SS-waves. By using the concept and properties of surface-to-surface propagator matrices, the propagator matrix of the SS-wave of a target reflector is explicitly obtained from the propagators of the PP- and PS-wave of the same reflector. Given that the elastic parameters describing S-wave velocities are known along the acquisition surface, this permits to determine the relative geometric spreading of the SS-wave, leading to a better reconstruction of the amplitude of the simulated SS-wave. Under isotropic conditions, the second-order derivatives of the SS-traveltime can, in the same way as for PP-waves, be applied to a tomographic estimation of the S-wave velocity model.

pdf**C. Vanelle and D. Gajewski****Application of Snell's law in weakly anisotropic media**

Vanelle and Gajewski suggest a method to evaluate Snell’s law in the presence of anisotropy. Their technique is based on first-order perturbation theory and can be used to solve the reflection/transmission problem at a boundary between two anisotropic media with arbitrary symmetry.

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### 2007

- Download the entire WIT report 2007 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**D. Anikiev, C. Vanelle, D. Gajewski, B. Kashtan, and E. Tessmer****Localisation ofseismic events by a modified diffraction stack**

Anikiev et al. apply a modified diffraction stack for the localisation of seismic events. Examples for data with a high noise level and near-surface complexities show that the technique yields reliable results for these situations. Furthermore, an additional example demonstrates that the method also leads to a good localisation accuracy even if the velocity model is not known.

pdf**M. Baykulov, H.-J. Brink, D. Gajewski, M.-K. Yoon****Revisiting the structural setting of the Glueckstadt Graben salt stock family, North German Basin**

Baykulov et al. applied CRS stack method to reflection data from the North German Basin which were recently released by the industry. The reprocessing of the data clearly demonstrates the capabilities of the CRS technique for low fold data. The images display a considerably improved SN ratio and show much more details than the CMP processing of the 1980s. Moreover, a velocity model consistent with the data was build and used to perform pre- and post-stack depth migrations which were so far not available for these data. The new depth images allowed an updated look on the petroleum system of the Glueckstadt Graben, which indicates new possible exploration targets.

pdf**M. Baykulov and D. Gajewski****Prestack seismic data enhancement with CRS parameters**

Baykulov and Gajewski performed partial stacking of prestack seismic reflection data based on the kine- matic wavefield attributes computed during the automatic CRS stack. The resulting CRS supergathers are more regularized and have better signal to noise ratio compared to original CMP gathers. The improved data can be used in any conventional processing tool instead of the original data, providing enhanced images of better quality. The CRS supergather method is especially suited for low fold seismic reflection data. Application of the new method to synthetic and real low fold data shows a clear improvement of seismograms as well as time and depth-migrated sections.

pdf**T. Bohlen, D. Köhn, A. Kurzmann, D. De Nil and N. Nguyen****Reflection seismic imaging by viscoelastic full waveform tomography**

Bohlen et al. discuss a relatively new wave equation based imaging method that utilizes the full information content of the multi-component elastic wave field. The elastic parameters of the sub-surface are derived by an iterative tomographic inversion method. The resolution of the derived velocity models is in the order of the seismic wavelength. Applications to synthetic data sets demonstrate the outstanding imaging potential of the method.

pdf**J.C. Costa, F.J.C. da Silva, E.N.S. Gomes, J. Schleicher, A. Mello, and D. Amazonas****Regularization in slope tomography**

Costa et al. propose a new, reflection-angle-based kind of smoothness constraint as regularization in slope tomography and compare its effects to three other, more conventional constraints. They find the smoothness constraints to have a distinct effect on the velocity model but a weaker effect on the migrated data. The new constraint leads to geologically more consistent models.

pdf**S. Dümmong and D. Gajewski****A multiple suppression method via CRS attributes**

Dümmong and Gajewski are presenting two approaches for identification of surface related multiples within the CRS workflow. One approach focusses on the multiple identification with CRS attributes (i.e. the angle of incidence). The second one is based on the multiple prediction by autoconvolving each stacked trace with itself (hybrid SRME-CRS approach). Both approaches are tested on two synthetic data sets.

pdf**F. Gamboa, A. L. Farias, L. Freitas and M. Tygel****Improving seismic vertical resolution by means of the Common-Reflection-Surface (CRS) method**

Gamboa et al. study the effect of enhancement of signal high frequencies on CMP and CRS stacked volumes. It is shown that high frequencies can be successfully recovered by means of the application of spectral whitening. Recovery is seen to be significantly better in CRS than in CMP stacked volumes.

pdf**E. Iversen and M. Tygel****Time-to-depth mapping and imaging of time-migrated seismic data with inherent velocity estimation: Revisited**

Iversen and Tygel revisit the problem of time-to-depth conversion of a given time-migrated section and a time-migration velocity field. The study, which extends the previous work described in WIT Report 2006, is now fully 3D with an accompanying 3D synthetic example.

pdf**E. Lima, L.T. Santos, J. Schleicher and M. Tygel****Fourth-order statistics for parameter estimation**

Lima et al. propose the use of a fourth-order “semblance” function as an alternative for the classical (second-order) semblance as a coherence measure to obtain CRS parameters from multicoverage data. Their first test show that this higher-order statistics measure better discriminates signal and noise, having, thus, the potential of producing cleaner sections and more reliable parameter estimates.

pdf**K. Meier, S. Dümmong, D. Gajewski and C. Hübscher****Comparison of prestack stereotomography and NIP-wave tomography for velocity modelbuilding: Instances from the Messinian evaporites**

Meier et al. give a comparison between two tomographic inversion schemes, namely prestack stereotomography and NIP-wave tomography. The results are compared for two examples from a real marine dataset from the Eastern Mediterranean. One example focusses on the vertical resolution of the velocity model and the other one on the lateral resolution of the obtained velocity distribution. The differences are discussed with respect to the different inversion problem formulations.

pdf**M. Pila, J. Schleicher and A. Novais****2.5D true-amplitude diffraction-stack redatuming**

Pila et al. derive a 2.5D true-amplitude diffraction-stack-type redatuming operator and present its specific form for zero-offset data. The operator consists of performing a single weighted stack along adequately chosen stacking lines. For simple types of media, they derive analytic expressions for the stacking lines and weight functions and demonstrate its functionality with numerical examples.

pdf**J. Schleicher, J.C. Costa, and A. Novais****Comparison of imaging conditions: application to Marmousi data**

Schleicher et al. compare the effects of different imaging conditions for common-shot wave equation migration on the final migrated images after stack using the Marmousi data set. They confirm the conclusion from the single-shot experiments that the most robust imaging condition with illumination correction is the one that divides the crosscorrelation of the up- and downgoing wavefields by the autocorrelation of the downgoing wavefield.

pdf**F.A. Silva Neto, J.C. Costa, M. Rian, J. Schleicher, and A. Novais****Obliquity correction for reverse time migration**

Silva Neto et al. propose a new imaging condition with obliquity correction for reverse time migration. Its implementation requires the determination of the Poynting vector of the source and receiver wavefields at the image point. Numerical examples show that the obliquity correction reduces backscattering artifacts and improves the illumination compensation.

pdf**E. Tessmer and D. Gajewski****Influence of a scattering surface layer on localization accuracy by reverse modelling**

Tessmer and Gajewski investigate the influence of a scattering surface layer on the accuracy of reverse modelling event localization.

pdf**B. Ursin and M. Tygel****AVO and AVA tuning and stretch effects**

Ursin and Tygel discuss tuning and stretch effects that appear on AVO and AVA in the presence of a thin layer.

pdf**M. von Steht and J. Mann****Velocity calibration and wavefield decomposition for walkover VSP data**

von Steht and Mann present a simple and efficient approach to calibrate the velocities at downhole receivers by means of walkover VSP data. This allows an accurate determination of emergence angles, as verified for wavefield decomposition.

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### Modelling

**L. Freitas, J. Stolfi and M. Tygel****Fast ray tracing in a cellular model**

Freitas et al. describe a fast method for seismic ray tracing in a cellular model, in which cells can have general polynomial shapes with non-planar bounding faces. Numerical examples are shown using Mod2B, an interactive prototype editor.

pdf**B. Kashtan and E. Tessmer****Transverse Rayleigh wave components**

Kashtan and Tessmer show that under certain conditions there is a Rayleigh wave which has a horizontal component of polarization perpendicular to its propagation direction. Numerical experiments using the pseudo-spectral Chebyshev method confirm this result. The amplitude of this wave is about 100 times smaller than that of the classical Rayleigh wave.

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### Other topics

**A. Gomes, L. Leite, J. Costa, Z. Heilmann, J. Mann****CRS Office: A Java graphical user interface for the conventional CRS stack**

Gomes et al. describe the development of CRS Office, a friendly Java graphical user interface for the CRS stack processing code of Dr. Jürgen Mann released in Karlsruhe, Germany, and an example of application to synthetic and real marine data from offshore Brazil.

pdf**T. Feskova, J. Miksat, T.M. Müller and F. Wenzel****3D seismograms in 2.5D heterogeneous structures**

Feskova et al. present a hybrid modeling procedure involving 2D FD and ray tracing techniques. The approach assumes that the travel path can be determined in the geometrical optic limit. The applicability is demonstrated by numerical experiments of elastic wave propagation for models of different complexity.

pdf**J. Schleicher, J.C. Costa, L.T. Santos, A. Novais, and M. Tygel****On the estimation of local slopes**

Schleicher et al. discuss several different ways of extracting the desired slope information from the data. Based on the observation that the inverse of the local slope can also easily be extracted from the data, they propose a simple, straightforward correction to linear plane-wave destructors and study the extraction numerically.

pdf**J. Schleicher and R. Aleixo****Traveltime approximations in VTI media**

Schleicher and Aleixo compare a number of traveltime approximations in VTI media that have been discussed in the literature and introduce a few new approximations. Some of the new traveltime formulas have rather simple analytic expressions and provide the same quality of approximation as the better of the established approximations.

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### 2006

- Download the entire WIT report 2006 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**D. Amazonas, J.C. Costa, R. Pestana, and J. Schleicher****Wide Angle FD and FFD Migration using Complex Padé Approximations**

Amazonas et al. show how complex Padé approximations can be used to derive two complex wide-angle pre-stack depth migration algorithms: finite differences (FD) and Fourier finite differences (FFD). These migration methods can handle evanescent waves and have improved impulse responses. The treatment of evanescent waves with the complex Padé approximation stabilizes the FFD algorithm and is more efficient computationally than Biondi’s unconditionally stable FFD algorithm.

pdf**D. Anikiev, D. Gajewski, B. Kashtan, E. Tessmer and C. Vanelle****Source localization by diffraction stacking**

Anikiev et al. apply a modified diffraction stack method to the problem of source localization. They investigate the localization with known and unknown velocity models.

pdf**G. Garabito, J.C. Cruz, and P. Hubral****Application of SA and VFSA global optimization algorithms for search of the 2-D CRS stacking parameters**

Garabito et al tested the performance of VFSA and SA optimization algorithms in Marmousi dataset by using the CRS stacking method. They observed that SA is more robust than VFSA algorithm. The results of the one-step CRS stack present a better resolution (good continuity of reflector horizons) in comparison with the results of the three-steps CRS stacking strategy.

pdf**G.G. Garabito, P. Chira-Oliva, J.C. Ribeiro Cruz, and M. Costa****CO CRS stack: a new strategy to simulate COs ections based on traveltime approximation for a diffracted central ray**

Garabito et al derived a particular traveltime formula for paraxial rays in the vicinity of a central ray associated to a diffraction point in depth. This formula presents a good fitting with respect to the reflected events. They propose this formula as an alternative to simulate Common-Offset (CO) sections. Finally, propose a new strategy to estimate the five parameters in the Finite-Offset (FO) CRS stacking method. For the first third steps use the SimulatedAnnealing(SA) global optimization method. For the fourth step recommend to use the Quasi − N ewton(QN ) local optimization algorithm.

pdf**E. Iversen and M. Tygel****Time-to-depth mapping and imaging of time-migrated seismic data with inherent velocity estimation**

Iversen and Tygel present a 3D time-to-depth conversion method that is based on tracing image rays into depth using a given time-migration velocity field. The method can be used both as a mapping scheme (which converts selected events in the time-migrated section into depth) or as an imaging scheme (which converts a time-migrated section into its corresponding full depth migrated section). Although all presented formulas are fully 3D, the method is illustrated in its simpler 2D case.

pdf**M. Kienast****Application and comparison of the CRS stack based minimum-aperture Kirchhoff migration in time and depth domain**

Kienast presents a real data example for CRS stack based limited-aperture migration in time and depth domain. Kinematic as well as dynamic aspects are considered for time and depth migration, and compared to conventional results.

pdf**T. Klüver****Diffraction traveltimes as moveout function for velocity analysis**

Klüver presents a new technique for the determination of migration velocity models. The method aims at kinematically fitting common image gathers and common reflection point gathers associated with selected picks in a poststack zero offset section.

pdf**K. Meier, S. Dümmong, D. Gajewski, and C. Hübscher****Velocity model building: A comparison between prestack Stereotomography and NIP-wave tomography**

Meier et al. give a short comparison between two tomographic inversion schemes, namely prestack stereotomography and NIP-wave tomography. The results are compared for a simple synthetic dataset and for a real marine dataset from the Eastern Mediterranean. The differences are discussed with respect to the different inversion approaches.

pdf**G. Melo Silva, J. Schleicher, and A. Novais****Poststack True Amplitude Wave-Equation Migration**

Melo Silva et al. transfer the concepts of true-amplitude one-way wave equations to Gazdag’s phase-shift migration. By analytically solving the true-amplitude one-way wave equations in vertically inhomogeneous media, they show that a true-amplitude phase-shift migration consists of the same phase correction as in standard phase-shift migration, plus an amplitude correction that can be applied at each depth level. Simple numerical examples demostrate the improvement of the amplitudes in vertically inhomogeneous media.

pdf**J. Schleicher, A. Novais, and J. C. Costa****Vertical image waves in elliptically anisotropic media**

Schleicher et al. derive a new image wave equation for remigration in elliptically anisotropic media by reparameterization of the kinematic expressions. A simple numerical example confirms that this image wave equation, which is a kind of medium-dependent one-way wave equation, can be used to improve well-ties, thus providing an estimate of the vertical velocity.

pdf**J. Schleicher, J.C. Costa, and A. Novais****A Comparison of Imaging Conditions for Wave-Equation Shot-Proﬁle Migration**

Schleicher et al. compare the effects of different imaging conditions for common-shot wave equation migration on the migration artifacts and on the migration amplitudes. The conclude that the most robust imaging condition is one that divides the convolved up- and downgoing wavefields after inverse Fourier transform.

pdf**B. Ursin and M. Tygel****Zero-offset seismic amplitude decomposition and migration**

Ursin and Tygel introduce natural amplitudes for the one-way normal and NIP waves, which provide a useful decomposition of the amplitude of the zero-offset ray. A possible application of the decomposition to a new true-amplitude migration scheme is also described.

pdf**C. Vanelle and D. Gajewski****Traveltime-based true-amplitude migration in anisotropic media**

Vanelle and Gajewski explain how their traveltime-based strategy for true-amplitude migration can be extended to include anisotropy. The new method provides a true-amplitude migrated image without requiring dynamic ray tracing (DRT), which is cumbersome in the presence of anisotropy. A simple example demonstrates that in addition to the depth image, the reconstruction of the reflection amplitudes for anisotropic multi-component data leads to the correct result.

pdf**M. von Steht****2D CO CRS imaging for multicomponent data recorded by the VSP geometry**

von Steht presents a poststack imaging sequence based on the CRS method for common offset adapted to handle vertical seismic profiling (VSP) walkaway data. A vivid synthetic example is used to visualize the quality of the image after depth migration. Furthermore the CRS-based wavefield separation for multicomponent data is applied for this specific geometry.

pdf**M. Yoon, M. Baykulov, S. Dümmong, H.-J.Brink, and D.Gajewski****New insights into the crustal structure of the North German Basin from reprocessing of seismic reﬂection data**

Yoon et al. applied CRS stack method to seismic reflection data from the North German basin which were recently released by the industry. The land data sets acquired in the early 80ies were reprocessed with the focus on the deeper structures within the basin. The images provide new insight for the sedimentary cover of the basin and for the deeper parts of the crust. The results display an almost flat Moho discontinuity even in the area of the Glückstadt Graben where a lower crustal high density body was discovered. The interpretation is in good agreement with recent results from gravity modeling in this area.

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### Rock physics and waves in random media

**V. Grosfeld and L.T. Santos****An AVO indicator based on the Impedance Concept**

Grosfeld and Santos review some of the most used attributes for AVO analysis and introduce a new one based on the reflection impedance function.

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### Other topics

**B.S.S. Barbosa, J.C. Costa, E.N.S. Gomes, and J. Schleicher****Sensitivity Analysis for Stereotomography in Elliptic and Anelliptic Media**

Barbosa et al. extend stereotomography to general anisotropic media and present an implementation for elliptical and anelliptical anisotropy, Numerical examples demonstrate the validity of the present approach for qP events and mild anisotropy, pointing towards the importance of transmission events from multiple-offset VSP experiments for the success of the approach.

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### 2005

- Download the entire WIT report 2005 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**S. Buske, M. Heigel, and S. Lüth****Fresnel-Volume-Migration of single-component seismic data**

Buske et al. describe an extension of Kirchhoff prestack depth migration. The so-called Fresnel-Volume-Migration restricts the migration operator to the physically relevant part of the subsurface using the concept of Fresnel-Volumes and the emergence angle determined at the receiver from a local slowness analysis. The application to a synthetic model as well as to a real data set over a salt pillow demonstrates the benefits of this method, e.g. enhanced image quality and resolution.

pdf**A.C. Camargo and L.T. Santos****Uniform resampling using the SINC function**

Camargo and Santos present an efficient algorithm for the uniform resampling problem, using Shannon Sampling Theorem (Sinc function) and the aproximation of the pseudo-inverse of a matrix. To illustrate the approach, we apply the algorithm to resample a seismogram and to recover a corrupted two-dimensional image.

pdf**J.C.R. Cruz, P. Chira, and F. de Souza****Identifying multiple reﬂections with the NIP and Normal hypothetical wavefronts**

Cruz et al. identify first-order interbed symmetric multiple reflections. For this, they compare param- eters of hypothetical NIP and N wavefronts obtained by forward modeling and Kirchhoff migration. This comparison is verified also with the NMO velocity.

pdf**C.A.S. Ferreira and J.C.R. Cruz****KGB-PSDM migration in constant gradient velocity media and sensitivity analysis to velocity errors. A comparison with Kirchhoff PSDM**

Ferreira and Cruz extend that KGB-PSDM algorithm to the case of a depth-dependent velocity medium. A sensibility analysis is made in order to test for possible errors in velocity models.

pdf**D. Gajewski, B. Kashtan, E. Tessmer, and C. Vanelle****Localization of acoustic emissions by back-projection: inherent localization and timing errors**

Gajewski, Kashtan, Tessmer, and Vanelle explain and verify by numerical studies that the localization of seismic events by reverse modeling or other back-projection methods possess inherent errors. The location and timing of the events by these methods are systematically shifted toward the receiver network and to earlier hypocentral times. The errors depend on the acquisition geometry and the length of the recorded signal.

pdf**Z. Heilmann, L. Leite, and A. Gomes****CRS-stack-based seismic imaging as a case study for basin reevaluation**

Heilmann et al. are giving attention to the seismic processing and interpretation of a land data set from the Takutu basin, Brazil. The presented extension of CRS-stack-based time-to-depth imaging supports arbitrary top-surface topography and is well suited to the specific problems of land data processing, namely, sparse data, complex geological structures, and complicated near surface conditions. The following processing steps were carried out: CRS stack, residual static correction, determination of a macrovelocity model via tomographic inversion, and Kirchhoff pre- and poststack depth migration.

pdf**B. Kashtan, E. Tessmer, and D. Gajewski****Investigation of the one-way wave equation**

Kashtan, Tessmer and Gajewski show that the commonly used acoustic 2D one-way wave equation needs to be modified in order to yield correct amplitudes. In order to yield correct results amplitudes from the one-way and the two-way wave equations need to be the same in the direction into which energy is propagated. They theoretically explain artifacts when using the one-way wave equation.

pdf**T. Klüver****Velocity model update using migration to residual time**

Klüver presents a new technique for migration based velocity model update. It is based on the same model parameterization as CRS-based tomography but partially overcomes the limitation to second order of that method.

pdf**N.-A. Müller****Correction of traveltimes and attributes**

Müller presents a technique for correcting traveltimes and wavefield attributes obtained by means of coherence analyses. Search aperture dependent “best fit” quantities are extrapolated to zero-aperture in order to obtain the desired attributes as well as a corrected stack section.

pdf**A. Novais, J. Costa, and J. Schleicher****Velocity determination by image-wave remigration**

Novais et al. present a stable implementation of image-wave remigration in the time domain, demon- strating the computational efficiency of the algorithm. An example using ground-penetrating-radar (GPR) data demonstrates how image-wave remigration can be used to estimate a model of the medium velocity.

pdf**L.T. Santos and M. Tygel****Inverting amplitude versus ray parameter curves using the reﬂection impedance concept**

Santos and Tygel propose an algorithm to invert elastic-parameter contrasts from Amplitude-versus-Ray Parameter curves using the reflection impedance approximation of the PP-reflection coefficient. First results shown on synthetic data indicate that the procedure may offer a promising alternative to existing methods of inverting reservoir attributes from AVO/AVA curves.

pdf**J. Schleicher and R. Aleixo****Time and depth remigration in elliptically anisotropic media using image-wave propagation**

Schleicher and Aleixo derive image-wave equations, that is partial differential equations that describe the dislocation of a reflector image as a function of the velocity model, for time and depth remigration in elliptically anisotropic media, under variation of migration velocity and medium ellipticity. A numerical example demonstrates the validity of the theory.

pdf**M. Spinner****True-amplitude CRS-based Kirchhoff time migration for AVO analysis**

Spinner presents an CRS-based approach for minimum aperture Kirchhoff migration in the time domain. The main focus of the method lies on the migration amplitudes and the resulting improvments in AVO/AVA analysis.

pdf**M. Yoon, M. Baykulov, S. Dümmong, H.-J. Brink, and D. Gajewski****Imaging of crustal reﬂection data with the common reﬂection surface (CRS) stack method – New insight into the crustal structure of northern Germany**

Yoon et al. applied the CRS stack method to crustal reflection data from the North German basin which were recently released by the industry. The data were acquired and processed in the early 80ies with the focus on the sedimentary fill of the basins. The focus of the reprocessing was moved to imaging of the deeper structures within the basin. The new results yielded improved images of structures in the lower and middle crust. Also, the visibility of the Moho was significantly enhanced. This example shows a first succesful application of the CRS stack method to real crustal reflection data.

pdf

### Rock physics and waves in random media

**M. Brajanovski, T.M. Müller, and B. Gurevich****Fracture related cross-over frequencies of seismic attenuation in porous rocks**

Brajanovski et al. analyze characteristic frequencies of seismic wave attenuation due to wave-induced flow in fractured porous rocks.

pdf**R. Ciz, E.H. Saenger, and B. Gurevich****Pore scale numerical modelling of elastic wave dispersion and attenuation in periodic systems of alternating solid and viscous ﬂuid layers**

Ciz et al. perform numerical simulations using the rotated staggered grid for an idealized porous medium, namely a periodic system of alternating solid and viscous fluid layers. The simulation results show excellent agreement with the theoretical predictions. Specifically the simulations agree with the prediction of Biot’s theory of poroelasticity at lower viscosities and with the viscoelastic dissipation at higher viscosities.

pdf**A. Davolio, V. Grosfeld, and L. T. Santos****Impedance-type approximations of the P–P and P–S reﬂection coefﬁcients and prediction of elastic parameters**

Davolio et al. make a review of impedance-type approximations for the P–P reflection coefficient and introduce the corresponding approximation for the P–S reflection coefficient. They also describe how to estimate the ratios of some elastic parameters, directly from the data, using the concept of the impedance function. Some illustrative examples for a well-log data are presented.

pdf**A. Gerner, E.H. Saenger, and S.A. Shapiro****Attenuation of seismic P-waves in multilayered gas hydrate-bearing sediments**

Gerner et al. investigate P-wave attenuation in vertical direction caused by interlayer flow and scattering in poroelastic media. Numerical and analytical results indicate that interlayer flow may be a significant attenuation mechanism in highly permeable sediments. Especially in the lower seismic frequency range poroelastic modeling yields attenuation values that are comparable to field observations.

pdf**T.M. Müller****Effective conductivity and diffusivity of randomly heterogeneous porous solids with compressible constituents**

Müller analyzes effective properties of diffusion waves in randomly inhomogeneous poroelastic solids.

pdf**E.H. Saenger, S.A. Shapiro, and Y. Keehm****Seismic effects of viscous Biot-coupling: ﬁnite difference simulations on micro-scale**

Saenger et al. consider viscous fluid effects on wave propagation. They implement an accurate approximation of a Newtonian fluid into a finite-difference approach. Biot-type effects can be observed in numerical experiments on a micro-scale, i.e from first principles.

pdf**E.H. Saenger, R. Ciz, B. Gurevich, and S.A. Shapiro****Slow compressional wave in porous media: ﬁnite difference simulations on micro-scale**

Saenger et al. model a Biot slow wave on microscale. Since the theory of dynamic poroelasticity was developed by Biot (1956), the existence of the type II or Biot’s slow compressional wave (SCW) remains the most controversial of its predictions. To our knowledge this is the first time that the slow wave is simulated on first principles.

pdf**S.R. Zanoth, E.H. Saenger, O.S. Krüger, and S.A. Shapiro****Leaky mode: a seismic wave attenuation mechanism in a gas-hydrate-bearing sediment**

Zanoth et al. consider the leaky mode, a possible attenuation phenomenon of seismic waves in a gas-hydrate-bearing sediment layer. This attenuation mechanism in horizontal direction occurs when a high-velocity layer is embedded in a low velocity zone. This is a typical situation for gas hydrate occurrences. We will demonstrate that the leaky mode is a significant attenuation mechanism which cannot be neglected.

pdf

### Modelling

**T. Bohlen and E.H. Saenger****Accuracy of heterogeneous staggered-grid ﬁnite-difference modeling of Rayleigh waves**

Bohlen and Saenger consider the accuracy of different finite-difference approaches for modeling Rayleigh waves. The conventional standard staggered-grid (SSG) and the rotated staggered grid (RSG) is investigated. For an irregular interface the RSG scheme is more accurate than the SSG scheme. The RSG scheme, however, requires 60 grid points per minimum wavelength to achieve good accuracy for all dip angles.

pdf**C. Lima, G. Garabito, and P. Chira****3-D CRS traveltime hyperbolic approximations for reﬂections and diffraction events**

Lima et al. give a theoretical revision about 3-D CRS Stack. They make a comparison of the CRS traveltime approximation for reflection and diffraction events with respect to true traveltimes. Although the 3-D ZO CRS operator have a better fit then the 3-D ZO CDS operator, the last also can be used for 3-D Stacking.

pdf**F.S. Neto, J. Costa, and A. Novais****2.5 D elastic ﬁnite-difference modeling**

Silva Neto et al. describe a velocity-stress formulation for elastic finite-difference modeling of elastic wavefields in 2.5 dimensions. The approach is appealing due reduced storage and computing time when compared to full 3D finite difference elastic modeling. Numerical experiments show the accuracy of the scheme.

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### Other topics

**G.L. Netzeband, C.P. Hübscher, and D. Gajewski****The structural evolution of the Messinian Evaporites in the Levantine Basin**

Netzeband, Hübscher, and Gajewski have shown that in the initial stages of salt movement in the Levantine Basin very little lateral evaporite movement has taken place in the past 5 Ma, the direction of this movement is controlled by the sediment load of the Nile River. Five sub-units of evaporite deposition have been found, which have been deformed syn-depositionally.

pdf**J. Schleicher and R. Biloti****A frequency criterion for smoothing with optimal cubic splines**

Schleicher and Biloti discuss a frequency criterion on how to choose the number of nodes for a smoothing by optimal cubic splines. They also compare smoothing results to those obtained by filtering using a moving average and a lowpass.

pdf**M. Tygel and B. Ursin****Convergence of the traveltime power series for alayered transversely isotropic medium**

Tygel and Ursin examine the power series representation of traveltime as a function of offset for multiply transmitted and reflected wave in VTI media. They show that there is convergence for sufficiently small offsets, except in the case of a vanishing NMO-velocity. This can happen for qSV propagation in some layer. The situation of on-axis triplication, which occurs when the squared NMO-velocity becomes negative is also discussed.

pdf**C. Vanelle and D. Gajewski****Application of Snell's law in weakly anisotropic media**

Vanelle and Gajewski suggest a method to determine the vertical slowness in a weakly anisotropic medium, if only the horizontal slowness components are known. The main applications for the method are the reflection-transmission problem between two anisotropic media, and the traveltime-based determination of geometrical spreading and true-amplitude migration weight functions for anisotropic media.

pdf

### 2004

- Download the entire WIT report 2004 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**R. Aleixo and J. Schleicher****Image-wave remigration in elliptically isotropic media**

Aleixo and Schleicher derive the image-wave equation, that is a partial differential equation that describes the dislocation of a reflector image as a function of the velocity model, for elliptically isotropic media. The main objective is to remigrate an isotropic into a medium with a certain degree of anisotropy.

pdf**R. Biloti and J. Schleicher****Dip-correction for coherence-based migration velocity analysis**

Biloti and Schleicher suggest a dip correction for coherence-based migration velocity analysis. They demonstrate how the velocity update can be improved when the reflector dip is taken into account. As an additional search parameter, the reflector dip is also determined. A simple synthetic example demonstrate the feasibility of the method.

pdf**T. Boelsen****2D CO CRS stack for top-surface topography**

Boelsen presents new hyperbolic traveltime formulas for the 2D CO CRS stack that are able to take top-surface topography into account. Two types of topography are considered, namely a rugged topography and a smooth one. Moreover, a stacking operator for a vertical seismic profile (VSP) acquisition geometry is derived. In addition, an approach to redatum the CO CRS stack section is proposed and tested with a synthetic data example.

pdf**T. Boelsen and J. Mann****2D CO CRS stack for ocean bottom seismics and multi-component data**

Boelsen and Mann discuss the application of the 2D CO CRS stack to ocean bottom seismics and show a simple synthetic data example with a comparison of model- and data-derived wavefield attributes. More- over, a new approach to stack multi-component data in order to obtain PP and PS CO CRS stacked sections is presented.

pdf**C.A.S. Ferreira and J.C.R. Cruz****Modiﬁed Kirchhoff prestack depth migration using the Gaussian Beam operator as Greenfunction – Theoretical and numerical results**

Ferreira and Cruz propose a modified true amplitude (diffraction stack) Kirchhoff prestack depth migration using as Green function a superposition of Gaussian beams (GB's). The process takes in consideration the explicit use of the Fresnel volume elements in order to enhance the resolution of the final imaging.

pdf**D. Gajewski and E. Tessmer****Reverse modelling for seismic event characterization – A new tool for passive seismology**

Gajewski and Tessmer introduce a seismic event localization method based on reverse numerical modelling, where event picking can be avoided. The quality of the spatial localization and of the estimation of the excitation time is demonstrated using 2- and 3-dimensional synthetic data sets. Cases with noise contaminated seismograms, macro models with incorrect velocities and the effect of sparse receiver arrays are studied for simple and complex subsurface models.

pdf**G. Garabito and W. Paschoal****2D-CRS stack: A comparison between the extended and global search strategies**

Garabito et al. present a short review of the two well stablished 2D-CRS parameters search strategies and present a comparison between the results of the application of both CRS stack implementations to the marmousi data set.

pdf**Z. Heilmann and M. von Steht****CRS-stack-based seismic imaging for rough top-surface topography**

Heilmann and von Steht present a recent extention of the CRS-stack-based imaging workflow able to support arbitrary top-surface topography. The implementation combines two different approaches of topography handling to a cascaded processing strategy demanding very little additional effort. Finally, the CRS stack and also CRS-stack-based residual static corrections can be applied to the original prestack data without the need of any elevation statics. The CRS-stacked ZO section, the kinematic wavefield attribute sections and the quality control sections can be related to a chosen planar measurement level by a redatuming procedure. Due to this redatuming procedure, the influence of the rough measurement surface can be entirely removed from the output sections of the CRS stack. Thus, an ideal input for the subsequent CRS-stack-based processing steps is provided.

pdf**C. Jäger****Minimum-aperture Kirchhoff migration using CRS attributes**

Jäger shows how CRS attributes can be used to determine optimum stacking apertures for Kirchhoff (true-amplitude) migration. In this way, the efficiency of the migration algorithm as well as the quality of the resulting images can be improved.

pdf**T. Kaschwich, C. Vanelle, and D. Gajewski****Traveltime-based anisotropic migration with angular parametrisation**

Kaschwich presents a new stratagy for the migration with angular parametrisation in anisotropic media. The method combines the conventional ray shooting with a hyperbolic traveltime interpolation.

pdf**T. Klüver****The effect of event consistent smoothing on CRS imaging**

Kluever reviews the event-consistent smoothing algorithm for the 2D case and introduces its extension to the 3D case. The effect of the smoothing on CRS results is demonstrated using a small 2D real dataset.

pdf**I. Koglin and E. Ewig****CRS-attribute-based residual static correction**

Koglin and Ewig briefly present how CRS atributes are used to obtain CRS moveout corrected CRS super gather which are necessary for the subsequent residual static correction. The theoretical background, some recent extensions of the implementation, and a real data example are discussed.

pdf**L. Leite, Z. Heilmann, I. Koglin, M. von Steht, and J. Mann****CRS data imaging: a case study for basin reevaluation**

Leite et al. processed seismic land data of the Takutu basin (Amazonas, Brazil) as an example not for comparison with other processing packages but to demonstrate once more the high potential of the data-driven CRS-stack-based imaging methods. The aim of this ongoing project is to establish a workflow for basin reevaluation for oil play. Based on the CRS attributes obtained during the CRS stacking process, the determination of a smooth macrovelocity model via tomographic inversion was conducted followed by pre- and poststack depth migration.

pdf**S. Lüth, A. Goertz, S. Buske, and R. Giese****Fresnel-Volume migration of elastic seismic data**

Lüth et al. present a method for imaging sparse three-component seismic reflection data in a heterogeneous 3D velocity model. The location of a reflection point is derived using the polarisation direction of the multicomponent data and the Fresnel volume of the respective wave path is then derived by paraxial ray tracing. The imaging condition is finally restricted to the Fresnel volume of the reflection wave path.

pdf**M. Salvatierra, F. Yano, L.T. Santos, J.M. Martínez, R. Andreani, and M. Tygel****A global optimization algorithm applied to the CRS problem**

Salvatierra et al. presents a global optimization scheme applied to the CRS problem in the 2-D situation. Numerical experiments illustrate the potential of the method.

pdf**C. Vanelle****Filling Gaps in Ray Traveltime Maps**

Vanelle suggests a simple technique to fill gaps in ray traveltime maps.

pdf**C. Vanelle, M. Spinner, T. Hertweck, C. Jäger, and D. Gajewski****Traveltime-based true-amplitude migration**

Vanelle et al. describe the traveltime-based implementation of true-amplitude migration. Application to a highly complex synthetic model and a real data set demonstrates the technique. Whereas the results are equivalent to migration with weight functions obtained from dynamic ray tracing, the efficiency of the traveltime-based implementation is considerably higher.

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### Rock physics and waves in random media

**V. Grosfeld and L.T. Santos****A comparison of seismic attributes**

Grosfeld and Santos review some different approximations for the P-P reflection coefficient and the associated seismic attributes. To illustrate the ability of the attributes to indicate the presence of oil or gas, numerical examples are also presented. Moreover, a new indicator is introduced, based on an impedance-type approximation for the reflection impedance.

pdf**A. Kaselow, K. Becker, and S. A. Shapiro****Stress sensitivity of seismic and electric rock properties of the upper continental crust at the KTB**

Kaselow et al. test their hypthesis that the general depth trend of P-wave, S-wave, and formation factor at the KTB test site can be explained as a result of progressive crack closure with increasing depth. They also show a comparison between laboratory and logging derived results of the rocks stress-sensitivity.

pdf**O.S. Krüger, E.H. Saenger, and S.A. Shapiro****Reﬂection coefﬁcients of fractured rocks: A numerical study**

Krüger et al. In this work we estimate the effective reflection coefficients of an interface between a cracked and an uncracked material. The study is based on computer simulations using the rotated staggered grid finite difference method

pdf**E.H. Saenger, O.S. Krüger, and S.A. Shapiro****Numerical considerations of ﬂuid effects on wave propagation: Inﬂuence of the tortuosity**

Saenger et al. consider effective elastic properties (i.e. velocities) in three different kinds of dry and fluid-saturated porous media. The synthetic results are compared with the predictions of the Gassmann equation and the tortuosity-dependent high-frequency limit of the Biot velocity relations.

pdf**M. Yoon, S. Buske, and S.A. Shapiro****Deep seismic imaging in the presence of heterogeneous overburden: Insights from numerical modeling**

Yoon et al. consider deep seismic imaging in the presence of heterogeneous overburden.

pdf

### Modelling

**J. Costa, A. Novais, F. de Assis Silva Neto, and M. Tygel****2.5D Acoustic Finite-Difference Modeling in variable density media**

Costa et al. extend the method of 2.5D FD modeling by out-of-plane Fourier transform to acoustic media with variable density. They demonstrate the quality of the method by a comparison to the analytical solution of the wave equation in homogeneous media and by a comparison to the 3D FD results for two inhomogeneous models, including the Marmousi model.

pdf**M. Tygel and L.T. Santos****Quadratic normal moveouts in isotropic media: aquick tutorial**

Tygel and Santos review and discuss the Taylor expressions of traveltime moveouts for reflection rays around a fixed zero-offset ray. These are referred to as normal parabolic and hyperbolic, or simply quadratic normal moveouts. General 2D/3D expressions, with the inclusion of topographic as well as inhomogeneous velocities are reviewed and discussed.

pdf

### Other topics

**S. Rentsch, S. Buske, S. Lüth, and S. A. Shapiro****Location of seismicity: a migration based approach**

Rentsch, Buske, Lüth and Shapiro propose a new approach for location of seismicity based on principles of wave field back propagation. This concept is characterised by a high degree of automation since time consuming manual picking of arrival times is not required.

pdf**S.A. Shapiro, S. Rentsch, and E. Rothert****Characterization of hydraulic properties of rocks using probability of ﬂuid-induced micro-earthquakes**

Shapiro, Rentsch and Rothert demonstrate that the probability of induced earthquakes occurring is very well described by the relaxation law of pressure perturbation in fluids filling the pore space in rocks. Using this observation they show that the spatial distribution of the density of earthquakes provides a possibility to estimate the hydraulic diffusivity on a kilometer scale with a high precision.

pdf**K. Sommer, D. Gajewski, and R. Patzig****Localization pitfalls of seismic events due to anisotropy – A KTB real data case study**

Sommer, Gajewski and Patzig present a real data case study and demonstrate the influence of anisotropy on the localization of hydraulically induced seismicity at the continental deep drilling site KTB (Germany). An unrecognized anisotropy affects the localization severely. In the KTB case, if anisotropy is not considered and station corrections are not applied, the center of the event cloud is dislocated 500 m to the south which is about 25% of the total lateral extent of the cloud. The anisotropic model perfectly centers the cloud at the injection well.

pdf

### 2003

- Download the entire WIT report 2003 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**F.J.C. Alves, G. Garabito, and L.W.B. Leite****Multiple Attenuation by Combining WHLP and CRS**

Alves et al. present a paper that is a computational exercise related to seismic multiple attenuation by combining two theories: the classical Wiener-Hopf-Levinson for prediction (WHLP), and the common-reflection-surface (CRS) stack, here denoted as WHLP-CRS.

pdf**S. Bergler and A. Müller****Short note: 3-D CRS stack software**

Bergler and Müller give a short overview on the current state of the 3-D CRS software developed at the University of Karlsruhe. Moreover, utility programs faciliating the choice of the 3-D CRS processing paramters are introduced.

pdf**P. Chira-Oliva, J.C.R. Cruz, G. Garabito, P. Hubral, and M. Tygel****2-D ZO CRS stack by considering an acquisition line with smooth topography**

Chira-Oliva et al. present a modified 2-D ZO CRS stacking operator in order to consider effects due to the smooth topography. By means of this new CRS formalism, they stack the land seismic data for obtaining a high resolution ZO seismic section, without applying static corrections. As by-products the 2-D ZO CRS stack method with smooth topography also provides accurate estimates of the CRS parameters.

pdf**E. Duveneck****3D tomographic velocity model estimation with CRS attributes**

Duveneck shows how kinematic wavefield attributes obtained from the application of the 3D CRS stack can be used in a tomographic inversion to determine a smooth 3D subsurface velocity model for depth imaging.

pdf**F. Gamboa, E. Filpo, and M. Tygel****Multiple attenuation using Common-Reﬂection-Surface attributes**

Gamboa et al. investigate the use of CRS attributes multiple identification and attenuation purposes. Various algorithms are proposed, together with synthetic examples that illustrate their application.

pdf**G. Garabito, P.A. Chira-Oliva, M. Tygel, and L.T. Santos****A Quick Review of 2D Topographic Traveltimes**

Garabito et al. review the CRS and Multifocus traveltime moveouts in the presence of strong topography. Simple examples designed to illustrate the accuracy of the traveltime expressions are provided.

pdf**G. Garabito, J.C.R. Cruz, P. Hubral, and M. Tygel****2-D Common-Reﬂection-Surface (CRS) stack based on simulated annealing and quasi-Newton: Application to Marmousi data set**

Garabito et al. present a new algorithm of the Common Reflection Surface (CRS) method based on global (Simulated Annealing - SA) and local (Quasi-Newton - QN) optimizations to estimate the CRS parameters from multicoverage data. We have applied the proposed SA-QN optimization to the Marmousi dataset with very good results. These results indicate that the procedure is able to provide highly accurate CRS parameters and images in complex seismic data.

pdf**Z. Heilmann, J. Mann, E. Duveneck, and T. Hertweck****CRS-stack-based seismic imaging workﬂow – a real data example**

Heilmann et al. present a recent application of a CRS-stack-based seismic imaging workflow to data acquired in the Oberrheingraben, Germany. The main objective of the presented exploration project was to image faults and fractures relevant for a planned geothermal power plant. The individual steps of the applied CRS-stack-based imaging workflow were 1) the CRS stack and attribute determination, 2) the determination of a smooth macrovelocity model by tomographic inversion using the CRS attributes, and 3) pre- and poststack depth migration using the obtained macrovelocity model.

pdf**T. Hertweck, J. Mann, E. Duveneck, and C. Jäger****CRS-stack-based seismic imaging workﬂow – theory and synthetic data example**

Hertweck et al. present the concepts of a seismic reflection imaging workflow based on the Common-Reflection-Surface stack. The consecutive processing steps are outlined and demonstrated for a synthetic data example. The workflow includes the application of the CRS stack itself together with an automated time migration, a CRS-attribute-based tomographic inversion to estimate a smooth macro-velocity model, and pre-/poststack depth migration by means of the obtained model.

pdf**C. Jäger, T. Hertweck, and M. Spinner****True-amplitude Kirchhoff migration, topography, and irregular acquisition geometry**

Jäger et al. show how true-amplitude Kirchhoff migration can be performed for data recorded with an irregular acquisition geometry on a non-flat measurement surface. They deal with problems usually known as acquisition footprint in the literature.

pdf**T. Kluever****Tomographic velocity modele stimation using ﬁnite-offset kinematic waveﬁeld attributes**

Kluever presents a tomographic inversion scheme which makes use of 2D finite-offset kinematic wavefield attributes to determine smooth, laterally inhomogeneous, isotropic subsurface velocity models.

pdf**I. Koglin and E. Ewig****CRS-attribute-based residual static correction**

Koglin and Ewig briefly present how CRS atributes are used to obtain CRS moveout corrected CRS super gather which are necessary for the subsequent residual static correction. The theoretical background and a first real data example are discussed.

pdf**F. Majana, W. Mascarenhas, M. Tygel, and L.T. Santos****Reﬁnement Step for Parameter Estimation in the CRS Method**

Majana et al. discuss three local optimization methods applied to refine the initial values for the attributes of the CRS method in 2D. The performance and accuracy of the methods are examined by means of illustrative synthetic and real data examples.

pdf**J. Mann and E. Duveneck****Short note: event-consistent smoothing of kinematic waveﬁeld attributes for stacking and inversion**

Mann and Duveneck present an event-consistent smoothing algorithm for the CRS wavefield attributes. Based on one of the wavefield attributes, namely the emergence angle of the normal ray, and the coherence measure associated with the CRS stacking operator, a combination of a median filter and averaging is applied. The attribute fluctuations due to noise as well as outliers to the pragmatic search strategy are strongly reduced in accordance to the theoretical background. All applications of the wavefield attributes, including the stack itself, benefit from this smoothing.

pdf**H. Perroud and M. Tygel****Nonstretch NMO**

Perroud and Tygel introduce a new implementation of the normal-moveout (NMO) correction called Nonstretch NMO. The procedure automatically avoids the undesirable stretch effects that are present in conventional NMO. In this way, a significant range of large offsets, that would normally be muted in the case of conventional NMO, can be kept and used, leading to better stack and velocity determinations. Illustrative applications to synthetic and real datasets, obtained from high-resolution (HR) seismic and ground-penetrating radar (GPR) measurements are provided.

pdf**J. Schleicher and C. Bagaini****Controlling Amplitudes in 2.5D common-shot migration to zero offset**

Schleicher and Bagaini realize a Common-Shot Migration to Zero Offset (CS-MZO), which transforms a common-shot section into a zero-offset section, as a Kirchhoff-type stacking operation for 3D wave propagation in a 2D laterally inhomogeneous medium. By application of suitable weight functions, data amplitudes are preserved or transformed by replacing the geometrical-spreading factor of the input reflections by the correct one of the output zero-offset reflections. A numerical example validates the process and highlights the differences between amplitude preserving and true-amplitude CS-MZO.

pdf**J. Schleicher, A. Novais, and F.P. Munerato****Migration velocity analysis by depth image-wave remigration: ﬁrst results**

Schleicher et al. study the finite-difference solution of the image-wave equation for depth remigration and possible applications. Grid dispersion and dissipation can only reduced to acceptable levels by the choice of very small grid intervals. First applications to inhomogeneous media point towards the method’s potential of being useful as a tool for migration velocity analysis.

pdf**E. Tessmer****Full-Wave Pre-Stack Reverse-Time Migration by the Fourier Method and Comparisons with Kirchhoff Depth Migration**

Tessmer tests full-wave pre-stack reverse-time migration using different types of wave-equations with synthetic data sets. By varying parameters like migration velocities, different degrees of macro model smoothing and by adding noise to the synthetics he shows the stability of the method. In addition he shows a comparison between reverse-time migration and Kirchhoff depth migration for a synthetic data set of the Picrocol model, which indicates that imaging with reverse-time migration is superior.

pdf**C. Vanelle, J. Dettmer, and D. Gajewski****Detection of caustics and interpolation of later-arrival traveltimes**

Vanelle et al. explain how the traveltime-based strategy for true-amplitude migration can be extended to include later-arrivals. They introduce a method for locating discontinuities of the wavefronts, that can also be applied to detect caustics. Examples on the interpolation of later-arrival traveltimes demonstrate the technique.

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### Rock physics and waves in random media

**N. Delépine, N. Cuenot, E. Rothert, M. Parotidis, S. Rentsch, and S.A. Shapiro****Characterization of ﬂuid transport properties of the Hot Dry Rock reservoir Soultz-2000 using induced microseismicity**

Delépine et al. estimate for the Soultz geothermal reservoir two independant permeability values, a permeability tensor and a heterogeneous reconstruction of the hydraulic diffusivity. The results agree very well with independent in-situ and laboratory tests.

pdf**A. Kaselow and S. A. Shapiro****Stress sensitivity of elastic moduli and electrical resistivity in porous rocks**

Kaselow and Shapiro give a short introduction into the extension of the stress sensitivity approach to arbitrary anisotropic media under arbitrary load and show that there are rocks where the stress sensitivity is also able to explain the stress dependence of electrical resistivity.

pdf**Y.A. Kravtsov, A. Kaslılar¸ , S.A. Shapiro, S. Buske, and T. Müller****Estimation of the statistical parameters from the traveltime ﬂuctuations of refracted waves**

Kravtsov et al. study the traveltime fluctuations of refracted waves in random elastic media in the framework of a geometrical optics approach. Covariance function of traveltime fluctuations is derived for the case of a constant gradient of the average wave velocity. The theoretical consideration is verified with the numerical modelling and the main statistical parameters -variance of refractive index, horizontal and vertical scales of inhomogeneities- are estimated.

pdf**T.M. Müller and B. Gurevich****Attenuation and dispersion of seismic waves in 3-D randomly inhomogeneous, porous rocks**

Müller and Gurevich use the Bourret approximation in order to describe the coherent wavefield in 3-D randomly inhomogeneous poroelastic structures. This model allows to quantify attenuation and dispersion of seismic waves propagating in porous rocks with meso-scale inhomogeneities. For example, the important problem how seismic waves respond to partial rock saturation can be tackled by this approach.

pdf**B. Orlowsky, E.H. Saenger, Y. Guéguen, and S.A. Shapiro****Numerical Rock Physics: Effects of parallel crack distributions on effective elastic properties**

Orlowsky et al. show the effects of parallel crack distributions on effective elastic properties. The numerical study is performed using the so-called rotated staggered finite-difference scheme.

pdf**S. Rentsch, S.A. Shapiro, and E. Rothert****Characterization of hydraulic properties of rocks using probability of ﬂuid-induced microearthquakes**

Rentsch et al. present a new approach for estimating the hydraulic parameters of rocks. This approach provides possibilities to characterize hydraulic properties on large spatial scales with high precision using probability considerations of fluid-induced micro earthquakes.

pdf**E.H. Saenger, O.S. Krüger, and S.A. Shapiro****Numerical Rock Physics: Fluid effects on wave propagation**

Saenger et al. consider three different kinds of 3D isotropic fractured media with a different pore structure. They have numerically tested effective velocity predictions of the Gassmann equation and the Biot velocity relations.

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### Modelling

**J. Costa, M. Schoenberg,and J. Urban****3D Raytracing through Homogeneous Anisotropic Layered Media with Smooth Interfaces**

Costa et al. show a fast raytracing in a piecewise homogeneous anisotropic medium in 3-D. The implementation is for a triclinic anisotropic medium.

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### Other topics

**S. Buske and Yu. Kravtsov****Divergence of geometrical optics series at the boundary of its applicability: two analytical examples in elementary functions**

Buske and Kravtsov demonstrate the behaviour of divergence of the geometrical optics series when the conditions for its applicability are violated. Two analytical examples in elementary functions are presented: a shear wave propagation in 1D elastic media with exponentially changing parameters and 2D Gaussian beam diffraction in free space. These examples evidence that accounting for higher terms in GO power series leads to divergence and therefore becomes completely senseless beyond the boundaries of GO applicability.

pdf**S.M. Soukina, D. Gajewski, and B.M. Kashtan****Determination of the elastic parameters of layered weakly anisotropic media using traveltimes and polarizations**

Soukina et al. present a joint inversion of qP - and qS-waves in piecewise homogeneous weakly anisotropic media using a linear formalism for both qP - and qS-waves. If the observed qS-wave polarization vectors are introduced into the inversion, the tomographic relations for qS-waves can be linearized and are formally identical to those for qP -waves. The inversion procedure was tested using synthetic noise-free and noisy data obtained for a layered model.

pdf**E.N.S. Gomes, J.C. Costa, J. dos S. Protázio, and I.A. SimõesFilho****Estimation of Fractures Orientation from qP reﬂectivity using Multiazimuthal AVO Analysis**

Gomes et al. estimate the fractures orientation through multiazimuthal AVO analysis of qP and its converted waves. They assume the fractured medium behaves as an effective transversally isotropic (TI) medium.

pdf**C. Vanelle and D. Gajewski****Determinationofsectoriallybest-ﬁtting isotropic background media**

Vanelle and Gajewski present expressions for sectorially best-fitting isotropic P- and S-velocities following from a generalisation of Fedorov’s (1968) technique. Examples for media with polar (VTI) and triclinic symmetry confirm the superiority of the sectorial fit over the commonly used global fit by Fedorov.

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### 2002

- Download the entire WIT report 2002 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**S. Bergler, G. Höcht, and J. Mann****Using co crs version 1.1: a manual**

Bergler et al. introduce the processing software cocrs which provides stacked common-offset sections and wavefield attributes from multi-coverage prestack data in a data-driven manner. The processing parameters are explained in detail to make the use of cocrs easier.

pdf**P. Chira-Oliva, M. Tygel, P. Hubral, and J. Schleicher****A fourth-order CRS moveout for reﬂection and diffraction events**

Chira-Oliva et al. discuss first comparisons between a new fourth-order traveltime expansion in terms of the zero-offset CRS parameters and the more classical hyperbolic moveout. The numerical examples suggest that the new fourth-order expression provides a better approximation to true traveltimes than the hyperbolic one.

pdf**E. Duveneck****Tomographic velocity model inversion with CRS attributes**

Duveneck presents a tomographic velocity inversion method based on Common-Reflection-Surface (CRS) attributes. The method constructs smooth laterally heterogeneous velocity models for depth imaging. It is demonstrated on a 2D synthetic example.

pdf**A. Goertz****True-amplitude multicomponent migrationof elastic waveﬁelds**

Goertz develops an extension to scalar true-amplitude imaging theory. It accounts for the vectorial properties of the elastic wavefield recorded with multicomponent receivers. With this approach, AVO curves for all occurring wave modes can be obtained.

pdf**T. Hertweck and C. Jäger****Short note: various aspects of Kirchhoff migration**

Hertweck and Jäger investigate various aspects of Kirchhoff migration. They show examples of depth migration with a macrovelocity model obtained by tomographic inversion based on CRS stack attributes, and pre- and poststack migration directly from topography. A brief but general overview of advantages and disadvantages of Kirchhoff migration is presented.

pdf**C. Jäger and T. Hertweck****Using Uni3D version v0.23: a manual**

Jäger and Hertweck give a description of Uni3D, an imaging tool for Kirchhoff true-amplitude migration. They concentrate on the technical aspects such as installation, compilation and explanation of all relevant parameters.

pdf**I. Koglin and E. Ewig****Residual static corrections by means of CRS attributes**

Koglin and Ewig give a short introduction to a new approach that uses the moveout corrected supergathers obtained by means of CRS attributes for residual static corrections. The theoretical background and first synthetic results are presented.

pdf**J. Mann and G. Höcht****Short note: the pulse stretch phenomenon in the context of data-driven imaging methods**

Mann and Höcht revisit the well-known pulse stretch phenomenon usually occuring during normal-moveout correction. In contrast to conventional NMO, data-driven imaging methods based on multi-parameter traveltime approximations like Multifocusing, delayed hyperbola approaches, or Common-Reflection-Surface stack are not subject to such effects. This contribution discusses the adaptation of the stacking operator to the actual reflection response and the behavior of the wavefield attributes along the seismic wavelet.

pdf**E. Menyoli and D. Gajewski****A strategy to image tectonically complex areas using CRS stack and prestack depth migration**

Menyoli and Gajewski present a workflow for estimating velocity/depth model for the DOBREflection 2000 line. We use the CRS software and classical software for processing, such as poststack and prestack depth migration for obtaining an accurate depth model of the inverted Foldbelt structures.

pdf**E. Menyoli, D. Gajewski, and C. Hübscher****Time migrated CRS images of complex inverted basin structures**

Menyoli et al. present poststack time migrated images of the Donbas Foldbelt data. The unmigrated stacked section was generated after applying the CRS stack method. The results show that in complex geology were CMP stacking and the subsequent poststack time or depth migration fails, the CRS stacking and the subsequent poststack time/depth migration gives high quality results which are easy to interpret.

pdf**H. Perroud, M. Tygel and S. Bergler****Velocity estimation by the CRS method: A GPR real data example**

Perroud et al. describe the use of the Common Reflection Surface (CRS) method to estimate velocities from Ground Penetrating Radar (GPR) data. Combination of the obtained depth-converted velocity map with in situ measurements of electrical resistivity enables to estimate both water content and water conductivity. These quantities are essential to delineate infiltration of contaminants from the surface after industrial or agriculture activities. The method has been applied to a real dataset and compared with the classical NMO approach. The results show that the CRS method provides a much more detailed velocity field, thus improving the potential of GPR as an investigation tool for environmental studies.

pdf**J. Schleicher, A. Novais, and F.P. Munerato****Finite-difference solution of the image wave equation for depth remigration: stability**

Schleicher et al. discuss the consistency and stability of a finite-difference scheme for the image wave equation for remigration. Numerical tests demonstrate that at the boundary of satisfying the strictest stability criterion, the implementational form of the chosen FD scheme is essential to obtain stable result with a limited numerical error.

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### Rock physics and waves in random media

**T.M. Müller, S.A. Shapiro, and C.M.A. Sick****Amplitude ﬂuctuations due to diffraction and refraction in anisotropic random media: Implications for seismic scattering attenuation estimates**

Müller et al. give an approximate formulation to describe scattering attenuation for plane waves propagating in weakly inhomogeneous and statistically anisotropic random media. Their calculations are based on the well-known Rytov approximation which is able to describe the log-amplitude variance of seismic primaries. This log-amplitude variance is then directly linked with the attenuation coefficient. At last they verified the analytic results by means of numerical experiments.

pdf**E. Rothert, S.A. Shapiro, S. Buske****Seismicity Based Reservoir Characterization Case Study: Correlation of Microseismicity with Reﬂectivity at the KTB**

Rothert et al. show the application and a new case study of the Seismicity Based Reservoir Characterization method (SBRC). Fluid induced microseismic events at the german KTB location are analysed in terms of a diffusive pore pressure relaxation process in order to estimate hydraulic parameters of the rock. For the first time, it is possible to study the depth-dependency of hydraulic parameters at one drilling site. Hypocenters of the events are compared with results of 3D reflectivity measurements. Good correlation are obtained with structural images which may explain the different spatio-temporal evolution features of the microseismicity. We are able to observe indications of the depth-dependency of hydraulic diffusivity at the KTB. We observe that rock volumes characterized by larger diffusivity also show larger reflectivity.

pdf**E.H. Saenger, O.S. Krüger, and S.A. Shapiro****Effective elastic properties of randomly fractured solids: 3D numerical experiments**

Saenger et al. consider 3D isotropic fractured media with ellipsoidal inclusions. They have numerically tested effective velocity predictions of different theoretical approaches: The theory for non-interacting cracks, the Kuster-Toksöz approach, the self-consistent theory, the differential effective medium (DEM) theory and the Gassmann-equation. Additionally,they have studied scattering attenuation of the meanfield predicted by the classical Hudson-approach.

pdf**S.A. Shapiro and A. Kaselow****Pore pressure dependency ofelastic anisotropy in rocks**

Shapiro and Kaselow give an extension of the piezosensitivty approach towards anisotropic porous rocks and show its application to metamorphic rock samples from the KTB deep drill hole.

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### Modelling

**R. Coman and D. Gajewski****3-D wavefront-oriented ray tracing: Estimation of traveltimes within cells**

Coman and Gajewski present two approaches which increase the efficiency of 3-D wavefront construction (WFC) methods. First, for the estimation of traveltimes within cells, they propose a distance-weighted averaging of extrapolated traveltimes. The extrapolation of traveltimes is performed under consideration of the wavefront curvature. Second, they introduce an insertion criterion for new rays. This criterion uses the difference in wavefront curvature between adjacent rays.

pdf**T. Kaschwich and D. Gajewski****3D anisotropic wavefront-oriented raytracing**

Kaschwich and Gajewski introduce a new implementation to compute traveltimes for 3D anisotropic media. To demonstrate the methodthey give several numerical examples.

pdf**A. Novais and L.T. Santos****2.5-D ﬁnite-difference solution of the acoustic wave equation**

Novais and Santos show how the medium symmetry in the 2.5-D situation can be used to accelerate the finite-difference computation of 3-D wave propagation by a repeated 2-D FD modeling in the out-of-plane Fourier domain. They derive a criterion for the wavenumber summation that realizes the inverse Fourier transform and demonstrate the quality of the process by numerical examples.

pdf**E.H. Saenger****A short note on accurate ﬁnite-difference modeling of anisotropic wave propagation**

Saenger shows that the rotated staggered grid (RSG) can be applied to the velocity-stress formulation of the viscoelastic wave equation and to the displacement-stress formulation of the elastic wave equation for anisotropic media. In both cases the implementation of the RSG expands the range of applications.

pdf**S.M. Soukina, D. Gajewski, and B.M. Kashtan****Determination of weak anisotropy parameters using traveltimes and polarisations**

Soukina et al. present a joint inversion of qP- and qS-waves in homogeneous weakly anisotropic media using a linear formalism for both qP- and qS-waves. If the observed qS-wave polarisation vectors are introduced into the inversion, the tomographic relations for qS-waves can be linearised and are thus formally identical to those for qP-waves. Numerical results for a homogeneous transversely isotropic model show that the full elastic tensor can be reconstructed.

pdf**C. Vanelle and D. Gajewski****Determining Geometrical Spreading from Traveltimes in Anisotropic Media**

Vanelle and Gajewski are currently extending their traveltime based strategy for amplitude preserving migration to anisotropic media. In this paper they describe the determination of geometrical spreading from traveltimes in the anisotropic case. This method is based on a hyperbolic traveltime expansion that also serves for the interpolation of traveltimes. They give several examples to demonstrate the technique.

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### Other topics

**R. Biloti, L.T. Santos, and M. Tygel****Automatic smoothing by optimal splines**

Biloti et al. present a new strategy to smooth plane curves, filtering out white noise as well as suppressing outliers. The key idea is to optimally adjust a cubic spline to the data in a least-squares sense. Some examples are provided to illustrate the wide applicability of the method to geophysical problems.

pdf**D. Gajewski and C. Vanelle****The Tenth International Workshop on Seismic Anisotropy**

Gajewski and Vanelle were co-organisers of the Tenth International Workshop on Seismic Anisotropy (10IWSA) sponsored by the WIT consortium. They givea brief report on the workshop.

pdf**L.T. Santos and M. Tygel****Impedance-type approximations of the P–P elastic reﬂection coefﬁcient: Modelling and AVO inversion**

Santos and Tygel introduce the new concept of Reflection Impedance for elastic media, which generalizes the Acoustic Impedance function, and show how to use it for approximate the P-P reflection coefficient and AVO inversion purposes.

pdf**C. Vanelle****A Tutorial onElliptical Anisotropy**

Vanelle summarises analytic expressions for properties of anisotropic media with elliptical symmetry. Based on these formulae, computer codes for the calculation of traveltimes and geometrical spreading in homogeneous elliptically anisotropic media, as well as for reflection and transmission coefficients between two half-spaces with elliptical anisotropy are available. These codes can be used for the evaluation and verification of the results from other programs,e.g., for the computation of traveltimes or AVO curves.

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### 2001

- Download the entire WIT report 2001 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**S. Bergler, E. Duveneck, G. Höcht, Y. Zhang, and P. Hubral****Common-Reﬂection-Surface stack for converted waves**

Bergler et al. describe how the recently developed 2-D finite-offset Common-Reflection-Surface (FO CRS) stack can be applied to multi-component seismic reflection data. They show that the data-derived wavefield attributes obtained from the FO CRS stack are of use to separate unconverted from converted primary reflections.

pdf**R. Biloti, L.T. Santos, and M. Tygel****Multiparametric traveltime inversion**

Biloti et al. propose a method, based on the well-established Hubral and Krey algorithm, to obtain a velocity model from the CRS attributes. The major improvements are: a strategy to represent interfaces as optimized cubic splines and the possibility of the layer velocities be recovered as gradients in depth. Two synthetic examples are presented.

pdf**S. Buske, T. Müller, C. Sick, S. Shapiro and M.-K. Yoon****True amplitude migration in the presence of a statistically heterogeneous overburden**

Buske et al. present a method for taking into account the amplitude losses due to scattering in a statistically heterogeneous overburden during migration. The scheme is implemented as an additional weighting term within the Kirchhoff integral formulation. The applicability is demonstrated with the help of a synthetic deep seismic data set.

pdf**P. Chira and P. Hubral****Moveout formulas for a curved 2D measurement surface and near-zero-offset primary reﬂections: theory and applications**

Chira and Hubral give a new analytic moveout formula for the CRS stack surface and a normal moveout velocity formula for a 2D curved measurement surface. These formulas are in fact valid for 3D media with a curved measurement surface. This new NMO velocity can be used to recover the interval velocities and the depths of reflectors with a generalized Dix-type inversion.

pdf**V. Grosfeld, R. Biloti, L.T. Santos, and M. Tygel****Topographic effects correction using CRS parameters**

Grosfeld et al. propose a strategy to correct the CRS stacked section, as well as the CRS attributes, for the topographic effects.

pdf**T. Hertweck, C. Jäger, A. Goertz, and J. Schleicher****Aperture effects in Kirchhoff migration**

Hertweck et al. investigate aperture effects in 2.5D Kirchhoff migration. They relate the terms of the Method of Stationary Phase, which mathematically describe the boundary effects, to simple geometrical situations. This provides a more physical and intuitive interpretation of the artifacts and helps to better understand methods to suppress them.

pdf**T. Hertweck, M. Riede, and C. Jäger****Modeling by true-amplitude demigration and its application in time-lapse seismics**

Hertweck et al. give a short introduction to modeling by demigration. They show an application of this method by means of simulating reservoir monitoring (time-lapse seismics). Seismograms for different stages of production are simulated and changes in the reservoir are quantitatively recovered.

pdf**G. Höcht and S. Bergler****CRS stacking formula for 3-D acquisition**

Höcht and Bergler present a traveltime formula that can be used to simulate a ZO volume by means of the CRS stack from multi-coverage reflection data acquired with a 3-D survey.

pdf**C. Jäger, T. Hertweck, and A. Goertz****Applications of the Uniﬁed Approach Theory**

Jäger et al. show that the CRS Stack is a powerful tool to gain a clear image of the subsur- face by comparing results with NMO/DMO/Stack. Furthermore, they present an application of cascading true-amplitude Kirchhoff migration and demigration, namely trace interpolation for a real data example.

pdf**I. Koglin****Effects of smoothing CRS stack attributes on inversion**

Koglin shows the effects of several smoothing methods applied to extracted CRS attributes. The smoothed CRS attributes are used for inversion purposes. A real data example shows the results of a subsequent depth migration.

pdf**L.T. Santos, M. Tygel, and A.C.B. Ramos****Reﬂection Impedance**

Santos et al. propose an approach called reflection impedance, which is based on constant ray parameter and a power relationship between density and S-wave velocity. This new method proved to be of better accuracy for angular impedance estimation and reflection coefficient recovery when compared with the elastic impedance approach.

pdf**J. Schleicher and L.T. Santos****Resolution of Kirchhoff depth migration: offset and angle dependence**

Schleicher and Santos investigate the resolution of Kirchhoff depth migration in dependence on source-receiver offset and reflection angle. They find that, when the aperture is large enough, resolution after migration is a function of angle rather than offset. Thus, in principle, achievable resolution does not depend on reflector depth. In an AVO/AVA analysis of large-offset data, the angle dependence must be taken into account as it may lead to degraded amplitudes at larger angles.

pdf**C. Vanelle and D. Gajewski****Determining the optimum migration aperture from traveltimes**

Vanelle and Gajewski show how the optimum migration aperture can be determined from traveltimes. They illustrate their method with examples and give estimates of possible savings in computational time.

pdf**C. Vanelle and D. Gajewski****Traveltime-based true-amplitude migration of PS converted waves**

Vanelle and Gajewski show how their technique of traveltime-based true-amplitude migration can be extended to converted waves. They illustrate their method with an example.

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### Rock physics and waves in random media

**Y.A. Kravtsov, T.M. Müller, S.A. Shapiro, S. Buske, M.-K. Yoon****Statistical properties of reﬂection traveltimes in 3-D randomly inhomogeneous and anisomeric media in presence of double passage effect**

Kravtsov et al. provide a detailed analysis of the statistical properties of seismic reflection traveltimes in randomly inhomogeneous media in order to characterize the inhomogeneities of the reflector overburden.

pdf**T.M. Müller, C. Sick, and S.A. Shapiro****Frequency and travel-distance dependencies of seismic scattering attenuation revealed by a weak ﬂuctuation approximation and numerical experiments**

Müller et al. present a scattering attenuation model based on the statistical wave propagation theory in random media. They present formulas to quantify scattering attenuation in complex geological regions using simple statistical estimates from well-log data. To verify the theory they perform numerical simulations of seismic wave propagation in 2-D random media using a finite-difference solution of the elastodynamic wave equation and find a good agreement between theoretical and numerical Q estimates.

pdf**E. Rothert and S.A. Shapiro****Seismicity based reservoir characterization - case studies and numerical veriﬁcations of the approach**

Rothert et al. show the application of the SBRC approach to characterize reservoirs in terms of hydraulic diffusivity or permeability in 3D on large spatial scales. Recently, methods were developed using the spatio-temporal evolution of fluid-induced microseismicity for reconstructing rock properties in heterogeneous, anisotropic, fluid-saturated media. For the first time, case studies on data from sedimentary environments are shown as well as numerical verifications of the approach.

pdf**E.H. Saenger, O.S. Krüger, and S.A. Shapiro****Seismic Signatures of Fractured Rocks: Numerical Considerations using the Rotated Staggered Finite Difference Grid**

Saenger et al. present the latest results of wave propagation in fractured media using the rotated staggered finite-difference grid. Viscoelastic wave propagation, a numerical accuracy consideration and a large-scale 3D FD simulation are shown.

pdf**S.A. Shapiro****Stress dependences of seismic velocities in porous and fractured rocks**

Shapiro uses the theory of poroelasticity to analyze stress dependences of seismic velocities. He shows that elastic properties of saturated rocks and their porosity depend mainly on the differential stress. Separating the porosity into compliant and stiff parts he derives equations which approximate well laboratory observations of seismic velocities under changing stresses.

pdf**C. Sick, T.M. Müller, S.A. Shapiro, and S. Buske****Amplitude-corrections for randomly distributed heterogeneities above a target reﬂector**

Sick et al. propose a method to correct transmission losses due to scattering attenuation. They show, by means of two examples, that the implementation of this procedure on synthetic data yields more reliable estimates of reflection coefficients.

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### Modelling

**R. Coman and D. Gajewski****Traveltime computation by wavefront-oriented ray-tracing**

Coman and Gajewski propose an efficient wavefront-oriented ray-tracing technique for the computation of multivalued traveltimes in a smooth 2D velocity model. The technique starts with few rays, which are propagated stepwise through the model, and inserts new rays if certain criteria are satisfied. The authors suggest new approaches for the insertion of rays and for the estimation of traveltimes at gridpoints. They also analyze the influence of the input parameters which control the wavefront and ray densities on the accuracy of the proposed technique.

pdf**A. Novais and L.T. Santos****2.5-D ﬁnite-difference solution of the acoustic wave equation**

Novais and Santos show how a finite difference scheme can be adapted to the 2.5-D situation. The full 3-D FD scheme can be reduced to a repeated 2-D FD scheme by applying the Fourier transform with respect to the out-of-plane coordinate to the 3-D wave equation and using the medium symmetry.

pdf**R. Portugal****The Smirnov's lemma applied to ray theory**

Portugal shows how the Smirnov’s lemma can be applied in ray theory. It can be used to establish the connection between the traveltime and the amplitude along a ray, transforming the transport equation into an ordinary differential equation, which is simply solved.

pdf**S.M. Soukina and D. Gajewski****A traveltime computation in 3-D anisotropic media by a ﬁnite-difference perturbation method**

Soukina and Gajewski use the finite-difference perturbation method for traveltime computation in 3-D arbitrary anisotropic media.

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### Other topics

**D.Gajewski and C. Vanelle****Extending the T**^{2}−X^{2}method to 3-D heterogeneous media

Gajewski and Vanelle introduce an extension of the well-known T 2 − X 2 method to 3-D heterogeneous media. They give an example of traveltime interpolation as one of the possible applications of their method.

pdf

### 2000

- Download the entire WIT report 2000 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**Biloti R., Santos L.T., and Tygel M.****Macro-Velocity Model Inversion from CRS Attributes: The Hubral and Krey algorithm revisited**

pdf**Chira-Oliva P. and Hubral P.****Analytic Moveout formulas for a curved 2D measurement surface and near-zero-offset primary reflections**

Chira-Oliva and Hubral provide an analytic 2D CRS stacking formula for a curved measurement surface. A new analytic expression for the NMO-velocity has been found.

pdf**Coman R. and Gajewski D.****Fast computation of 3D traveltimes and migration weights using a wavefront oriented ray tracing technique**

Coman and Gajewski present a wavefront oriented ray-tracing (WORT) technique for a fast computation of traveltimes and migration weights in a smooth 3D velocity model. In this method, we propagate a wavefront stepwise through the model and interpolate output quantities (ray quantities, e.g.,traveltimes, slownesses) from rays to gridpoints. In contrast to Vinje's wavefront construction method, our technique is based only on kinematic ray tracing.

pdf**Garabito G., Cruz J.C.R., Hubral P., and Costa J.****Common reflection surface stack: a new parameter search strategy by global optimization**

Garabito et al. present a new optimization strategy for determining the CRS parameters and simulating zero-offset section based on the CRS stack formalism. This is a three step in cascade process: 1) Two-parameters global optimization; 2) One-parameter global optimization; and 3) three-parameters local optimization.

pdf**Goertz A., Riede M., and Hertweck T.****AVO curves from prestack depth migrated images based on the Unified Approach Theory**

Goertz et al. show examples of true-amplitude PreSDM based on the Unified Approach theory (Hubral et al., 1996). By comparing the true-amplitude migrated results with Zoeppritz' equations, they show that the method is capable of performing AVO/AVA analysis in the depth domain with high precision. This is especially advantageous when trying to invert for fine-scaled amplitude variations below a complex verburden.

pdf**Hertweck T., Riede M., and Goertz A.****Aspects of the unified approach theory to seismic imaging: theory, implementation, and application**

Hertweck et al. present a seismic imaging tool which is based on the unified approach theory. With the help of Kirchhoff-type true-amplitude migration and demigration, they are able to perform various kinds of image and configuration transformations.

pdf**Koglin I. and Vieth K.****Data-driven macro-velocity model – a real data example**

Koglin and Vieth present a 2-D velocity model that is exclusively data-driven. The common-reflection-surface stack attributes are used for the inversion. These are smoothed with a sophisticated algorithm to obtain a robust inversion.

pdf**Mann J. and Gerst A.****New features of the Common-Reflection-Surface Stack**

The Common-Reflection-Surface (CRS) stack as presented in the preceeding WIT re- ports assigns only one parameter set to each ZO sample to be simulated. Mann and Gerst now present an extended CRS stack strategy that is able to detect and characterize an arbitrary number of contributing events for each ZO sample. Thus, conflicting dip situations can be resolved to simulate the interference of intersecting events and to characterize the contributing events separately.

pdf**Menyoli E. and Gajewski D.****Poisson's ratio analysis and reflection tomography**

Menyoli and Gajewski present a method for determining Poisson' s ratio and updating S-wave velocity using converted wave migration incorporated in reflection tomography. The method based on eliminating residual moveout from migrated CRP gathers is fast and target oriented and does not assume flat reflectors or lateral invariance in model. The method is demonstrated using a synthetic 2D seismic section.

pdf**Schleicher J., Santos L., and Tygel M.****Seismic migration by demodeling**

Schleicher et al. investigate the asymptotic inverse Kirchhoff-Helmholtz integral under more realistic conditions and compare the results of this 'migration by demodeling' integral to those of conventional true-amplitude Krichhoff migration.

pdf**Schleicher J. and Santos L.****Offset-dependent resolution of seismic migration**

Schleicher and Santos study the resolving power of seismic migration as a function of source-receiver offset. In a simple numerical example, they compare the achieved resolution with the ray-theoretical prediction. They find that the region of influence after migration is well described by the difference between the time-domain Fresnel zone and its paraxial approximation.

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### Rock Physics and Waves in Random Media

**Goertz A. and Kaselow A.****A High-Frequency Seismic Experiment to Measure Seismic Signatures of Fluid Flow In-situ**

The article by Goertz and Kaselow describes a high-frequency, high-resolution seismic experiment carried out by University of Karlsruhe last spring within a gallery system. The experiment was designed to measure hydraulic properties with seismic methods. The installations of the rather unique test site used for the experiment allows for the calibration of techniques for 4D seismic monitoring.

pdf**Müller T. M., Shapiro S. A., and Sick C.****A weak fluctuation approximation of the primaries in typical realizations of wavefields in random media**

Müller et al. propose a broad frequency range theory to describe seismic primaries (time harmonic and transient transmissivities) in statistically isotropic heterogeneous 3-D and 2-D media. This formalism is a 3-D analog of the O'Doherty and Anstey theory. It relates properties of the primaries to the first two statistical moments of the medium heterogeneities.

pdf**Müller T. M. and Shapiro S. A.****A new model of scattering attenuation: theory and application**

Müller and Shapiro use the formalism for primaries in 3-D statistically isotropic media (see the Mueller et al contribution) in order to explain seismic attenuation due to scattering. On the example of the German KTB data set they show that scattering attenuation has a significant impact on the wavefield propagation.

pdf**Rindschwentner J.****Estimating the Global Permeability Tensor using Hydraulically Induced Seismicity – Implementation of a new Algorithm**

Rindschwentner implemented a new algorithm for estimating a permeability tensor at reservoir scale using hydraulically induced seismicity. With the new algorithm data sets from Soultz-sous-Foreˆts (France), the KTB site (Germany) and Fenton Hill (USA) were reprocessed and thus the algorithm tested. The algorithm facilitates the interpretation of possible fluid flow paths.

pdf**Saenger E. and Shapiro S.****Effective velocities in fractured media: Intersecting and parallel cracks**

Saenger and Shapiro are able to model the effective velocities of fractured media using the rotated staggered finite difference grid. The numerical study of dry rock skeletons can be considered as an efficient and well controlled computer experiment. Based on this considerations we present analytical descriptions for effective elastic properties for fractured media.

pdf**Shapiro S., Rothert E., Rath V., and Rindschwentner J.****Characterization of fluid transport properties of reservoirs using induced microseismicity**

Shapiro et al. propose an extension of the SBRC approach to estimate the large scale permeability of reservoirs using seismic emission (microseismicity) induced by fluid injection. They show that in a homogeneous medium the surface of the seismicity triggering front has the same form as the group-velocity surface of the low-frequency anisotropic second-type Biot's wave (i.e. slow wave). The approach is generalized for a 3-D mapping of the permeability tensor of heterogeneous reservoirs and aquifers. An equation describing kinematical aspects of triggering front propagation in a way similar to the eikonal equation for seismic wavefronts is derived and used to invert for the hydraulic properties of rocks. The method is applied to several data sets and tested on numerical models.

pdf

### Modelling

**Buske S.****First arrival traveltimes and amplitudes by FD solution of eikonal and transport equation**

Buske presents a method for the computation of first-arrival traveltimes and amplitudes by a finite-difference solution of the eikonal equation and the transport equation. It is based on the formulation of these equations as hyperbolic conservation laws and their numerical solution using ENO upwind schemes. Highly accurate traveltimes and smooth amplitudes are obtained which is demonstrated for the Marmousi model.

pdf**Coman R. and Gajewski D.****Hybrid Method for Traveltime Computation in a Complex 3D Model**

Coman and Gajewski present a hybrid method for computing multi-arrival traveltimes in weakly smoothed 3D velocity models. The hybrid method is based on the computation of first-arrival traveltimes with a finite-difference eikonal solver and the computation of later arrivals with the wavefront construction method. For a faster traveltime computation we implement a wavefront construction method without dynamic ray tracing.

pdf**Soukina S. and Gajewski D.****An FD eikonal solver for 3-D anisotropic media**

Soukina and Gajewski present an FD eikonal solver scheme for general anisotropic media which is based on a perturbation method. Traveltimes are calculated for an elliptically anisotropic reference medium. The correction terms required for the traveltimes of the general anisotropic medium are then computed by a perturbation technique.

pdf**Vanelle C. and Gajewski D.****Second-order interpolation of traveltimes**

Vanelle and Gajewski present a fast and efficient algorithm for traveltime interpolation. High accuracy is achieved because second order derivatives are taken into account. Examples including the highly complex Marmousi model demonstrate the quality of the method.

pdf**Vanelle C. and Gajewski D.****True-amplitude migration weights from traveltimes**

Vanelle and Gajewski developped a method to determine weight functions for a true- amplitude migration. Traveltimes on coarse grids are the only necessary input data, no dynamic ray tracing is required.

pdf

### Other Topics

**Leite L. W. B., Rocha M.P.C.d., and Alves F.J.****Attenuation of Primary Multiples and Peg-legs: Comparison of WHL and KBC Methods**

The KBC and WHL methods are here compared and applied by Leite et al. to the multiple suppression of peg-legs related to upper low velocity layers (weathering zone), and to deeper high velocity layers (diabase sills).

pdf

### 1999

- Download the entire WIT report 1999 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**Cruz J.C.R., Chira P., and Garabito G.****Sensibility Analysis of the Multifocusing Traveltime Approximation**

Cruz et al. present a sensibility analysis of the functional that simulates the observed data with respect to the searched-for wavefront parameters. The most important result is the very high sensibility of the multifocusing traveltime on relation to B_0 and KNIP. The KN parameter presents a strong ambiguity and is poorly determined during the optimization procedure.

pdf**Majer P., Höcht G., Mann J., and Vieth K.****Inversion by means of kinematic waveﬁeld attributes**

Majer et al. present an inversion method which make use of data-derivated kinematic wavefield attributes to determine a 2 D macro-velocity model. This attributes are provided by the CRS Stack method. By means of geometrical optics primary reflection events of a zero-offset section with the associated wavefield attributes determine reflection points of interfaces in the subsurface. The interfaces are constructed layer by layer with interpolating spline functions. First appliacations of the algorithm are shown for two synthetic examples.

pdf**Tygel M., Schleicher J., Santos L.T., and Hubral P.****An asymptotic inverse to the Kirchhoff-Helmholtz integral**

Tygel et al. propose a new asymptotic inverse to the forward Kirchhoff-Helmholtz integral. Analogous to the forward integral, the new inverse consists of a summation along the reflection traveltime surface of the reflector. A simple numerical example shows how this can be used for migration.

pdf**Tygel M., Santos L.T., Schleicher J., and Hubral P.****Kirchhoff imaging as a tool for AVO/AVA analysis**

Tygel et al. show that the methods of true-amplitude PreSDM and MZO can be used to perform an AVO/AVA analysis. By means of a simple but illustrative example, they discuss the advantages and disadvantages of both methods.

pdf

### Rock Physics and Waves in Random Media

**Müller T.M. and Shapiro S.A.****Seismic pulse propagation in 2-D and 3-D random media**

Müller and Shapiro extended the O'Doherty-Anstey approach for primary arrivals to the case of statistically isotropic randomly heterogeneous media. They are able to predict the seismic pulse evolution in typical realizations of seismograms in the range of week wavefield fluctuations. This makes possible a Green's function construction taking into account effects of isotropic random heterogeneity.

pdf**Saenger E.H. and Shapiro S.A.****Calculation of effective velocities in cracked media using the rotated staggered ﬁnite-difference grid**

Saenger and Shapiro propose to model the effective velocities of fractured media using the rotated staggered finite difference grid. In contrast to the standard staggered grid the rotated one does not have instability problems by modeling wave-difraction effects in media with fractures. Thus, such a numerical modeling can be considered as an efficient and well controlled computer experiment. Therefore, it is a promising tool for a study of elastic properties of dry rock skeletons. In this paper the importance of the critical porosity concept is demonstrated for the case of intersecting fractures.

pdf**Shapiro S. A.****An Inversion for Fluid Transport Properties of 3-D Heterogeneous Rocks Using Induced Microseismicity**

Shapiro proposes an extension of the SBRS approach to estimation of permeability tensors to the case of 3-D heterogeneous structures. The approach is based on a geometrical optic approximation for triggering fronts and provides a possibility at least semi qualitatively characterize hydraulically heterogeneous media using microseismic data.

pdf

### Modelling

**Bergmann T. and Gajewski D.****Numerical Modeling of Non–Linear Elastic Wave Phenomena**

Bergmann and Gajewski present their first results on developing a finite-difference (FD) formulation for the simulation of non-linear elastic waves. The results show that conventional FD approaches applied for linear problems may not extended to the non-linear case. For this reason, the authors show a new algorithm and make related important aspects in terms of physics and computation evident.

pdf**Coman R. and Gajewski D.****3-D traveltime computation using a hybrid method**

Coman and Gajewski present a hybrid method for computing multi-arrival traveltimes in 3-D weakly smoothed media. The method is based on the computation of first-arrival traveltimes with a finite-difference eikonal solver and the computation of later arrivals with the wavefront construction method (WFCM). The detection and bounding of regions where later arrivals occur is done automatically. The hybrid method is faster than WFCM.

pdf**Karrenbach M.****Combining Fast Marching Level Set Methods with Full Wave Form Modeling**

By combining fast marching level set methods with full wave form modeling Karrenbach takes advantage of numerical properties of both methods. He is able to reduce the computational expense associated with full wave form finite difference methods by decomposing the computational domain dynamically into subdomains. The size and shape of these subdomains is derived from the shape of the wave front given by an asymptotic Eikonal solution.

pdf**Karrenbach M.****Full Wave Form Modeling In Time-Lapse Studies**

The paper by Karrenbach describes the importance of full wave form modeling techniques in time-lapse studies, where preliminary time-lapse tests are computed numerically in an elastic 3D SEG/EAGE salt model. Recent activities of the SEG 3D modeling committee show that, while 3D full wave forms studies are indeed much desired, their computational expense has been prohibitively high up to now. However, new advances in numerical algorithms and cheap high-performance hardware computer hardware might allow realistic studies in the near future on a routine basis.

pdf**Kaselow A. and Karrenbach M.****Seismic Modeling In Reservoir Rocks**

Kaselow et al. model changes in p-wave and s-wave velocity in reservoir rocks that are due to changes in porosity and fluid content. They present a technique that computes the seismic wave response from a reservoir, whose shape and constitution changes over time, allowing to conduct feasibility studies in realistic reservoirs in order to optimally control production.

pdf**Menyoli E. and Gajewski D.****Simultaneous computation of P- and S-wave traveltimes for pre-stack migration of P-S converted waves**

Menyoli and Gajewski used the first order perturbation principle to simultaneously compute P- and S-wave traveltimes in a 2D model. It is demonstrated on a constant gradient velocity model with a parabolic lens at the centre. This perturbation method is useful for a simultaneous kinematic Kirchhoff migration of converted waves with slightly different macro models.

pdf**Pohl M., Wenzel F., and Karrenbach M.****A Chebyshev method on 2D generalized coordinates**

To reduce the computational burden in 3D full wave form modeling Pohl et al. sug- gest the use of optimal gridding procedures for certain characteristic seismic reservoir geometries. The grid is adapted to the major layering features of the reservoir and uses a spectral method to compute derivatives and produces accurate and artifact-free numerical solutions. A 2D modeling example attempts to grid a salt dome structure optimally, such that some of the major grid contours follow the overburden layers as well as the salt dome interfaces.

pdf**Portugal R., Santos L., and Schleicher J.****Analysis of an acoustic wave equation for cylinder symmetric media (2.5D)**

Portugal et al. describe of 3-D wave propagation in a 2-D medium (2.5-D situation) by means of a simple 2.5-D wave equation. A comparison to alternative approximations in homogeneous and vertical-gradient media shows that the accuracy of a previously suggested approximate 2.5-D wave equation (Liner's equation) depends on how well the rms velocity can be approximated by a constant velocity.

pdf**Schleicher J., Tygel M., Ursin B., and Bleistein N.****The Kirchhoff-Helmholtz integral for anisotropic elastic media**

Schleicher et al. introduce the Kirchhoff-Helmholtz modeling integral to general anisotropic elastic media, using the natural extension of the Kirchhoff approximation of the scattered wavefield and its normal derivative for that media. After its asymptotic evaluation, the anisotropic Kirchhoff-Helmholtz integral reduces to the zero-order ray theory approximation of the reflected response from the interface.

pdf**Schleicher J., Tygel M., Ursin B., and Bleistein N.****Geometrical-spreading decomposition in anisotropic media**

Schleicher et al. generalize the decomposition formula for the geometrical-spreading factor to anisotropic media in terms of second-order mixed derivatives of the traveltime as well as group and phase angles at the reflection point.

pdf**Vanelle C. and Gajewski D.****Three-Dimensional Dynamic Waveﬁeld Properties**

Vanelle et al. introduce a new representation of the ray propagator valid in an arbitrary 3-D coordinate system. Its relation to the Bortfeld and Cerveny formulations is explained. Applications like traveltime interpolation and the computation of geometrical spreading demonstrate the versatility of the method.

pdf

### OtherTopics

**Birgin E.G., Biloti R., Tygel M., and Santos L.T.****Restricted optimization: a clue to a fast and accurate implementation of the Common Reﬂection Surface Stack method**

Birgin et al. introduce a new optimization algorithm to directly extract the Common Reflecting Surface (CRS) parameters out of coherency analyses applied to multicoverage data. Numerical results obtained in sunthetic examples confirm the good performance of the method, both in accuracy and computational effort.

pdf**Ettrich N., Gajewski D., and Kashtan B.****Reference ellipsoids for anisotropic media**

Ettrich et al. present simple relations to compute the best fitting ellipsoid for an arbitrary anisotropic medium. The fit can be applied globally or locally, e.g., in a cone of interest for vertically propagating waves. This model can serve as a background medium to compute wave field properties in arbitrary anisotropic media using perturbation techniques. It provides improved results when compared with the best fitting isotropic background medium particularly if strong P-wave anisotropy is present (e.g., shales).

pdf**Leite L.W.B. and Rocha M.P.C.d.****Deconvolution of non stationary seismic process with inelastic models**

The report of Leite and da Rocha deals with the application of Kalman's method to the deconvolution of the source wavelet as a time varying pulse that serves to model the inelasticity of the medium. The wave propagation is given by the Goupillaud solution. We demonstrate the necessity for applying a low-pass equalization to compensate for the amplification of the high frequency content of the data when submitted to deconvolution.

pdf**Mauch R.****Coherency Analysis of Seismic Data**

The report by Mauch compares various coherency measures analytically as well as by numerical examples. A common notation allows easy comparison of different coherency definitions. Synthetic as well as real data examples are used to contrast the performance of different coherency criteria.

pdf

### 1998

- Download the entire WIT report 1998 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**Bader M.****The dynamics of velocity independent partial and full prestack time migration**

pdf**Birgin E.G., Biloti R., Santos L.T., and Tygel M.****Traveltime Multiparameter Estimation Using Bound Constrained Optimization: A First Approach**

Birgin et al. describe a new algorithm to extract from multicoverage data, the traveltime parameters required for CRS stacking. The algorithm uses a newly developed spectral projected gradient method combined with a global optimization technique. First experiments indicate that the method is able to produce accurate results in an efficient way.

pdf**Cruz J.C.R. and Urban J.****Numerical Analysis of Two and One–Half Dimensional (2.5–D) True–Amplitude Diffraction Stack Migration**

Cruz and Urban derive the weight function and the diffraction stack integral operator for the two and one half dimensional (2.5-D) seimic models and apply it to a set of synthetic seismic data in a noisy enviroment. The result shows the accuracy and stability of the 2.5-D migration as a tool for obtaining the reflectivity properties of the earth subsurface, which is of great interest for a AVO or AVA analysis.

pdf**Höocht G., Mann J., and Jäger R.****The Common Reﬂection Surface Stack – Part I: Theory**

G. Höcht et al.: The common reflection surface stack is a macro velocity model independent method to simulate zero-offset sections. It is based on attributes of wavefronts associated with hypothetical experiments that are used to describe the kinematic reflection response of inhomogeneous media. In this context we derive the stacking operator and with respect to application its more convenient Taylor series expansions.

pdf**Jäager R., Mann J., and Höcht G.****The Common Reﬂection Surface Stack – Part II: Application**

In the second part of The Common Reflection Surface Stack R. Jäger et al. apply the common reflection surface stack method to synthetic data. In addition to the simulated zero-offset section we obtain a set of data-derived wavefront attributes. We compare them to the model-derived attributes exposing a wide agreement. We discuss different strategies to determine the attributes with respect to accuracy and computional costs.

pdf**Mann J.****Derivation and Implementation of the Seismic Image Wave Theory and its Application to Seismic Reﬂection Data**

Jürgen Mann shows that seismic image wave methods allow to transform a seismic image with respect to a change in an imaging parameter which depends on the imaging method under consideration. This strategy is dicussed for different imaging problems: post-stack time migration, post-stack depth migration, dip moveout correction, and migration to zero-offset. For migration the imaging parameter is the constant migration velocity, whereas for the latter two imaging problems it is the source/receiver offset.

pdf**Pasasa L., Wenzel F., and Zhao P.****Prestack Kirchhoff depth migration with dynamic wavefronts applied to SEG/EAGE Salt dataset**

Pasasa et al. demonstrate the superior performance of their novel technique of wave front extrapolation on a computational grid. The approach is used in Prestack Kirchhoff Migration of the SEG/EAGE Salt data set and results in unprecedented highresolution images.

pdf**Tygel M., Santos L.T., Schleicher J., and Hubral P.****The Kirchhoff-Helmholtz Integral Pair**

Tygel et al. introduce a new inverse integral formula to the classical Kirchhoff-Helmholtz forward modeling integral. The new formula is more natural than the conventional Kirchhoff migration integral. This new inverse formula consists of an integration along the reflection traveltime surface, reconstructing the Huygens sources along the reflector.

pdf**Vieth K.****Spatial Positioning of Reﬂectors Using the tau-p Transform (Cross-Section Processing)**

Vieth et al.: Instead of picking data in in- and cross-line sections the entire wavefield of the common-shot sections is used for computing dip and strike of a reflector.

pdf

### Rock Physics and Waves in Random Media

**Bojinski S., Shapiro S.A., Gold N., and Stanullo J.****Statistical characterization of fractured rocks by seismic waveﬁeld analysis**

Stephan Bojinski reports about his Thesis on seismic characterization of randomly fractured media.

pdf**Müller T M. and Shapiro S.A.****Dynamic equivalent medium approach for 2-D and 3-D random media**

For waves in 2-D and 3-D randomly heterogeneous media Tobias Müller is going to develop an approximation of the Green Function which takes into account effects of small-scale heterogeneities. His formalism is similar to the generalized O' Doherty-Anstey formula valid in multilayered structures. However, one should emphasis the increased complexity of the problem now. In his contribution Tobias shortly describes his approach.

pdf**Saenger E.H., Gold N. and Shapiro S.A.****Modeling of high contrasts in elastic media using a modiﬁed Finite Difference grid**

In order to understand the wave propagation in fractured structures we have to perform a modeling in media with high-contrast inclusions. Erik Saenger will present the modified Finite Difference grid, which permits to model waves in such situations.

pdf**Shapiro S.A., Audigane P., and Royer J.****Reservoir-scale In-situ Permeability Tensor from Induced Microseismicity**

In 1998 we continued to develop the method of the SBRC (Seismicity Based Reservoir Characterization). The corresponding contribution of S. A. Shapiro with his coauthors describes in details an approach to the seismicity-data inversion for the permeability tensor for the case of poroelastic media with anisotropic fluid transport.

pdf**Shapiro S.A. and Hubral P.****Elastic Waves in Random Media. Fundamentals of Seismic Stratigraphic Filtering**

Serge Shapiro gives a short summary of his and Peter Hubral' s book on seismic strategraphic filtering.

pdf**Vieth K. and Shapiro S.A.****Crack imaging in randomly heterogeneous media**

Vieth shows his first results on crack imaging in randomly heterogeneous media. He suggests to apply a simple post-migration approach to detect fractures embedded in randomly heterogeneous structures.

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### Modelling

**Ettrich N.****Traveltime computation for 3D anisotropic media**

Ettrich has developed a 3D Finite Difference eikonal solver for elliptical anisotropic media. It allows for arbitrary orientation of the tensor ellipsoid and for strong anisotropy. It serves as the background medium to compute traveltimes for arbitrary anisotropic media using a perturbation approach. A second-order approximations of the eikonal equation results in a high accuracy with relative errors in the order of a few permille.

pdf**Falk J., Teßmer E., and Gajewski D.****Numerical modeling of borehole effects in cross-well seismics**

Falk et al. present a modelling technique for wave propagation simulation based on the Finite Difference techniques which allows efficient computations of wave fields even if small scale heterogeneities are present in the model. It is demonstrated on an cross-well experiment where the influence of the source and receiver well is included. The scattering of borehole guided waves results in very complex seismogramms.

pdf**Gajewski D.****Determining the ray propagator from traveltimes**

Gajewski uses the hyperbolic variant of the paraxial approximation to determine the complete ray propagator from traveltimes. The ray propagator enables the evaluation of many important properties of seismic waves, like migration weights, divergence corrections etc. Moreover, the propagator provides a very efficient technique to interpolate traveltimes, which is demonstrated on some examples.

pdf**Goertz A. and Karrenbach M.****Seismic Modeling of Complex Fault Zones**

Goertz et al. use 3D finite difference techniques to perform full wave field modeling of a complex fault zone. Synthetic benchmark data sets are used to enhance imaging techniques. Modeling of rock properties within the fault zone enables them to simulate 4D seismic monitoring experiments.

pdf**Karrenbach M.****Distributed 2D Seismic Modeling and Processing**

M. Karrenbach shows applications of parallel computing to seismic processing and full wave form modeling. Seismic processing and modeling show a large degree of parallelism on various levels that can be exploited in order to speed up computation and turn around time. A complete parallel processing sequence is applied to the Mobil AVO data set and a parallel 2D modeling run is carried out to produce a complete prestack data set from the SEG/EAEG Salt model. Runtime and scalability are measured on a IBM SP-2.

pdf**Karrenbach M. and Traub B.****Green's Function computation with recursive cell tracing**

pdf**Leidenfrost A. and Gajewski D.****A 3-D FD Eikonal Solver for Non-Cubical Grids**

A 3-D Finite-Difference eikonal solver for non-cubical grids was developed by Leidenfrost et al. A carefully chosen set of grid spacings for a non-cubical grid can reduce the model size and thus save computational time. Moreover, it may even allow stronger velocity contrasts in the model without the appearance of acausalities. Numerical examples demonstrate the functionality of the method.

pdf**Pohl M., Igel H., and Wenzel F.****Wave propagation on irregular grids**

Pohl et al. compute the elastic wave equation solution on a irregular computational grid in order to reduce unphysical diffractions that can arise from the typical stair- casing effect when applying conventional finite differences to a regularly gridded model. Examples of wave propagation in 2 dimensions are shown for a homogeneous medium using a irregular grid, as well as a 2-layer model, where the layer boundary exhibits topography.

pdf**Portugal R.S.****Analysis of an acoustic wave equation for cylinder symmetric media (2.5D)**

pdf**Santos L., Schleicher J., Hubral P., and Tygel M.****Is Seismic Demigration Equivalent to Forward Modeling?**

Santos et al. investigate the seismic imaging process called demigration in greater detail. They argue that demigration is not the same as forward modeling and point out the main differences.

pdf**Schleicher J., Ursin B., and Tygel M.****The Kichhoff-Helmholtz Integral for Anisotropic Elastic Media**

Schleicher et al. discuss the Kirchhoff integral for general anisotropic elastic media. They show hot standard Kirchhoff-Helmholtz approximation can be generalized for this case. If one elementary seismic wave is considered, a scalar reflection coefficient describes the amplitude change under specular reflection.

pdf**Tessmer E.****Seismic ﬁnite-difference modeling with spatially varying time steps**

Ekkehart Tessmer optimizes computational effort in finite-difference seismic modeling by using domain dependent time step sizes. Applications demonstrate the high accuracy of the method and its efficiency.

pdf**Tygel M. and Ursin B.****Weak–Contrast Edge and Vertex Diffractions in Anisotropic Elastic Media**

Tygel and Ursin introduce a new representation integral to model scattering from a weak-contrast interface within a general elastic, anisotropic medium. Asymptotic evaluation of the integral leads to an appealing description of the total sctattered field as a sum of individual contributions such as specular reflections, as well as i edge and edge diffractions.

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### Other Topics

**Karrenbach M. and Jacob M.****Seismic Java Applications**

M. Karrenbach et al. use the novel programming language Java in a computational interdisciplinary project between the geophysics and computer science. Basic seismic processing steps are programmed in Java and High Performance Fortran and their run-time, scalability measured on a wide variety of parallel high-performance computers and workstations. The Mobil AVO data set is used a benchmark data set to which some standard processing steps are applied.

pdf**Karrenbach M.****Large-Scale Computation and Visualization**

M. Karrenbach reports on large-scale computational and visualization facilities that are available to conduct research in seismic algorithm development. The High Performance Computing Center at Stuttgart offers a variety of highly parallel computers as well as a 3D immersive virtual reality environment for analyzing seismic data and velocity models. Computational steering of large-scale simulations and processing runs are possible from within this environment. As oil companies install such environments more frequently, access of researchers to similar tools is important.

pdf**Mauch R.****Coherency Analysis and Correlation Procedures**

pdf**Popov M.M., Schitov I.N.****What may happen if the velocities of qS waves in an anisotropic inhomogeneous medium coincide at a point?**

Popov and Schitov present the results for the problem which models wave propagtion in anisotropic inhomogeneous media when the velocities of two qS waves coincide at a point. These results allow to anticipate that generally one qS wave being incident at such a point gives rise to two qS waves behind this point. The ray ansatz becomes singular in a vicinity of such points and cannot describe the wave phenomenon properly.

pdf**Tygel M., Santos L.T., and Schleicher J.****Multifocus Moveout Revisted: Derivations and Alternative Expressions**

Tygel et al. review the basic derivations and results concerning the traveltime moveout formula of Gelchinsky and coworkers. This formula describes traveltimes of rays located around a fixed central ray and it is called multifocus moveout. They also present a new higher-order multifocus formula and provide an alternative form suitable for implementation.

pdf

### 1997

- Download the entire WIT report 1997 here (password required).
- Download the table of contents and WIT info here.

### Imaging

**Hubral P., Schleicher J., and Mueller T.****Review: Seismic Reﬂection Imaging**

pdf

### Imaging A: True Amplitude Image Transformations

**Martins J., Schleicher J., Tygel M., and Santos L.****2.5D true-amplitude Kirchhoff migration and demigration**

pdf**Novais A., Santos L., Tygel M., and Ursin B.****A uniﬁed Born–Kirchhoff representation for acoustic media**

pdf**Oliveira A., Tygel M., and Filpo E.****On the application of true-amplitude DMO**

pdf**Santos, L.T., Schleicher, J., and Tygel, M.****2.5D true-amplitude offset continuation**

pdf**Santos L., Schleicher J., Tygel M., and Hubral P.****Modeling by demigration**

pdf**Schleicher, J., Hubral, P., Tygel, M., and Jaya, M.S.****Minimum Apertures and Fresnel zones in migration and demigration**

pdf**Tygel, M., Schleicher, J., Hubral, P., and Santos, L.T.****2.5-D True-Amplitude Kirchhoff Migration to Zero Offset in Laterally Inhomogeneous Media**

pdf**Ursin B. and Tygel M.****Reciprocal volume and surface scattering integrals for anisotropic elastic media**

pdf

### Imaging B: Macromodel-independent Zero-offset Simulations

**Cruz J., Hubral P., Tygel M., and Schleicher J.****The common-reﬂecting-element (CRE) method revisited**

pdf**Höcht G., Jäger R., and Hubral P.****A new look at subsurface illumination in seismic imaging**

pdf**Müller T., Tygel M., Hubral P., and Schleicher J.****Eigenwave based multiparameter traveltime expansions**

pdf**Müller T.****Common Reﬂection Surface Stacking**

pdf**Perroud H., Hubral P., and Höcht G.****Common-reﬂection-point stacking in laterally inhomogeneous media**

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### Imaging C: Imaging in General

**Jaya M.S., Hubral P., and Botelho M.****Constructing migrated image scans by poststack remigration**

pdf**Mann J. and Jaya M.S.****3D ﬁnite difference post-stack time and depth remigration**

pdf**Pasasa L., Wenzel F., and Zhao P.****Imaging complex 2D structure with non-Fermat arrival Kirchhoff depth migration**

pdf**Schleicher J., Hubral P., Höcht G., and Liptow F.****Seismic constant-velocity remigration**

pdf

### Rock Physics

**Shapiro S.A.****Review: Rock Physics and Waves in Random Media**

pdf**Bojinski S., Shapiro S., Gold N., and Stanullo J.****Seismic characterization of statistical properties of fractured composite materials**

pdf**Gold N. and Shapiro S.****Upscaling in elastic random media**

pdf**Shapiro S.A., Royer J., and Audigane P.****Estimating the Permeability from Fluid-Injection Induced Seismic Emission**

pdf**Shapiro S.A. and Mueller T.M.****Seismic signatures of permeability**

pdf**Weiss A.****What Higher Order Statistics can reveal on the Seismogram**

pdf**Werner U. and Shapiro S.A.****Frequency-dependent shear-wave splitting in ﬁnely layered media with intrinsic anisotropy**

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### Modeling A: Asymptotic Methods

**Gajewski D.****Review: Modeling: Asymptotic Methods**

pdf**Ettrich N.****Finite-difference traveltime computations for anisotropic media**

pdf**Ettrich N.****A hybrid method for traveltime computation**

pdf**Falk J. and Tessmer E.****Numerical Studies of Realistic Single Well Monitoring and Walkaway VSP Conﬁgurations**

pdf**Koslowski O. and Ettrich N.****Computation of frequency-dependend traveltimes**

pdf**Leidenfrost A. and Gajewski D.****Strategies for 3D travel time computation**

pdf

### Modeling B: Full Wave Form Modeling

**Karrenbach M.****Review: Full Wave Form Modeling**

pdf**Karrenbach M.****Modeling of Physical Systems**

pdf**Laux S.****Calculation of selected waveﬁelds with the reﬂectivity method**

pdf**Pohl M. and Karrenbach M.****Reﬂectivity modelling: a tool for testing processing algorithms**

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### Computer Science and Artiﬁcial Intelligence

**Karrenbach M.****Review: Computer Science and Artiﬁcial Intelligence**

pdf**Essenreiter R. and Karrenbach M.****Multiple Reﬂection Attenuation in Marine Seismograms using Backpropagation Neural Networks**

pdf**Karrenbach M. and Jacob M.****Large-Scale Parallel Geophysical Algorithms in Java: A Feasibility Study**

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### Anisotropy

**Gajewski D.****Review: Anisotropy**

pdf**Gajewski D., Kashtan B., and Zillmer M.****Normal moveout velocities in 3D arbitrary anisotropic media**

pdf**Ruedas T. and Teßmer E.****2D seismic modeling in transversely isotropic media with a Chebyshev-Fourier method in consideration of the free surface and the surface/grid interface topography**

pdf**Zillmer M., Gajewski D., and Kashtan B.M.****P-wave AVOA for vertically fractured media**

pdf