Dimitri Bevc

Flooding the topography; wave-equation datuming of land data with rugged acquisition topography

Wave-equation datuming overcomes some of the problems that seismic data recorded on rugged surface topography present in routine image processing. The main problems are that (1) standard, optimized migration and processing algorithms assume data are recorded on a flat surface, and that (2) the static correction applied routinely to compensate for topography is inaccurate for waves that do not propagate vertically. Wave-based processes such as stacking, dip-moveout correction, normal-moveout correction, velocity analysis, and migration after static shift can be severely affected by the nonhyperbolic character of the reflections. To alleviate these problems, I apply wave-equation datuming early in the processing flow to upward continue the data to a flat datum, above the highest topography. This is what I refer to as “flooding the topography.” This approach does not require detailed a priori knowledge of the near-surface velocity, and it streamlines subsequent processing because the data are regridded onto a regularly sampled datum. Wave-equation datuming unravels the distortions caused by rugged topography, and unlike the static shift method, it does not adversely effect subsequent wave-based processing. The image obtained after wave-equation datuming exhibits better reflector continuity and more accurately represents the true structural image than the image obtained after static shift.

Smoothing imaging condition for shot-profile migration

Amplitudes in shot-profile migration can be improved if the imaging condition incorporates a division deconvolution in the time domain of the upgoing wavefield by the downgoing wavefield. This division can be enhanced by introducing an optimal Wienerfilterwhichassumesthatthenoisepresentinthedatahas a white spectrum. This assumption requires a damping parameter, related to the signal-to-noise ratio, often chosen by trial and error. In practice, the damping parameter replaces the small valuesofthespectrumofthedowngoingwavefieldandavoidsdivision by zero. The migration results can be quite sensitive to the damping parameter, and in most applications, the upgoing and downgoing wavefields are simply multiplied. Alternatively, the division can be made stable by filling the small values of the spectrumwithanaverageoftheneighboringpoints.Thisaveraging is obtained by running a smoothing operator on the spectrum ofthedowngoingwavefield.Thisoperationcalledthesmoothing imaging condition. Our results show that where the spectrum of the downgoing wavefield is high, the imaging condition with dampingandsmoothingyieldssimilarresults,thuscorrectingfor illumination effects. Where the spectrum is low, the smoothing imaging condition tends to be more robust to the noise level present in the data, thus giving better images than the imaging condition with damping. In addition, our experiments indicate that the parameterization of the smoothing imaging condition, i.e., choice of window size for the smoothing operator, is easy and repeatable from one data set to another, making it a valuable additiontoourimagingtoolbox.

Anti-aliased Kirchhoff 3-D migration

A significant degradation in the quality of Kirchhoff 3-D migration images often arises because the migration operator summation trajectory is too steep for the input seismic trace spacing and frequency content. We present an operator anti-aliasing method that suppresses this problem, based on local triangle filtering. The N-point anti-alias triangles are efficiently applied as 3-point filters after causal and anticausal integration of the seismic trace data. We implement our method on a massively parallel CM-5 in a memory and floating-point efficient algorithm, and compare our anti-aliasing method to a standard Kirchhoff migration using a 3-D salt intrusion dataset from the Gulf of Mexico. Our results indicate that our anti-aliasing method greatly enhances the 3-D resolution of steep salt-sediment interfaces and faults, and suppresses false reflections caused by conventional Kirchhoff-migration aliasing artifacts.

Automated velocity model building with wavepath tomography

Wavefield-continuation migration generally is recognized as superior to Kirchhoff methods in complex velocity models, such as below rugose salt bodies. It accounts for multipathing, sharp velocity contrasts, and the limited bandwidth of seismic wave propagation. Wavepath tomography builds the velocity model in a way that is consistent with the wavefield-migration operator. Traveltime residuals are back-projected along a wavepath instead of rays. The actual wavefield-continuation operator is used to represent the wave propagation between surface source/receiver pairs and subsurface reflection points. A wavepath is obtained by multiplying impulse responses from a surface location and a reflection point. The inversion matrix is kept to a manageable size by restricting the wavepath to the first Fresnel zone. The considerable expense of computing a single wavepath kernel in comparison to ray tomography is partially offset by the smaller number of back projections necessary to sample the velocity model adequately. We have used wavepath tomography to build subsalt velocity models using 2D synthetic data. Wavepath tomography was implemented in 3D.

Robust Imaging Condition For Shot-Profile Migration

For shot-profile migration, illumination compensation can be achieved if the imaging condition incorporates a deconvolution (division in the frequency domain) of the upgoing wavefield by the down-going wavefield. To avoid division by zero, the deconvolution requires the selection of a damping parameter that turns out to be quite difficult to select. Consequently, a cross-correlation of the two wavefields is often selected. Alternatively, the zeros in the spectrum of the down-going wavefield can be filled with an average of the neighboring points. Therefore, instead of dividing by the wavefield, we can divide by a smoothed version of it. Smoothing is robust and easy to parameterize. It also corrects illumination problems in the migrated images.

Velocity model building by wavefield-continuation imaging in the deepwater Gulf of Mexico

Wavefield-continuation-based migration algorithms that downward extrapolate the 3D prestack wavefield (commonly known as “wave-equation migration”) have been recently shown to produce better imaging results than Kirchhoff migration in many synthetic and real data cases (Popovici, 2000). Wavefield-continuation methods are potentially more accurate and robust because they are based on the full wave equation and not on an asymptotic solution based on ray theory. In addition, wavefield-continuation methods handle multipathing naturally in contrast to Kirchhoff methods, focusing and defocusing effects of velocity variations are correctly modeled, antialiasing is handled implicitly, and amplitudes are consistent with the wave equation.

Data parallel wave‐equation datuming with irregular acquisition topography

Seismic data gathered on land is distorted by irregular acquisition topography. Seismic imaging algorithms are generally applied to data which is redatumed to a planar surface. In regions of mild topography where the near surface velocity is much slower than the subsurface velocity, a static shift is adequate for this transformation. However, when the necessary shift increases in magnitude and when the near surface velocity is not much slower than the subsurface velocity, the static approximation becomes inadequate. Under these circumstances static shift distorts the wave field and degrades velocity analysis and imaging. In this case wave equation datuming is more appropriate than static shift.

Robust Illumination Compensation for Shot-Profile Migration

For shot-profile migration, illumination compensation can be achieved if the imaging condition incorporates a deconvolution (division in the frequency domain) of the up-going wavefield by the down-going wavefield. To avoid division by zero, the deconvolution requires the selection of a damping parameter that turns out to be quite difficult to select. Consequently, a cross-correlation of the two wavefields is often selected. Alternatively, the zeros in the spectrum of the down-going wavefield can be filled with an average of the neighboring points. Therefore, instead of dividing by the wavefield, we can divide by a smoothed version of it. Smoothing is robust and easy to parameterize. It also corrects illumination problems in the migrated images.

Integrated reservoir, petrophysical, and seismic simulation of CO2 storage in coal beds

In this paper, we present results of an integrated simulation study to assess the effectiveness of seismic imaging for monitoring CO2 sequestration. We considered two scenarios. In the first, injected CO2 remained confined within a shallow coal formation. In the second, the sequestered CO2 gas leaked through a semi-permeable shale layer to an overlying sand unit sealed above. In both scenarios, the CO2 injection process resulted in enhanced production of coal-bed methane. The reservoir and seismic simulations required the construction of 3D geologic and facies models, the estimations of seismic velocities based on rock physics correlations, and the development of geostatistical dual-porosity reservoir descriptions of the coal and overlying shale and sand units. We ran the 3D reservoir simulations with GEM 2008.10, an equation-of-state compositional reservoir simulator from Computer Modeling Group with the capability to model adsorption of injected CO2 in coal, desorption of CH4 , and matrix shrinkage-swel...

Which depth imaging method should you use? A road map through the maze of possibilities

Todays explorationist is confronted with a large array of three-dimensional depth imaging options, ranging from a variety of Kirchhoff implementations to a variety of wave-equation implementations. Historically, the choice of a depth migration algorithm was simple: Kirchhoff was the only practical option. This has changed. Advances in computing and clever algorithms have made wave-equation migration an economically feasible alternative. However, so many choices mean that making the right choice of imaging method for a given objective can be a daunting task. In this article we briefly examine the origins of the various imaging methods, describe their relative approximations, and assess their relative merits and applicability.