James L. Black

True-amplitude imaging and dip moveout

True‐amplitude seismic imaging produces a three dimensional (3-D) migrated section in which the peak amplitude of each migrated event is proportional to the reflectivity. For a constant‐velocity medium, the standard imaging sequence consisting of spherical‐divergence correction, normal moveout (NMO), dip moveout (DMO), and zero‐offset migration produces a true‐amplitude image if the DMO step is done correctly. There are two equivalent ways to derive the correct amplitude‐preserving DMO. The first is to improve upon Hale’s derivation of F-K DMO by taking the reflection‐point smear properly into account. This yields a new Jacobian that simply replaces the Jacobian in Hale’s method. The second way is to calibrate the filter that appears in integral DMO so as to preserve the amplitude of an arbitrary 3-D dipping reflector. This latter method is based upon the 3-D acoustic wave equation with constant velocity. The resulting filter amounts to a simple modification of existing integral algorithms. The new F-K an...

Effect of Irregular Sampling On Prestack DMO

The theoretical derivation of most DMO algorithms assumes a uniform midpoint distribution for each common-offset, common-azimuth set of traces, Deviation from uniformity leads to artifacts similar to those caused by missing traces in post-stack migration. Despite the fact that many 3-D geometries do not satisfy these assumptions, good stacked sections are often produced by DMO because of the attenuation of artifacts that takes place in the stacking process. Applying DMO in a full prestack mode offers the advantage of improved velocity analysis, but artifacts caused by irregularities in the offset, midpoint, and source-receiver azimuth distributions can cause problems. A practical extension of the DMO algorithm can be used to approximately correct these artifacts and to predict the reliability of the output traces prior to stacking them.

Frequency dispersion in finite‐difference migration

We introduce a practical measure that predicts the frequency dispersion in implicit time‐domain finite‐difference migration. This measure of dispersion can be readily computed as a function of velocity, dip, and the sampling parameters (depth interval, time interval, trace interval). One result of this analysis is that smaller sampling intervals can often lead to poorer results by an unbalancing of canceling errors. Another result is that, even if the errors are kept in balance for one event, it is not possible to minimize simultaneously the dispersion for all events, since many different dips and velocities occur on a typical seismic section. We also extend the computation of the dispersion measure to include cascaded finite‐difference migration. Cascading does not reduce the magnitude of wavelet dispersion, but it does make the control of dispersion easier because it avoids the problem of choosing parameters in the presence of multivalued velocity. We calibrate and confirm our theoretical dispersion mea...

Networked parallel 3‐D depth migration

Powerful RISC-based workstations, capable of sustaining 10 MFLOPS or more on seismic algorithms, offer a new way of performing 3-D seismic computations. The algorithms are executed on a loosely-coupled set of workstations connected by a network to a large-capacity computer that manages the seismic data volume and participates in the computation. Such configurations already exist in many organizations. The main inhibitor to harnessing this power is lack of an adequate analysis of the issues involved in modifying seismic software to execute robustly and efficiently across a network. Such an analysis is the purpose of this paper. One-pass 3-D finite-difference depth migration has been chosen as a test case for network parallel computing because it involves handling of very large (several Gbytel datasets with challenging communication patterns. A standard version of this algorithm has been developed, analyzed, and tested under several parallel execution environments, Linda* and Express’ . including Network A special notation has been developed to make the analysis more transparent. The analysis technique is applicable to other coarse-grained MIMD computations.

Limitations of Steep-Dip Migration

We quantify the positioning errors associated with time migration followed by image-ray depth conversion. We estimate these errors through an analysis of a dipping layer beneath a laterally varying velocity field. Our analysis shows that the errors become appreciable as the dip increases, even if the velocity gradient is moderate. We derive simple rules-of-thumb that indicate when a steep-dip depth migration is preferable to time migration followed by image-ray correction. We support our theoretical work with synthetic and field data examples.

Practical, scalable, modern 3-D seismic processing

Seismic data processing transforms a large amount (often terabytes) of surface collected data into an accurate image of the subsurface. The key components are wavelet processing (e.g. noise attenuation, deconvolution, multiple attenuation) and imaging.

Prestack remedial migration kinematics

time migration mispositions events when the velocity changes laterally. These errors increase with lateral velocity variation, depth of burial, and dip angle 8. Previous analyses of zeroo&set time migration on several model types have yielded simple universal “rules of thumb” for these errors to first order in the lateral gradient. I have now extended the analysis to preslach time migration and have obtained surprisingly simple results on a model with constant lateral velocity gradient, V(Z) = u(z,,,)t G.(z -z,,,). The + error is 3AtanzB+3A(h/.z,,,)~, and the L error is -2A tan3 8, where A( z, z) contains the information about depth of burial and magnitude of lateral gradient. These rules can be used to determine when prestack depth migration is needed. More interestingly, these equations define a correction technique called “preatack remedial migration.” Remedial migration transforms a time-migrated image into a depth migrated image at the same velocity, o(z, y, s). Thus my analysis is the first step in extending remedial migration to the prestack domain.