Matthew A. Brzostowski

3-D tomographic imaging of near‐surface seismic velocity and attenuation

As a result of the similarity between velocity and attenuation imaging, we have implemented both using the same 3-D tomography software, with simple variable changes. The resulting sets of linear equations are solved by the Simultaneous Iterative Reconstruction Technique (SIRT). The algorithm is applied to 3-D estimation of near‐surface velocity and attenuation distributions from 3-D surface‐survey field data from the Ouachita frontal thrust zone in southeastern Oklahoma; the images obtained correlate well with the known surface geology. Resolution analysis by computation of point spread functions indicates highest resolution in the direction parallel to the densest distribution of survey points (the receiver lines).

Systematics of time-migration errors

Even if the correct velocity is used, time migration mispositions events whenever the velocity changes laterally. These errors increase with lateral velocity variation, depth of burial, and dip angle θ. Our analyses of two model types, one with an implicit gradient and one with an explicit gradient, yield simple “rules of thumb” for these errors to first order in the lateral gradient. The x error is A(1+3tan2θ), and the z error is -2Atan3, where the quantity A = A(x, z) contains the information about depth of burial and magnitude of lateral gradient. These rules can be used to determine when depth migration is needed. Further analysis also shows that the image‐ray correction to time migration is accurate only at small dip. For dipping events, the image‐ray correction must be supplemented by a shift in x of the form 3Atan2θ and a shift in z given by -2Atan3θ. These time‐migration corrections take the same form for both the models we have studied, suggesting a general scheme for correcting time migration, w...

Archiving the Apollo active seismic data

The Apollo missions included several scientific experiments on the Moon, some of which were dedicated to seismic exploration. The seismic experiments consisted of both passive and active instruments. The passive seismic data were initially analyzed and studied by a group of scientists from Columbia University, the University of Texas, MIT, and the University of Hawaii, and led by Garry Latham. Yosio Nakamura (University of Texas), a member of that group and a leading authority on the internal structure of the Moon and moonquakes, has continued to study those data. Besides measuring natural seismic activities in the Moons interior, the passive data also recorded man-made impacts such as the S-IVB (third stage of the Saturn launch vehicle) and LM (lunar module) crashing into the surface. The active seismic experiment included the use of three different sources fired either while the astronauts were on the Moon or remotely after they had departed. The active data were studied by a group headed by Robert Kov...

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...

Converted-Wave Prestack Depth Migration of North Sea Salt Domes

We show the benefit of not only imaging salt dome flanks with pre-stack depth migration but with converted-wave pre-stack depth migration.

Efficient one-pass 3-D time migration

An efficient one‐pass 3-D time migration algorithm is introduced as an alternative to Ristow’s splitting approach. This algorithm extends Black and Leong’s ky‐separation approach with a time‐dependent Stolt stretch operation called dilation. Migration using ky dilation consists of a single pass over the 3-D data volume after ky slices are formed with each ky slice downward continued independently. A number of downward continuation algorithms based upon the 3-D wave equation may be used. Dilation accommodates any lateral variations in velocity before the 3-D data volume is decomposed into ky slices via a Fourier transform. An inverse dilation operation is performed after the downward‐continuation operation and after the data volume have been inverse Fourier transformed subsequently along the ky direction. Migration using the ky‐dilation approach yields a one‐pass 3-D time migration algorithm that is practical and efficient where the medium velocity is smoothly varying.

Efficient one‐pass 3‐D depth migration

We introduce an efficient one-pass 3-D depth migration algorithm as an alternative to the spli t t ing approach (Claerbout, 1985). This algorithm extends the k separation approach (Black and Leong, 1987) with a time-dependent modifying operation we call dilation. Dilation in conjunction with parallel operations of downward continuation on the k slices yields a depth migration Y algorithm with better efficiency and accuracy characteristics than the splitting approach. k -dilation migration c o n s i s t s o f a Y single pass over the 3-D data volume with each k slice downward continued independently. Y Any downward-continuation algorithm based upon the 3-D wave equation may be used. Before the 3-D data volume is decomposed, the lateral velocity variations are accomodated with dilation. Dilation is a time-dependent modifying operation which transforms a time and spatially-variant velocity field into a time-variant velocity field only. The reverse operation is conducted after the migration and inverse k transformation. Analytic, model Y and field data studies indicate that migration us ing k separation in conjunction with Y dilation is a viable means of performing depth migration.

An introduction to this special section—migration

The last special section on migration (December 2002) contained numerous examples that demonstrated the flexibility and robustness of the Kirchhoff method, including some enhancements to better preserve amplitudes and handle very steep dips. At that time, wave-equation migration was in its infancy and data usually had to be decimated to keep processing costs down. However, during the last two years, the clustering of high-speed, Linux-based computers and the development of clever algorithms have made wave-equation migration a more feasible option. For decades, geophysicists have known that wave-equation migration is a better solution than Kirchhoff since it can address the propagation of the wavefield recursively in depth over an incremental step and, thus, generally yields better subsurface images. However, a major drawback of early wave-equation-migration algorithms was their inability to generate angle gathers for residual moveout information and velocity model updates. Not anymore. As this special sec...

Schiehallion: A 3‐D time ‐ lapse processing case history

We present the results of comparing two vintage streamer surveys over the Schiehallion field, west of the Shetland Isles. The objective of the study was to determine the detectability threshold for towed streamer time-lapse 3-D data since there had been no production from the field between the two surveys. The primary area of concern was whether we could reprocess both surveys and then produce a meaningful difference volume. Meaningful in this case means that the difference amplitudes would be diagnostic of reservoir changes and not differences arising from changes in the acquisition scheme or processing methodology. This is a particularly challenging task when dealing with streamer data. Our results indicate that we can process streamer data and generate difference volumes 20 db below the original survey amplitudes.

Parallel geophysical processing

The use of massively parallel processors (MPP) systems is becoming more widespread in the seismic industry as it begins to take advantage of their strength in solving data processing problems. Today it is common for 3-D prestack depth migration and other computer or I/O intensive processes to be run on such platforms. This paper outlines how we have adapted to MPP in order to run our seismic processing algorithms as efficiently as possible.