3-D Prestack Imaging on Massively Parallel Computers
Authors: Lynn W.S. , Perkins Wesley , Cabrera Julian , French W.S. 
Published: October 2008

Abstract
For 3-D pre-stack imaging to be a viable process, computer power must be sufficient to efficiently work with data sizes on the order of one TeraByte (one triltion bytes). Massively parallel computers provide a platform whereby such data volumes can be migrated with reasonable run times. 3-D DMO, 3-D MZO (migration-to-zem offset) and 3-D pre-stack depth migration are computationally intensive algorithms that easily fit into the paradigm of parallel computation. In this paper, we discuss the implementation of these algorithms on a 128-node parallel computer. Run-time speedups for these algorithms, compared with conventional non-parallel computers, are consistently well over an order of magnitude.

Introduction
As an industry, we have been performing iterative 2-D prestack time and depth migrations for the past several years. To date, 3-D pre-stack imaging has not been common practice (if practiced at all). Computer run times have been prohibitively long to even try 3-D pre-stack imaging, except in limited circumstances. In that interpretation is usually requiti to estimate and refine velocity-field information, many iterations of migration processes are needed to converge on an accurate representation of the velocity field. This only exacerbates the long rim-time problem.
Massively parallel computers offer a solution to the heavy demands of 3-D prestack imaging. These algorithms and, indeed, most seismic data-processing algorithms are easily parallelized. In fact, in many cases, algorithm coding is simplifkd because the programmer need not spend as much time coding around machine limitations. To facilitate the writing of seismic-data processing algorithms and simplify their use for processors, we have written a seismic-processing operation system for massively parallel MIMD (multipleinstruction, multiple-data) computer architecture. We are currently using the software in a production environment on a 128-node Intel i860 supercomputer with the following parameters:Peak computational 10 Gflops (at 32-bitpower preeision)Distributed memory 2 GBytesDisk storage 96 GBytesOn-line tape storage 1.5 TBytes
Because the computational power, memory, disk storage, and on-line tape storage are all independently configured using parallel arehiteetum, they can each be expanded indefinitely; and the software contains no hardware limits.
In the following sections, we describe the implementation and the results of two heavy number-crunching algorithms: 3-D MZO and 3-D prestack depth migration.

Migration to Zero Offset
In practice, seismic-reflection data are reeorded using source and receiver pairs that are separated by some distance. In processing, DMO is applied to move recorded data from the source-receiver midpoint to the surface location where a coincident (zero-offset) source-receiver pair would have recorded a reflection from the same subsurface point. For a constant-velocity model, 3-D DMO moves refkxtions along the line connecting the source to the receiver. l%usj N operations are applied to a given input trace where N is the number of desired stacked traces located on a line between the source and receiver.