20 Prestack Kirchhoff Depth Migration on a MIMD Parallel Computer
Authors: Charrette E.E. 
Published: October 2008

ABSTRACT
Two algorithms are presented to perform Kirchhoff2-D pre-stack depth migration on a multiple instruction, multiple data (MIMD) parallel computer. Both algorithms exploit the main advantage of the MIMD architecture, the ability to have each processor execute a unique part of the algorithm concurrently. In the first implementation, one of the processors is reserved for calculating transit times to each point in the image space, while the remaining processors perform the imaging step. This algorithm was efficient on machines with only a few (:s; 32) processors, but inefficient on larger machines. The inefficiency arose because the processor which did the raytracing could not compute the travel times as fast as the remaining nodes performed the imaging. This led to an uneven distribution of work and a performance plateau. The problem was alleviated by assigning more processors to the raytracing task. In the second implementation, the travel time maps were accessed sequentially from the pool of raytracing nodes; On smaller machines (Le. configurations where each imaging node operated on data from several shot points), the second algorithm performed as well as the first. On larger machines, where there might be only one shot point per imaging processor, the second algorithm showed linear speed up until the number of processors exceeded the number of shot points. The second algorithm was tested on a nCUBE 2 parallel computer with 128 computing elements (maximum configuration is 8192 computing elements) and four disks. Using this configura.tion it took less than 2 minutes to read the data from disk (378 shot records, 96 receivers/shot, 2000 samples/traces), perform the migrations (474 × 237 node image space), and output the final image. Performing the same task on a traditional supercomputer would take approximately 15 minutes. The speedup obtained by the parallel implementation makes interactive 2-D pre-stack depth migration a reasonable endeavor.

INTRODUCTION
Seismic migration is the procedure which attempts to convert seismic data recorded at the surface to an accurate picture of the subsurface geology. In regions with complex structure, migration is generally performed either by a finite-difference method (e.g., Claerbout and Doherty, 1972), a Kirchhoff summation method (e.g., Schneider, 1978) or by a Fourier transform method (e.g., Stolt, 1978). Regardless of the implementation, the migrations are most accurate in constant velocity media. In regions with steep dip, the Kirchhoff method yields the best results and is most suitable to pre-stack applications (Lamer and Hatton, 1976). For these reasons, that is the algorithm which will be investigated here.

Time Migration vs Depth Migration
The term depth migration is generally reserved for migration algorithms which transform offset-time sections to offset-depth sections. Until recently, most migration algorithms were time mi. gration procedures. The output of a time migration algorithm is a offset vs migrated time section. The advantage of depth migration over time migration is that it forms a more accurate image in regions with significant lateral velocity variations. Increased accuracy is obtained by properly handling wave phenonema such as refraction. In general, depth migration is five times more computationally intensive than time migration.