Introduction

Three-dimensional seismic reflection data are being acquired on an increasingly routine basis. These data offer the potential for extremely high-resolution 3-D images of subsurface geology and subsequent estimation of earth physical properties (Lumley and Beydoun, 1991). Data sets range in size from a few Gigabytes (Gb) to hundreds of Gb. Wave-equation imaging (migration) of these 3-D prestack data requires on the order of hundreds to tens of thousands of Tflop (10¹⁴ - 10¹⁶ floating point operations). Evidently the computational challenge is both daunting and exciting.

We approach this computational problem by utilizing a Connection Machine. The CM is a massively parallel computer which can perform billions of floating point operations per second (Hillis, 1985). Since January 1991, Thinking Machines Corporation has provided the Stanford Exploration Project with two CM sequencers, each sequencer consisting of 4096 processors and 32 Mb core memory. Our goal was to develop a 3-D prestack time migration algorithm using the CM resources at SEP, which meets or exceeds some minimum requirements for 3-D prestack image processing.

The algorithm we present is efficient for migrating data sets in which the dimensions of the image space are smaller than, or comparable in size to, the prestack migration aperture. In this case, each input trace needs to be summed into every output trace. A more general algorithm would required a different, more complicated strategy for data communication. As we discuss in the next section, the first field data sets we plan to migrate meet the former requirements and can thus be efficiently migrated with our algorithm.

The content of this paper proceeds as follows. First, we review the minimum computational requirements for 3-D prestack time migration in relation to SEP's computing environment. Next, we discuss the geometry of our 3-D Kirchhoff prestack time migration algorithm and give some examples illuminating algorithm structure using the Fortran 90 parallel language. Finally, we present some timings using a 3-D point-diffractor synthetic seismogram example.