The computational problem we are attacking is the prestack time migration of a 3-D seismic reflection data set to produce 3-D images of subsurface geology. We will use the dimensions of a Unocal 3-D survey as an example of the minimum computational requirements. One of us (David) hopes to get a suitable 3-D data set at SEP for a 3-D seismic reservoir characterization project (Lumley, 1991). Whether we obtain the Unocal data or not, using it as a real example to compute minimum requirements is a worthwhile exercise.
The Unocal data consists of 390 shot gathers, 480 traces per shot, of which we are interested in about 3000 samples per trace. This represents a data volume of about 2.25 Gb per 3-D data set. The 3-D volume we wish to image needs to be a reasonable minimum of about 64 by 64 surface positions, by about 1024 pseudodepth (vertical traveltime) samples. This image volume represents about 4 million voxels, or 16 Mb. Using an estimate of 65 floating point operations (flop) per image voxel per trace (the amount required in our algorithm to calculate the migration traveltimes, amplitudes, linearly interpolate trace values, weight and sum into the migration image), a single 3-D prestack time migration of the Unocal data requires a minimum of about 50 Tflop ( floating point operations). This would require a minimum of 60 cpu days on a 10 Mflop/s workstation such as an IBM RS/6000, 30 cpu days on a 20 Mflop/s mini-supercomputer such as a Convex C-2, or 6 cpu days minimum on a 100 Mflop/s supercomputer. Our CM code runs at about 400 Mflop/s on our 8k cpu machine, suggesting a minimum time of about 1.5 cpu days to do a single 3-D prestack migration at SEP using both sequencers. Even more exciting is the potential scalability of our code to a full 64k cpu Connection Machine, which would run at over 3 Gflop/s, suggesting a full 3-D prestack time migration of a real, although admittedly small, 3-D data set in just over 4 cpu hours.