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.