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The above outlined algorithm is implemented on the Connection Machine.
Finitedifferences algorithms are very well suited to
massively parallel
computers, since the computational grid exactly maps onto the
layout of processors.
I found that my code ran at about 113 Mflops on a 4K machine.
The algorithm could be much faster, if it were not for the boundary conditions,
which are used to prevent reflections from the side and bottom boundaries.
Using a oneway wave equation with absorbing boundaries necessitates the use of
different finitedifference stencils in the interior and at various locations
at the boundary.
domains
Figure 2 The computational domain in this implementation is divided into three parts: interior, exponentialdamping boundary and oneway wave equation absorbing boundaries. In each of those domains different finite difference operators can vary in form domain to domain. An elegant solution is to have a superstencil, so that the same stencil can be used in all domains. This implies some computational overhead and increased memory use.

 
If the memory of the machine is big enough, an efficient implementation
is possible, where spatially variable finitedifference coefficients are used.
The shape of the stencil is constant over the entire grid.
Using the SEP machine, which has small memory, I could not apply this elegant
approach efficiently, since I would have had to
truncate my problem size unrealistically.
I really liked to use the Connection Machine as a movie program, seeing
wave propagation snapshots as they are calculated. This instant
feedback makes the machine useful as a teaching tool.
Zxseis
Figure 3 Shot gather generated by a vertical source and horizontal inline receiver.
Zzseis
Figure 4 Shot gather generated by a vertical source and vertical receiver.
Xxseis
Figure 5 Shot gather generated by a horizontal inline source and a horizontal inline receiver.
Xzseis
Figure 6 Shot gather generated by a horizontal inline source and a vertical receiver.
zimagestack
Figure 7 Elastic stiffnesses imaged using 16 shots. Source vector was vertical.
ximagestack
Figure 8 Elastic stiffnesses imaged using 16 shots. Source vector was vertical.
Next: Conclusions
Up: Karrenbach: Prestack reversetime migration
Previous: SYNTHETIC EXAMPLE WITH TRANSVERSE
Stanford Exploration Project
12/18/1997