PRACTICAL ISSUES FOR THE CONNECTION MACHINE

The above outlined algorithm is implemented on the Connection Machine. Finite-differences 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 one-way wave equation with absorbing boundaries necessitates the use of different finite-difference 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, exponential-damping boundary and one-way 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 super-stencil, 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 finite-difference 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.

 

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Figure 8 Elastic stiffnesses imaged using 16 shots. Source vector was vertical.