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Seismic modeling represents a difficult numerical challenge and consumes a significant amount of CPU time on the largest available supercomputers. With the advent of massively-parallel supercomputers, there is a possibility of drastically reducing the execution time for some of these codes. Many of the algorithms used in seismic modeling use explicit numerical methods on regular structured grids. Because of the regularity of the interconnections and the locality of the calculations, those types of problems usually map well onto massively parallel computers. In this paper the acoustic wave equation with sponge boundary conditions will be used as an example to show how to map and optimize an explicit finite difference algorithm onto a massively parallel machine. This algorithm is part of a seismic modeling code developed jointly by Mobil Research and Thinking Machines to run on a CM-2 connection machine. This program achieved a sustained performance of 14.1 billion numerical operations per second (14.1 Gigaflops) including I/O on a 65536 processor CM-2 supercomputer. To obtain this floating point rate the stencil compiler was used. This compiler implements several levels of optimization to maximize the number of useful foaling point operations. This is done by removing bottlenecks and overheads that tend to degrade the flop rate. The stencil compiler optimizations include speedups in interprocessor grid communications. a more efficient use of the floating point unit, instruction sequencer and memory interface. In recognition of this performance, this -work was awarded the 1989 Gordon Bell Prize in the performance category and received an Honorable Mention in the 1990 competition. This yearly prize is given by the editors of IEEE Software Magazine in recognition of "outstanding achievements in the application of parallel processing to scientific and engineering problems" with the winning entry "running faster than any other comparable engineering or scientific applicat- ion".