Three-dimensional wave equation computations on vector computers

There are now several laboratories worldwide which routinely perform three-dimensional (3D) physical modeling of acoustic phenomena of interest to seismologists. Corresponding computerized mathematical models have been limited to two dimensions on conventional computers due to the immense computational requirements of accurate full-size problems. The introduction of high-performance vector processors in the 100 + MFLOP range has at last made 3D computerized models a practical reality. Several major oil companies and large seismic contractors have installed such processors and are contributing to research and development in this area as an improved tool in the search for fossil energy sources. We now have such models and we have some limited experience in using them, however, much more work is required before these mathematical models can routinely supplant the physical ones. Here we describe one such model which was developed for the Cyber 205. A two-dimensional (2D) model for the VAX-11 with FP5-100 Array Processors was modified to three dimensions and vectorized suitably for the larger system. We state the acoustic wave problem in mathematical form and present the algorithm used for its solution. We then review the theoretical justification for selecting this particular algorithm. We also discuss the most important technical aspects of implementing the algorithm in vector form on the Cyber system. We present typical output and finally we give timing results for several model sizes, both 2D and 3D, on the Cyber 205 and 2D on the VAX-11 with FPS-100 Array Processors.