Finite Difference Seismic Modeling on the Connection Machine
Authors: McCowan D.W. 
Published: October 2008

ABSTRACT
References and figures at end of paper. It appears that, short of superconductivity, digital engineers are very close to the ultimate computational speeds that are possible with single processors. All new supercomputers have resorted, each to a different degree, to breaking up the computational sequence into parallel components. Parallel processing, therefore, appears likely to be with us for some time. The purpose of this paper is to show how recent progress in numerical analysis has made processing seismic data on a Massively-Parallel Computer (MPC) possible. Seismic computing's natural divisibility into small pieces and its localized communication pattern give strong impetus toward performing it on massively-parallel SIMD computer architecture. It is true that we will have to modify or scrap some of our traditional algorithms in favor of new ones in order to reap the full benefit of the parallel computer but this is already happening in some laboratories. The net result of this research will be dramatic speedups and consequent cost reduction in our processing centers.
It appears that, short of superconductivity, digital engineers are very close to the ultimate computational speeds that are possible with single processors. Vector computers, whose architecture is based on pipelining, proved to be only an interim solution. They were, in fact, just a more efficient utilization of a single processor. All new supercomputers have resorted, each to a different degree, to breaking up the computational sequence into parallel components. This runs the spectrum from a few processors as in the CRAY Y-MP series, through hundreds of processors in the NCUBE machine to thousands in the Thinking Machines Corp. (TMC) CM2 machine. Parallel processing, therefore, appears likely to be with us for sometime.
The common parallel architecture machines fall into three major categories: Tightly-Coupled (e.g., CRAY), Multiple Instl1lction Multiple Data (e.g., NCUBE), and Single Instruction Multiple Data (e.g., TMC). The historical progression of supercomputer development has been in this order. In other words, practical Tightly-Coupled machines came into use first followed by MIMD and lastly by SIMD. There is a growing body of lore in the seismic data processing industry as to the relative benefits of these different architectures. Selection criteria include speed, ease of coding, and, of course, cost. There is a fourth, somewhat amorphous criterion: applicability. Some algorithms are "naturals" for certain computer architectures and contrary wise. Because parallel supercomputer architectures evolve, the algorithms that run on them must also evolve. In fact, the numerical mathematical literature is filled with new algorithms for new architectures. The purpose of this paper is to show how recent progress in numerical analysis has made processing seismic data on a Massively-Parallel Computer (MPC) possible.
11le TMC model CM2 connection Machine is an example of a MPC with 64K possible processors. Based on SIMD architecture, its processors either execute the same instruction or remain idle.