How much precision do we need in wave-equation based migration?

Robert G. Clapp

bob@sep.stanford.eda

Seismic processing has always been computationally intensive. Data problems are growing in size, there is a continual push for faster processing turn around times, and a need for more sophisticated (computationally demanding) methodologies. As a result the industry is always interested in new technologies that promise significant speedups.

Three technologies that are currently look promising are Floating Point Gate Arrays (FPGAs)He et al. (2004), Graphical Processing Units (GPUs), and the Cell processor. All of these technologies, at least in theory, promise at least an order of magnitude speed up compared to a traditional processor, either today or in the near future. A primary bottleneck with each technology is the time involved in transfering data from main memory, through the processor, to the hardware, and back. There are two different ways to address this problem, a faster interconnect or transfering less data. Currently there is significant work being done to provide a faster interconnect, but these are generally theoretical at this stage and only reduce, but don't eliminate the problem. Therefore it is worth attacking the problem of reducing the amount of data that needs to be transfered.

Donoho and Polzer (1999) discuss methodologies for compressing sesimic data. A more basic approach is to build on the sine-bit recording experienceCochran (1973). It was shown that by just recording whether the earth was moving up or down, a good representation of the earth could be generated Houston and Richard (2004).

In this paper I attempt to test the degradation in image quality of reducing the precsion of a downward continuation based migrationGazdag and Sguazzero (1985) . I show that nearly identical results can be achieved by using 1/4 of the number of bits to describe the input. In addition I demonstrate that the migration result is only marginally affected by reducing the precision within the migration algorithm. I conclude by commenting on what these results mean the viability of FPGAs for migration.