INTRODUCTION

Modeling algorithms in the frequency-wavenumber domain are special candidates for implementation on parallel computers as the frequency components are independent, allowing the computations to be done in parallel in surface coordinates. The three dimensional case offers a perfect mapping on the parallel computer memory, by storing the data in a serial fashion along the time dimension and in parallel on different processors in the surface coordinates. After Fourier transforming the data along the time axis, we can process each frequency independently, a slice at a time.

I selected two Fourier domain modeling algorithms which handle lateral velocity variations. The modeling algorithms are the conjugate transpose of the migration algorithms (Claerbout, 1992). The Phase Shift Plus Interpolation migration algorithm was presented by Gazdag and Sguazerro (1984) and the Split-step Fourier migration was presented by Stoffa et al. (1990). The two algorithms are extremely similar, and the three dimensional extension of the two dimensional version is quick and painless. I coded the modeling algorithms by transposing and conjugating the migration algorithms that I had at hand (Popovici, 1991). I wrote the parallel FORTRAN 90 version of the code to run on the Connection Machine. I compared the modeling results of the two programs on 2-D and 3-D synthetic models.