A Fourier integral algorithm and its GPU/CPU collaborative implementation for one-way wave equation migration

Pre-stack one-way wave equation (OWE) is a useful tool for seismic imaging and modeling. Since the idea of OWE appeared in the 1970s, geophysicists have made great effort to improve the accuracy of the one-way wave equation extrapolators. In this paper, we present the idea of solving OWE using the Fourier integral method, which represents OWE as a Fourier integral equation and solves it in dual spaces (both space and wave-number domains). By doing this, we can propagate wave-fields up to nearly 90° angle from the vertical direction in the presence of lateral velocity variations. The proposed method is stable, does not suffer from the numerical dispersion, and overcomes the azimuthal anisotropy problem when extended to three dimensions. The computation cost of the Fourier integral method is too high and was considered impractical for a conventional computer. In this paper, we take advantages of the Graphic Processing Unit (GPU) and use the matrix multiplication technique to accelerate the algorithm. The speedup ratio we obtained is tens of hundreds times so that the method can be applied to a real project for pre-stack depth imaging.