Stable optimization of finite-difference operators for seismic wave modeling

The finite difference scheme is now widely used in the reverse time migration and full waveform inversion. Their results are dependent on the accuracy of finite difference operators. In this paper, we combine the cosine function with the original window function to construct a new window function, in order to obtain higher precision finite difference operators. The absolute error curves of the optimized finite difference operators are close to zero for low wavenumbers. In other words, we do not observe an oscillating curve of absolute errors produced by other optimized methods. In order to overcome the limitations of a single graphics processing unit (GPU), we developed the multiple-GPU method for the elastic wave equation. Numerical experimental results show that our new window function can control the numerical dispersion better than the binomial window and scaled binomial window, and the multiple-GPU computation is very stable.