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.

有限差分方案现已广泛用于反向时间偏移和全波形反演中。他们的结果取决于有限差分算子的精度。在本文中，我们将余弦函数与原始窗口函数相结合，以构造一个新的窗口函数，以获得更高的精度有限差分算子。对于低波数，优化的有限差分算子的绝对误差曲线接近于零。换句话说，我们没有观察到其他优化方法产生的绝对误差的振荡曲线。为了克服单个图形处理单元（GPU）的局限性，我们针对弹性波方程开发了多GPU方法。