波动方程变网格步长有限差分数值模拟

Wave equation numerical modeling by finite difference method with varying grid spacing

(中国石油大学(华东),山东东营257061)

China University of Petroleum (East China), Dongying 257061, China

有限差分算法是常用的正演模拟方法之一，传统的有限差分方法在处理近地表低速层模型或地层中夹有低速、高速层模型时，为了得到较高精度的模拟结果，通常需要减小网格步长，这样既增加了计算时间，又浪费了计算机内存资源。为此，采用具有较好性能的变网格算法来解决这一问题。设计了近地表低速层和地层中夹有低速层两种模型，分别采用传统常网格有限差分算法(大网格步长和小网格步长)和变网格步长有限差分算法对模型进行了数值模拟，并对比了模拟结果。变网格步长有限差分算法不仅提高了模拟结果的分辨率，而且降低了内存需求量，减少了计算时间。此外，变网格算法具有较高的灵活性，可以根据实际情况，综合考虑计算时间、内存需求量和模拟结果的分辨率来优选网格步长。

Finite difference algorithm is one of the conventional forward modeling methods. In order to get accurate simulation results, the grid spacing usually decreases during the processing of near surface low-velocity model or low-/high-velocity interbed model by using traditional finite difference method. However, the processing increases the computation time and wastes the memory resource of computer. Therefore, the varying grid spacing method was adopted to solve the problem. Two models (near surface low-velocity model and low-velocity interbed model) were designed. The traditional finite difference method (including large grid spacing and small grid spacing) and varying grid spacing finite difference method were separately used to simulate the two models. The comparison of the results show that the varying grid spacing finite difference method not only can improve the resolution of simulation and reduce computation time, but it needs small memory as well. Meanwhile, the varying grid spacing method is flexible, which can synthetically consider computation time, memory and resolution of simulation to optimize grid spacing.