地震波数值模拟中的频散压制方法分析

Analysis of dispersion suppression in wave equation numerical simulation

(1.中国石油勘探开发研究院西北分院,甘肃兰州730020;2.中国石油大学(华东)，山东东营257061)

Northwest Branch, Research Institute of Petroleum Exploration and Development, CNPC, Lanzhou 730020, China

波动方程有限差分法正演模拟对认识地震波传播规律和指导地震资料解释等具有重要的意义。但差分算法固有的数值频散在正演模拟中是一种严重的干扰，会降低波场模拟的分辨率。为提高模拟精度，同时又尽可能减少计算量，采用定量分析的方法，对比分析了横纵网格比变化时入射方向和差分精度等因素对数值频散的影响，分析结果表明，矩形网格较之正方形网格能更好地压制频散，同时可以避免高阶差分导致的低计算效率。模型试验表明，该方法切实可行，能较好地适应实际地震勘探中的波场模拟。

Finite-difference simulation of wave equation is very important for understanding the laws of seismic wave propagation and guiding geological interpretation of seismic data. However, inherent numerical dispersion of finite difference algorithm is a serious disturbance in forward modeling, which decreases the resolution of wave field simulation. To improve the simulation accuracy and to make the increment of computation amount the smallest, the quantitative comparison was used to compare the effect of incident direction and difference accuracy on numerical dispersion with the changing of the ratio of horizontal and vertical gird. The results show that the rectangular grid is better than square mesh in suppressing dispersion and can avoid the low computational efficiency caused by high-order difference. The model test results indicate that this method is feasible and suitable for wave field numerical simulation in practical seismic exploration.