双相各向同性介质伪谱法地震波场数值模拟

Numerical simulation of seismic wave field by pseudo-spectrum method in isotropic two-phase media

(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)地球资源与信息学院，山东东营 257061)

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

伪谱法是一种模拟精度和计算效率都较高的地震波场数值模拟方法。该方法通过对空间坐标的快速傅里叶变换实现数值计算，在时间域直接采用差分运算代替导数的求解，避免了求偏导数；不存在有限差分和有限元等方法对高频成分限制的问题，可以实现全频带地震波场模拟；对内存容量的需求远远低于有限元法。利用伪谱法实现双相各向同性介质地震波场数值模拟的基本原理是：首先基于Biot模型给出双相各向同性介质弹性波波动方程；然后推导出二维双相各向同性介质的伪谱法计算公式；最后对给定的介质模型进行模拟试算。模拟结果表明，弹性波在双相各向同性介质中以快纵波、横波和慢纵波3种方式传播。基于模拟结果，分析了各类波的传播规律，讨论了耗散系数和孔隙度对地震波传播的影响。

Pseudo spectral method has high simulating accuracy and high computational efficiency. Compared to finite difference method and finite element method, it has such advantages: 1) it uses fast Fourier transform in space coordinate to calculate the time in time domain and can avoid computing the partial derivative; 2) it can realize complete frequency band seismic wave simulation without any limitation by finite difference method and finite element method on high frequency component; and 3) it has a lower dispersion and needs only a small memory requirements. So the pseudo spectral method has been used in the wave field simulation of isotropic two-phase media. Firstly, elastic wave equation of isotropic two-phase media was given based on Biot model. Then, the iterative formulate of pseudo spectral method was derived for 2-D isotropic two-phase media. Finally, the wave field simulation for the given media model was realized. Simulation results show that the elastic wave propagates in fast P-wave, S-wave, and slow P-wave in isotropic two-phase media. Based on simulation results, the propagation laws of various wave was analyzed and the effect of dissipation coefficient and porosity on seismic wave propagation discussed.