双相各向同性介质伪谱法地震波场数值模拟

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.

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

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.