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-spectrmn method in isotropic two-phase media

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 Fou- rier transform in space coordinate to calculate the time in time do- main and can avoid computing the partial derivative;2)it can real- ize 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 formu- late 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 co- efficient and porosity on seismic wave propagation discussed.