横向各向同性介质优化差分系数法地震波场数值模拟

Optimized difference coefficient method seismic wave field numerical simulation in vertical transverse isotropic medium

在应用有限差分法地震波场数值模拟过程中,数值频散是关键问题之一。为压制地震波场模拟中的数值频散,针对1阶速度—应力方程的交错网格空间离散差分算子,本文分别引入强约束条件和弱约束条件,构造了不同的Lagrange函数;然后通过求取条件极值得到优化差分算子。将其应用于横向各向同性(VTI)介质波场数值模拟,结果表明采用优化空间差分算子能有效压制数值频散,并可提高差分近似导数的精度。

In applying finite difference seismic wave field numerical simulation, the numerical dispersion is one of key issues. In order to suppress numerical dispersion in seismic wave field simulation the difference operator was discreted in staggered grid space of one-order velocity-stress equation, in this paper strong constraint condition and weak constraint condition were introduced, different Lagrange functions were constructed respectively, then optimized difference operator was obtained through estimation of conditional extremum. The optimized difference operator was applied to wave field numerical simulation in vertical transverse isotropic medium, the results show that the application of optimized space difference factor could effectively suppress numerical dispersion, and raise the accuracy of difference approximate derivative.