非均匀TI介质P-SV波传播交错网格高阶有限差分数值模拟

High-order Staggered-grid Finite Difference Numerical Modeling for P-SV Wave Propagation in Heterogeneous Transversely Isotropic Media

摘要:

给出了在非均匀横向各向同性(TI)介质情况下,四阶时间精度、高阶空间精度的一阶速度-应力P-SV波的波动方程交错网格有限差分解法。首先根据一阶速度(应力)波动方程把速度(应力)对时间的一阶和三阶导数转换为应力(速度)对空间的导数,从而在使用四阶时间精度有限差分格式计算某一时刻的波场时只需要前面两个时间步的波场值;然后在空间上采用高阶有限差分格式以提高数值模拟的精度。数值模拟结果和实测垂直地震剖面(VSP)记录符合得很好,说明该方法是可行的。

Abstract:

A set of stagger-grid finite-difference operations with 4-order temporal accuracy and high order spatial accuracy to one-order velocity--stress P-SV wave equations is presented in heterogeneous transversely isotropic （TI） media. First using the one-order velocity--stress P-SV wave equations, the first and third order temporal derivatives of particle velocity/stress are transformed into spatial derivatives of stress/particle velocity, thus only two former time-step wave fields are needed to compute wave fields for the current time step with the 4-order temporal accuracy finite-differente approximation. Then the high-order spatial finite-difference approximation is used to improve numerical modeling precise. High consistency between the modeling vertical seismic profiles （VSP） records and the field ones demonstrates well feasibility of the present technique.