三维各向同性介质弹性波方程交错网格高阶有限差分法模拟

Numerical simulation of elastic wave equation in 3-D isotrop-ic media with staggered-grid high-order difference method

石油大学CNPC物探重点实验室,北京 100083

CNPC Key Lab of Geophysical Exploration, China University of Petroleum, Beijing 100083, China

给出了三维各向同性介质中一阶应力-速度弹性波方程交错网格任意偶数阶精度有限差分格式,推导出了三维各向同性弹性介质完全匹配层吸收边界条件公式和相应的交错网格高阶有限差分格式。对三维French 模型进行了弹性波模拟,结果表明,该方法模拟精度高,边界吸收效果好。在三维French模型的xoz平面和yoz 平面的弹性波场快照中可以见到断面反射波、侧面反射波和散射波等波场特征。多次侧面反射波和多次散射波说明不同三维构造所形成的波场是相互影响的。

The problems in complex area can be effectively solved by the elastic wave exploration. The characteristics of wave fields and propagation of elastic wave in complex media can be studied using 3-D numerical modeling. The paper presents a staggered-grid any even-order accurate finite-difference scheme of first-order stress-velocity elastic wave equation and its stability condition in 3-D isotropic media, derives a perfectly matched absorbing layer (PML) boundary condition and its staggered-grid high-order accurate difference scheme in 3-D elastic media The results of numerical modeling for 3-D French's model indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The elastic wave fields from different 3-D structure are interacted, which can be proved by the multiple reflected waves related side face of two coves and multiple scattered waves of two coves.