Lebedev网格与标准交错网格耦合机制下的复杂各向异性正演模拟

Numerical simulation with coupling Lebedev and standard staggered grid schemes for complex anisotropic media

针对复杂各向异性介质,采用Lebedev网格与标准交错网格耦合的有限差分数值模拟算法,在对称性较低的各向异性介质(如具有倾斜对称轴的TI介质,单斜各向异性介质等)区域使用Lebedev网格,而在其他区域则选用标准交错网格,既避免了标准交错网格在模拟各向异性介质时波场插值带来的误差,又降低了Lebedev网格在内存和计算量上的消耗。在此基础上,还推导了该算法耦合区域内的高阶差分格式,采用新的变量插值方法,使得在较大空间采样间隔下,耦合机制过渡区域产生的虚假反射误差及全局误差仍能得到很好的控制,使用内存更是呈几何倍数降低,计算时间也随之减少,从而能高效、精确地模拟地震波在非均匀各向异性介质中的传播特征。

This paper adopts the finite-difference(FD) forward modeling algorithm with coupled Lebedev and standard staggered grid schemes for complex anisotropic media,which means that the Lebedev grid is used only inside the media with lower symmetry(such as TI media with titled symmetry axis,monoclinic anisotropy),while the standard staggered grid is used in other regions.This algorithm avoids the errors introduced by wavefield interpolation of standard staggered grid scheme and reduces the consuming on memory and computation of Lebedev scheme.On this basis,we present the high-order FD relations in the transitional region of the coupled scheme and a new method for interpolating variables.This high-order coupled scheme could efficiently control the reflection error and overall error produced by different types of wave incident to the coupling interface even with big space sampling interval.At the same time,it provides a geometric savings in memory and the computation time decreases as well,thereby simulating the peculiarities of the wavefield in heterogeneous anisotropic media with high efficiency and accuracy.