各向异性介质中三分量地震记录的FCT有限差分模拟

FCT finite difference modeling of three-component seismic records in anisotropic medium

基于声波或弹性波方程的有限差分方法是数值模拟地震波场或合成VSP地震记录的有力工具。然而传统的有限差分方法在每一波长内采样太少时，会存在严重的数值频微，降低数位结果的分辨率。本文将流体动力学方法中的通量校正传输技术（FCT）与求解各向异性波动方程组的有限差分方法结合，获得了一种适用于求解各向异性介质中二阶声波和弹性波方程的FCT有限差分算法，有效地压制了传统有限差分数值模拟中的数值频微。横向各向同性介质中的波场快照和VSP三分量地震记录合成均表明这种FCT技术和有限差分法的结合不仅能消除粗网格条件下数值频微而引起的伪波动，而且还能有效地压制大梯度变化、间断等所引起的数位解的不稳定。

The finite difference methods based on acoustic or elastic wave equation are very useful tools for wave-field numerical modeling or VSP data synthesizing. However,usual finite difference methods for solving these equations cause severe numerical dispersion to reduce the resolution of resultant wave field when insufficient samplings are taken in one wavelength- FCT finite difference method for easy solving the second-order acoustic and elastic wave equations in anisotropic medium has been formed by combining the flux-corrected transport (FCT) technique in hydrodynamics with the finite difference method that is used to solve wave equation system in anisotropic medium j and it suppresses effectively the numerical dispersion which occurs in usual finite-difference numerical modeling. The wave field snapshotand three-component VSP data synthesizing in transversely isotropic medium show that the good combination of FCT technique with finite difference method can eliminate the false ripples due to numerical dispersion in coarse grid,and suppress satisfactorily the numerical solution unstability caused by big gradient change,discontinuity and so on.