Elastic Wave Forward Modeling Based On Fourier Finite Difference

Numerical simulation of seismic wavefield is an important mean to study the propagation law of seismic wavefield in the earth media.The Fourier finite difference(FFD)method based on acoustic approximation is not enough to illustrate the propagation law of seismic wavefield in the earth media.Thus,numerical simulation of seismic wavefield based on elastic approximation has important theoretical meanings and value.This paper extends acoustic FFD method to elastic equations and builds the FFD method based on elastic equations.In the first,this paper builds the decoupled 2-order elastic displacement equations based on wavefield decomposition.Then the FFD method based on decoupled 2-order elastic displacement equations are obtained.Thirdly,more derivation is applied to the decoupled 2-order elastic equations in order to obtain the wavenumber-space domain extrapolation method based on the decoupled 1-order elastic equations.In the last,combining finite difference method(FDM)with Fourier Transform to build the FFD method based on decoupled 1-order elastic velocity-stress equations,which is fit for density-varying media.In terms of spatial accuracy,the FFD method based on decoupled 1-order elastic velocitystress equations built in this paper is a kind of spectrum method and has high spatial accuracy.Regarding time accuracy of numerical simulation,the wavenumber-space operators can compensate the error caused by the 2-order time difference by combing media parameters with simulation parameters and can improve the time accuracy.Results of numerical simulation indicate that the FFD method based on decoupled 1-order elastic velocity-stress equations is fit for complicated media.