Wave equation and numerical simulation for qP wave in VTI media with modified acoustic approximation
In anisotropic media,qP and qS waves are usually coupled to propagate together.The decoupling of qP and qS waves is an important part of the theoretical study of seismic wave propagation.The classic acoustic approximation decouples the qP wavefield by setting the vertical velocity VS0 of qSV wave as zero,but there are problems such as degraded qSV waves.In this paper,the acoustic approximation was modified by considering the VS0 as a function of the wave numbers kx,kzand the anisotropy parametersε,δ,and the dispersion relation and wave equation for qP wave in VTI media with the modified acoustic approximation were then derived.This wave equation for qP wave,containing elliptic terms and non-elliptic terms,was solved by using the hybrid finite difference/pseudo spectral method:the finite difference method for solving the elliptic terms and the pseudo spectral method for solving the non-elliptic terms.The dispersion analysis and numerical examples show that the qP wave equation with the modified acoustic approximation as a pure qP wave equation without any degenerate qSV wave is in good agreement with the simulation results of the elastic wave equation and has high accuracy.It is stable in VTI media with bothε≥δandε＜δ,and more accurate than the simulated results with the acoustic approximation.
modified acoustic approximationwave equationpure qP wavehybrid finite-difference/pseudo-spectral methodVTI media
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维普
