Research On High-order Finite Difference Forward Modeling Method Of QP Wave Equation In HTI Media

The underground medium is anisotropic.In theory,the HTI medium model is used to replace the extensively dilatable medium caused by vertical cracks.This paper deeply researches the high-order finite-difference forward modeling method of scalar wave in HTI medium,deduces the equation expression of qP wave integration in HTI medium,researches the split perfect matching layer absorption boundary condition suitable for the integral equation of HTI medium,and establishes the wave equation of qP wave in HTI medium.In this paper,a high-order finite difference numerical algorithm for the qP wave wave equation in HTI media is established,and the stability and dispersion relationship of the equation are analyzed,and the forward operator and post-stack forward operator of the HTI media one-way wave split step method common shot point record are studied.According to the three basic equations of generalized Hookes law,geometric equation and differential equation of motion,the elastic wave equation of HTI medium is derived.Establish and solve the Christoffel equation to obtain the coupled wave equation of the HTI medium with P-wave and S-wave.Then the coupling equations are decoupled and combined with the Alkhalifah acoustic approximation hypothesis to obtain the qP wave approximation equation of the HTI medium.Perform second-order time integration of the approximate equation to obtain the equation after the integral processing of the qP wave in the HTI medium,which can directly eliminate the slow shear wave interference in the anisotropic medium.A high-order finite difference scheme suitable for the post-integral equation of HTI media is derived,and the stability analysis and dispersion analysis of the discrete equation are carried out.A variety of model examples are used to study the propagation law of qP waves in HTI media,and the correctness of the method in this paper is verified by migration imaging.Starting from the firstorder CPML absorbing boundary,the fourth-order CPML absorbing boundary conditions suitable for the integral equation of HTI media are derived.The layered model is numerically simulated,and the absorption effect and calculation efficiency of the split fully matched layer(SPML)absorption boundary and the CPML absorption boundary are compared.The results show that the absorption effect of CPML is better and the calculation speed is faster.The one-way wave equation can avoid the interference of multiple waves,the calculation efficiency is high,and get the composite record with high signal-to-noise ratio can be obtained.The split-step Fourier(SSF)method is a commonly used one-way wavefield continuation method.It has the advantages of fast calculation speed and ability to deal with the lateral velocity changes of the target medium.This paper derives the one-way wave operator for isotropic media,and then starting from the HTI medium qP wave dispersion equation uses the SSF method wave field continuation operator to obtain the HTI medium one-way wave splitstep method operator.On the basis of positioning principle,digital geophone principle,isochronous principle and explosive reflector principle,the forward simulation and migration of HTI medium common shot point and the post-stack forward simulation and migration are realized,then verify the correctness of the forward modeling method by migration.