Optimized pure visco-acoustic wave equation and its numerical implementation in 3D TI and OA media
The anisotropy and viscosity are widely existed in earth media,which affect the kinematic and dynamic characteristics during seismic wave propagation.Therefore,it should be taken into full consideration when studying the propagation of seismic wave in underground media.The existing anisotropic wavefield extrapolation methods mainly use pseudo-acoustic wave equations based on the acoustic approximation,which are easy to encounter pseudo-shear wave pollution and instability when the medium parameters can't meet approximated conditions.To address this problem,this paper applies an optimization scheme to expand the original coupled anisotropic pure acoustic wave dispersion relation,and then Proposes Optimized Pure Acoustic Wave Equations(PAWEs)in 3D TI(Transversely Isotropy)and OA(Orthorhombic Anisotropy)media.The derived PAWEs are computed by combining finite-difference and Poisson solver effectively.Meanwhile,considering the absorption and attenuation effect of underground media,the Viscous Anisotropic PAWEs(VAPAWEs)are exploited by combining the developed PAWEs and standard linear solid model.Phase velocity analysis indicates that the optimized scheme can produce high accuracy approximated results.Several numerical examples demonstrate that the proposed VAPAWEs can produce accurate and stable P-wave response,and availably simulate the amplitude loss and phase dispersion of pure acoustic wave.In conclusion,the proposed equations can provide effective assistances for seismic imaging and inversion in anisotropic attenuation media.
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