Summary
The underground medium is far from being isotropic and elastic. Such simplifications in modeling the seismic response of real geological structures may lead to misinterpretations, or even worse, to overlooking useful information. The existence of anisotropy and viscosity affect the effect of migration seriously. So, in this paper, based on the dissipation mechanism of standard linear solid model, we derive a pure viscoacoustic wave equation of TTI media in the time domain, which describes the attenuation characteristics of seismic wave by a Pseudodifferential operators in the equations. The results of numerical simulation show that the equation propagation can not only describe the propagation of pure scalar wave in anisotropic media accurately, but also reflect the effect of absorption and attenuation.
Introduction
At present, there are two kinds of methods to implement scalar wave RTM in anisotropic medium, those are pseudoacoustic wave RTM and pure acoustic wave RTM. At first, Alkhalifah (1998) first proposed the pseudo-acoustic wave equation in transversely isotropic media, which includes fourth-order partial derivatives of the wavefield in time and space equation. Zhou et al. (2006) and Du et al. (2008) simplified the fourth-order differential equation into two coupled second-order differential equations. However all of this does not eliminate the effect of shear wave completely. By reason of the instability for the residual shear, Fletcher et al. (2009) proposed adding nonzero S-wave velocity terms to overcome the problem. Duveneck et al. (2011) proposed a TTI acoustic formulation according to the anisotropic elastic equations. Zhang et al. (2012) pursued a stable TTI acoustic wave equations by introduce selfadjoint differential operators and proved the new equations are stable in the sense that energy of the wavefields is conserved during the propagation.
On the other hand, Liu et al. (2009) derived the pure Pwave and SV wave equation by solving the coupled equations. Reynam et al. (2011), Ge Zhan et al. (2011) give the pure P-wave and pure SV wave equation by solving the decoupling of the dispersion relation P and SV waves. Owning to the huge amount of calculation in the spatial domain, they implemented it in the frequency-wavenumber domain. When the anisotropy parameter variation is not intense, Chu (2013) proposed numerical interpolation scheme, which can solve instability problems caused by anisotropy parameter changing in spatial domain. Xu et al. (2014) proposed a new algorithm of pure quasi-P wave equation, which decomposes the pseudo-differential operator into two solvable operator: one Laplacian operator and one scale operator, and applied it for reverse time migration in anisotropic media.
