Seismic Wavefield Modeling In 3D TTI Media

In this paper, we systematically describe the basic theories of staggered grid finite defference and perfectly matched absorbing layer(PML) used in seismic wavefield modeling in 3D TTI media for the first time.Firstly, we reviewe the history and study stage of anisotropic elastic wavefield modeling, then summarized various types of elastic wave model in TTI media and the exact expression of elastic constants matrix in each model is given. As the basis of modeling, we present the computing method of elastic constants in TTI media introduced by Jianlin Zhu.Basing on the study above, we establish the first order stress-velocity wave equation system and its difference form, then give a particular description of the calculation progress for 3D wave equation system using the staggered grid method. Besides, we introduce the basic theory of PML and deduced the nonspliting PML for fisrt-order wave equation system and the splitting PML for second-order wave equation system referring some scholar's work. At the last of chapter 3, the stability condition formula of staggered grid finite difference method is derived.Last but not least, we analyze the numerical examples obtained by staggered grid finite difference method including the seismic wave propagation in 3D TTI media, PML absorbing artificial boundary reflected wave, and the seismic azimuthal seismological record in VSP, then we can get some conclusions:1,The Staggered grid finite difference as the power tool for 3D wavefield research can simulate the wave paropagation in 3D anisotropic media fastly and accurately2,Basing on other scholars'work, I deduce the nonsplitting PML for fisrt-order wave equation system and the splitting PML for second-order wave equation system., and the absorbing effects are very good.3,The propagation signatures of seismic wave in TTI media depend on not only the anisotropic coefficients of TI media but also the dip angle and strike angle of the symmetry axes.4,According to the modeling results, we can see that: the azimuthal anisotropic signatures of the P wavefront can be used in the parameter inversion of TI media, though it is much more complex than azimuthal anisotropic media. Considering the complexity of the shear wave, we should differ SH wave dan SV wave prior to parameter inversion based on shear wave splitting.