A Study On Propagation Signatures Of Seismic Wave In TTI Media

In this paper, we present and systematically describe the analyticexpression of phase velocities and group velocity of Transversely isotropicmedia with a tilted symmetry axis (TTI), and the modeling of TTI mediaaccording to our areas of professional research interest.Firstly, we have reviewed the history and study states of anisotropicelastic wave propagation signatures, summarized several types of elasticwave models in TTI medium and the exact expression of elastic constantsmatrix in each model is provided. As the base of modeling, the calculationmethod of elastic constants in a material with transversely isotropic mediawith a tilted symmetry axis background is given according to Thomsen andJianlin Zhu's theory for calculating elastic constants of TTI media andRotation of the matrix of elastic constants. Then the phase and group velocityformulas in VTI media and the analytic description of 3D phase velocity andgroup velocities of transversely isotropic media with a tilted symmetry axisof plane wave propagation are deduced according to Christoffel equation andthe theory of coordinate rotation, and the 2D phase and group velocities ofTTI medium are calculated. We also analyze the feature and plot the 3Dcurve of phase and group velocity of three types body wave.According to the study above, the one-order elastic wave equationsexpressed with particle velocity and stress are established for the TTI media,and the approach to solve the 2-D wave equation with staggered gridfinite-difference is described. After the deduction of high order temporal andspecial difference approximation to the wave equation, because the TTImedia have 21 nonzero(but not independent) elastic constants, we putforward a new style staggered grid finite-difference method with a auxiliarygrid, then modeling the propagation signatures of TTI medium by thismethod firstly. The phenomenon of S-wave splitting and the diamond-shapedwave front of SV-wave in acoustic VTI media are clearly observed insnapshots. The snapshots of wave propagation in an infinite TTI media andsynthetic three components surface for a flat layered model are presented. Wealso used vertical source excitation and absorb condition in the implement ofnumerical modeling.As the same time, we also model the propagation signatures of TTImedium by using pseudo spectrum method. Firstly, we deduce the 2D waveequation without sources of elastic energy in TTI media, and present thetheory of pseudo spectrum method and the expression of time difference. Theboundary condition can create a periodic divergent wave field by the reasonof periodic boundary condition in Fourier transform, and this field willswamp the effective wave field. So, we eliminate the effect of wraparound bythe anti-periodic extension method (Takashi). The snapshots of wavepropagation in an infinite TTI media and synthetic three components surfacefor a flat layered model are presented.Finally, we give out versus of staggered grid finite-difference methodand pseudo spectrum method, the execution time of pseudo spectrum methodis faster than staggered grid finite-difference method, and it is the limit ofapproximation order of finite difference method. Because of pseudo spectrummethod calculate the space difference by Fourier transform, its accuracy willhigher than finite difference method. Meanwhile, the calculation procedure ismuch simplicity, and the code developed much easier. Pseudo spectrummethod gives a powerful forward method for inversion and migration.