Study On Wave Equation Modeling Of Constant-Q Attenuating Anisotropic Media

Real subsurface media can commonly show the viscoelastic behavior and anisotropy characteristic.For better forecasting and recognition of hydrocarbon formation,accurate seismic wave simulation requires considering the earth's viscosity including attenuation and dispersion effects and anisotropy characteristics.In this study,we deduced constant-Q visco-acoustic and viscoelastic velocity-stress equation based on the Kjartansson constant-Q model theory.Then I present a new viscoelastic anisotropic constitutive relation and establish the corresponding time-domain viscoelastic VTI,TTI wave equation with incorporating anisotropy theory.Compared with the approximate constant Q viscoelastic anisotropic theory based on generalized Zener model which proposed by Carcione(1995)and widely used in the past,it avoid introducing memory variables(related with the stress and strain relaxation time),and has a simple form of wave equation,each parameter have a clear physical meaning.The fractional order derivative is the key to implement attenuation and unify viscoelastic and pure elastic cases.Then I evaluate the applicability and efficiency of our theory and algorithm through numerical modeling of some typical geological model by using the rotated staggered grid finite-difference method.In addition,based on stochastic medium theory,I describe and build a crack-holes,anisotropic random medium model,etc.then we analyze the effect of scattering of small-scale heterogeneity on seismic wave field.Meanwhile,for the finite difference numerical simulation method,we study a series of the optimization method to suppress numerical dispersion,improve the absorption boundary to improve the accuracy.