Viscoacoustic VTI and TTI wave equations and their application for anisotropic reverse time migration: Constant-Q approximation

Ali Fathalian, Kristopher A. Innanen

We investigated the simulation of Viscoacoustic wave propagation and reverse time migration (RTM) in transversely isotropic (TI) media, vertical TI (VTI) and tilted TI (TTI), within approximating constant-Q. Reverse time migration (RTM) is based on two-way wave equation and has advantages over than other imaging methods. Such wave propagation can be modeled with a finite difference scheme by introducing a series of standard linear solid (SLS) mechanisms, and it can be carried out within a computationally tractable region by making use of perfectly-matched layer (PML) boundary conditions. The Viscoacoustic wave equation for VTI and TTI mediums have been derived using the wave equation in anisotropic media by setting shear wave velocity as zero. Using the TI approximation and ignoring all spatial derivatives of the anisotropic symmetry axis direction leads to instabilities in some area of the model with the rapid variations in the symmetry axis direction. A solution to this problem is proposed that involves using a selective anisotropic parameter equating in the model to reduce the difference of Thompson parameters in areas of rapid changes in the symmetry axes. To eliminate the high-frequency instability problem, we applied the regularization operator and built a stable Viscoacoustic wave propagator in Ti media. After correcting for the effects of anisotropy and viscosity, the anisotropy RTM image in attenuation media with high resolution is obtained and compared with the isotropic RTM image.