Abstract: An improved method for P-wave modeling in inhomogeneous transversely isotropic media with tilted symmetry axis (TTI media), suitable for anisotropic reverse-time migration, is based on an acoustic TI approximation. The resulting wave equations (2.20) & (2.21) are derived directly from first principles, Hooke's law and the equations of motion, and therefore make no assumptions on spatial variation of medium parameters. Like in the acoustic VTI case, the wave equations are written as a set of two second-order partial differential equations. However, unlike in the acoustic VTI case, the acoustic TTI wave equations contain mixed second-order derivatives. The discretization scheme uses centered finite-difference operators for first- and second-order derivative operators to approximate the mixed and non-mixed second-order derivatives in the wave equation. The discretization scheme is stabilized by slightly weighing down the mixed derivatives, with almost negligible effect on the wave field kinematics.

Abstract: An improved method for P-wave modeling in inhomogeneous transversely isotropic media with tilted symmetry axis (TTI media), suitable for anisotropic reverse-time migration, is based on an acoustic TI approximation. The resulting wave equations (2.20) & (2.21) are derived directly from first principles, Hooke's law and the equations of motion, and therefore make no assumptions on spatial variation of medium parameters. Like in the acoustic VTI case, the wave equations are written as a set of two second-order partial differential equations. However, unlike in the acoustic VTI case, the acoustic TTI wave equations contain mixed second-order derivatives. The discretisation scheme uses centered finite-difference operators for first- and second-order derivative operators to approximate the mixed and non-mixed second-order derivatives in the wave equation. The discretization scheme is stabilized by slightly weighing down the mixed derivatives, with almost negligible effect on the wave field kinematics.