Equivalent anisotropic first-order pseudo-acoustic wave equations modeling and its efficiency analysis

In order to overcome the limitations of anisotropic elastic wave equations modeling, this paper studied anisotropic pseudo-acoustic wave modeling by using staggered-grid finite-difference method. Starting from two different ideas, i.e., Hooke’s law and qP-qSV dispersion relation for VTI media, two first-order pseudo-acoustic wave equations in two forms for VTI media are given. Meanwhile, a new VTI first-order stress-velocity equations is derived through introducing the pseudo-velocity components of the wavefields, and then they are generalized to TTI media through the rotated coordinate system. Then the staggered-gird high-order finite-difference forms of the first-order pseudo-acoustic wave equations and the corresponding PML boundary condition are deduced. Finally, the inherent qSV-wave artifact generating mechanism and suppression method are discussed briefly. Numerical results show that the three first-order pseudo-acoustic wave equations are equivalent in kinematics and dynamics. Compared with anisotropic elastic wave modeling, they can save computational memory and enhance the efficiency. Anisotropic factor can affect the travel-time and amplitude of the reflection wave so we cannot ignore them in subsequent processing，inversion and interpretation. The reverse-time migration results of VTI-HESS model also validate the method proposed in this paper.