A Concise Anisotropic Slope Tomography Based on 2-D Quasi-Acoustic Eikonal Equation for VTI Media

Abstract

Slope tomography is an appealing tomographic method for velocity and anisotropic model building. We present a concise anisotropic slope tomography based on the 2-D quasi-acoustic eikonal equation in transversely isotropic (TI) media with a vertical symmetry axis (VTI). First, we establish the Frechet derivatives of the 2-D qP-wave in VTI stereotomography by applying the ray perturbation theory to the 2-D quasi-acoustic eikonal equation for VTI media. Second, we devise an anisotropic slope tomography instead of an anisotropic stereotomography based on the derived Frechet derivatives because slope tomography is more concise, as well as stable for real applications. Besides, we adopt a similar strategy that is recently developed, parsimonious adjoint slope tomography, to calculate the scatterer coordinates after the parameters of the macro model are updated. With the help of a kinematic remigration of invariants observed at the surface, we outline a concise anisotropic slope tomography in VTI media. Compared with the recently developed anisotropic adjoint slope tomography, we still establish the linear system based on the ray perturbation theory and solve it using a conjugate gradient algorithm. The synthetic and real data examples show that the anisotropic parameters and the scatterer coordinates can be updated alternately and effectively by combining the kinematic remigration in VTI media with a 2-D qP-wave slope tomography.