2-D inversion of P-wave polarization data to obtain maps of velocity gradient

Gradient mapping is a technique employed in the interpretation of tomographic velocity images for delineating geological structures. In this paper, a tomographic method is proposed for determining relative velocity gradient field from seismic polarization directions. This inverse problem is iteratively resolved by the damped least squares method. With Hamiltonian formulation of ray theory and under the assumption that the medium is weakly inhomogeneous, the problem formulation for polarization direction is approximately expressed as a function of relative velocity gradient. Explicit expressions of the Frechet derivatives of polarization directions with respect to model parameters are given. The proposed tomographic method is illustrated by conducting synthetic experiments for showing the ability of our method to recover relative velocity gradient field as well as its potential applicability to complex media. The test results demonstrate that the proposed method is a promising approach for imaging geological structures.