Estimation of anisotropy parameters in vertical transverse isotropy media using the ray-based tomography

In seismic exploration, it is very important to consider the presence of anisotropy in order to image the subsurface correctly. The knowledge of anisotropic parameters leads to more precise characterization of reservoir, fracture density and flow paths. However, conventional geophysical methods do not directly measure these parameters, and it is useful to have a method to estimate them from seismic data. In the weak transverse isotropy approximation, the fields to be considered are the vertical and horizontal velocity components and the Thomsen parameters $\epsilon$ and $\delta$. We present a method for estimating the anisotropic Thomsen parameters in the presence of weak vertical transverse isotropy using P-wave traveltime tomography based on anisotropic ray tracing. Depending on the available information, we propose different approaches to retrieve the unknowns. A conventional three-dimensional traveltime tomography algorithm has been extended to include anisotropic ray tracing and using the algebraic reconstruction technique or modified simultaneous iterative reconstruction technique to retrieve the unknowns. We test the method on synthetic examples for the inversion of transmitted and reflected traveltimes, and we evaluate the sensitivity of the tomographic results to the available information. Furthermore, we also consider the case of tilted transverse isotropy in a seismic reflection example.