The procedure used to estimate elastic constants in heterogeneous TI media is a generalization of the technique presented in Michelena (1992c) for estimating elastic constants in homogeneous TI media. For homogeneous media, traveltimes from different wave types are fitted with elliptically anisotropic models. The elliptical velocities that result are then transformed into elastic constants. For heterogeneous media, the elliptical fit is performed by using anisotropic traveltime tomography, and the transformation to elastic constants is performed locally at each point in space.
The examples presented in this paper show that the procedure is accurate as long as the maximum aperture satisfies the following constraints: it must be not too small because that would impede the estimation of the NMO velocities and not too large because the elliptical approximation might not be adequate.
In this paper, I tested the algorithm with simple layered models. The estimation of elastic constants in media with more complex heterogeneities may require traveltimes from wider apertures, which could yield in less accurate results. This problem can solved by using traveltimes from all wave types from different recording geometries.