Obtaining the elastic constants of a homogeneous TI medium from P-, SV- and, SH-wave traveltimes is a two-step procedure. The first step is to obtain direct and normal moveout (NMO) velocities by separately fitting traveltimes from each wave type with elliptical velocity functions. The second step is to map these elliptical velocities into elastic constants (Michelena, 1992c). In this paper I show that when the medium is heterogeneous, the elastic constants can be estimated by applying the procedure for homogeneous media many times to a heterogeneous model described as a superposition of homogeneous blocks. These blocks should incorporate our previous knowledge about the structure. The direct and NMO velocities needed at each block are estimated tomographically, as explained in Michelena et al. (1993) and Michelena (1992a).
I start by explaining how the data aperture should be constrained to use the algorithm and how those constraints affect the estimation of both anisotropy and heterogeneity. Then, I show the application of the technique using synthetic P- and SV-wave traveltimes generated through a heterogeneous TI model. Finally, I present a field data example from a west Texas oil field. This example shows how the estimation of the elastic constants can add useful information when we study the properties of reservoir and nonreservoir rocks.