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.

11/17/1997