CROSSWELL TOMOGRAPHIC ESTIMATION OF ELASTIC-CONSTANTS IN HETEROGENEOUS TRANSVERSELY ISOTROPIC MEDIA

The procedure to estimate elastic constants of a transversely isotropi c medium from limited-aperture traveltimes has two steps. First, P- an d SV-wave traveltimes are fitted with elliptical velocity functions ar ound one of the axes of symmetry. Second, the parameters that describe the elliptical velocity functions are transformed analytically into e lastic constants. When the medium is heterogeneous, the process of fit ting the traveltimes with elliptical velocity functions is performed t omographically, and the trans-formation to elastic constants is perfor med locally at each position in space. Crosswell synthetic and field d ata examples show that the procedure is accurate as long as the data a perture is constrained as follows: it should not be too large otherwis e the elliptical approximation may not be adequate, and it should not be too small because the tomographic estimation of elliptical velociti es fails, even if the medium is actually isotropic.