The procedure to estimate elastic constants of a transversely isotropic medium from limited aperture traveltimes consists of two steps. First, P- and SV-wave traveltimes are fitted with elliptical velocity functions around one of the axes of symmetry. Second, the parameters that describe the elliptical velocity functions are transformed analytically into elastic constants. When the medium is heterogeneous, the process of fitting the traveltimes with elliptical velocity functions is performed tomographically and the transformation to elastic constants is performed locally at each position in space. Cross-well synthetic and field data examples show that the procedure is accurate as long as the data aperture is properly constrained.