So far, I have assumed that the axis of symmetry is vertical. If the axis of symmetry is nonvertical we need to find its inclination first, for example, by fitting SH-wave traveltimes with heterogeneous elliptically anisotropic models, as explained in Michelena (1992a). Once the inclination of the axes of symmetry of the different blocks has been estimated, the elliptical group velocities of P- and SV-waves at each block are estimated using only rays that travel near the axes of symmetry. Finally, the elliptic parameters are locally transformed into elastic constants, as explained in the section ``Homogeneous media''. This process assumes the axes of symmetry of the different blocks of the model are in the same plane of the survey, as explained also by Michelena (1992a).
The elastic constants estimated in this way are referred to different coordinate frames, one for each different axis of symmetry. For purposes of interpretation, having the elastic constants relative to different frames is not a problem as long as we also use the inclination of the axes of symmetry. However, for further computations (finite difference modeling, for example) it might be necessary to transform the elastic constants to a common frame. This can be done by using Bond's transformation matrices (Auld, 1990).