This section contains examples that illustrate how four elastic constants of a homogeneous TI medium can be estimated when the data are (a) P- and SV-wave traveltimes from VSP geometries with different apertures, (b) P- and SV-wave traveltimes from cross-well geometries with different apertures, and (c) P-wave traveltimes from cross-well and VSP geometries with different apertures.
The impulse response is given, and it is the same for all examples. The elastic constants that describe the medium are: W_{11}= 2256^{2}, W_{33} = 1919^{2}, W_{13}= 1699^{2}, and W_{44} = 658^{2}, all with units of (m/s)^{2} (Byun and Corrigan, 1990). I calculate the ellipse that fits the impulse response near the chosen axis by using a ray along the axis and a ray close to the axis. Once I have found the four needed elliptical parameters I use equations (22), (23), or (24) to convert those elliptical parameters into elastic constants.