Determination of rock-sample anisotropy from P- and S-wave traveltime inversion

We determine anisotropy of a rock sample from laboratory measurements of P- and S-wave traveltimes using weak-anisotropy approximation and parametrization of the medium by a special set of anisotropy parameters. For the traveltime inversion, we use first-order velocity expressions in the weak-anisotropy approximation, which allow to deal with P and S waves separately. Each wave is described by 15 anisotropy parameters, 9 of which are common for both waves. The parameters allow an approximate construction of separate P- or common S-wave phase-velocity surfaces. Common S-wave concept is used to simplify the treatment of S waves. In order to obtain all 21 anisotropy parameters, P- and S-wave traveltimes must be inverted jointly. The proposed inversion scheme has several advantages. As a consequence of the use of weak-anisotropy approximation and assumed homogeneity of the rock sample, equations used for the inversion are linear. Thus, the inversion procedure is non-iterative. In the approximation used, phase and ray velocities are equal in their magnitude and direction. Thus, analysis whether the measured velocity is the ray or phase velocity is unnecessary. Another advantage of the proposed inversion scheme is that, thanks to the use of the common S-wave concept, it does not require identification of S-wave modes. It is sufficient to know the two S-wave traveltimes without specification, to which S-wave mode they belong. The inversion procedure is tested first on synthetic traveltimes and then used for the inversion of traveltimes measured in laboratory. In both cases, we perform first the inversion of P-wave traveltimes alone and then joint inversion of P-and S-wave traveltimes, and compare the results.