Group- and Phase-Velocity Inversions for the General Anisotropic Stiffness Tensor

Robert W. Vestrum

Using forward models and geometrical analysis, criteria are established for deciding whether group or phase velocities are calculated from experimentally measured traveltimes in anisotropic samples.

With these results, two experiments were carried out: one to obtain phase velocities across an anisotropic sample; another to acquire group velocities across a second sample of the material. I designed numerical inversions for the 21 independent stiffnesses of the material from either group- or phase-velocity data. I then compared the accuracy, robustness and computational complexity of the two inversion procedures - group velocity to stiffnesses and phase velocity to stiffnesses.

My group-velocity inversion overcomes the difficulty of calculating group velocity in a prescribed direction and can calculate group velocities accurately even in directions near shear-wave singularities. Although phase velocities are easier to calculate than group velocities, the group-velocity inversion performed better in laboratory tests because group velocities are easier to measure.