From group or phase velocities to the general anisotropic stiffness tensor

Robert W. Vestrum, R. James Brown

Two numerical inversions were designed to calculate the 21 independent stiffnesses that define, in general, an anisotropic medium from either group- or phase-velocity data. The accuracy, robustness and computational complexity of the two inversion procedures - group velocity to stiffnesses and phase velocity to stiffnesses - were then compared.

This 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.