Relation of the wave-propagation metric tensor to the curvatures of the slowness and ray-velocity surfaces

Summary

The contravariant components of the wave-propagation metric tensor equal half the second-order partial derivatives of the selected eigenvalue of the Christoffel matrix with respect to the slowness-vector components. The relations of the wave-propagation metric tensor to the curvature matrix and Gaussian curvature of the slowness surface and to the curvature matrix and Gaussian curvature of the ray-velocity surface are demonstrated with the help of ray-centred coordinates.

Keywords

Ray theory, elastic anisotropy, Finsler space, metric tensor, slowness surface, ray-velocity surface, ray-centred coordinates.

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