Abstract
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.
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Klimeš, L. Relation of the Wave-Propagation Metric Tensor to the Curvatures of the Slowness and Ray-Velocity Surfaces. Studia Geophysica et Geodaetica 46, 589–597 (2002). https://doi.org/10.1023/A:1019551320867
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DOI: https://doi.org/10.1023/A:1019551320867