Relation of the Wave-Propagation Metric Tensor to the Curvatures of the Slowness and Ray-Velocity Surfaces |
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Authors: | Klimeš L. |
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Affiliation: | (1) Department of Geophysics, Charles University, Ke Karlovu 3, 121 16 Praha 2, Czech Republic |
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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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Keywords: | ray theory elastic anisotropy Finsler space metric tensor slowness surface ray-velocity surface ray-centred coordinates |
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