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

**Ludek Klimes**
### 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.

### Whole paper

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*Studia Geophysica et Geodaetica*, **46** (2002), 589-597.

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