## 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, seismic anisotropy, Finsler space, metric tensor,
slowness surface, ray-velocity surface, ray-centred coordinates.

### Whole paper

The
image of the paper in GIF 150dpi (348 kB)
is designed for an instant screen preview.

The paper is available in
PostScript (94 kB)
and GZIPped PostScript (37 kB).

### Final version of this paper

Klimes, L. (2002):
Relation of the wave-propagation metric tensor
to the curvatures of the slowness and ray-velocity surfaces.
*Studia geophys. et geodaet.*, **46**, 589-597.

In: Seismic Waves in Complex 3-D Structures, Report 12,
pp. 79-87, Dep. Geophys., Charles Univ., Prague, 2002.

SW3D
- main page of consortium ** Seismic Waves in Complex 3-D Structures **.