## Gaussian packets in smooth isotropic media

**Ludek Klimes**
### Summary

Gaussian packets are high-frequency asymptotic
space-time solutions of the wave equation.
We briefly review the derivation of the evolution equations for paraxial
Gaussian packets propagating in a smooth stationary non-dissipative
isotropic medium.
The central point of a Gaussian packet moves along the
spatial central ray according to the ray tracing equations.
The first derivatives of the complex-valued phase function
of the Gaussian packet at the central point
are determined by ray tracing, and are real-valued.
The shape of a Gaussian packet is determined by the
second derivatives of the complex-valued phase function.
The equations for these second derivatives,
derived in general Cartesian coordinates,
nicely decouple in ray-centred coordinates.
The 2 x 2 matrix of the second derivatives
of the phase function in the plane perpendicular to the central ray
describes the Gaussian beam corresponding to the Gaussian packet,
and is calculated by dynamic ray tracing in the same way
as for the Gaussian beam.
The evolution of the remaining second derivatives of the phase function
of the Gaussian packet may be expressed in terms
of the complex-valued matrix of geometrical spreading
of the Gaussian beam.

### Keywords

Gaussian packets, Gaussian beams, space-time ray theory,
complex-valued phase function, inhomogeneous media.

### Whole paper

The
image of the paper in GIF 150dpi (611 kB)
is designed for an instant screen preview.

The paper is available in
PostScript (153 kB)
and GZIPped PostScript (49 kB).

In: Seismic Waves in Complex 3-D Structures, Report 14,
pp. 43-54, Dep. Geophys., Charles Univ., Prague, 2004.

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