## Gaussian beams in inhomogeneous anisotropic layered structures

**Vlastislav Cerveny** **&**
**Ivan Psencik**
### Summary

Gaussian beams concentrated close to rays of high-frequency seismic body waves
propagating in an inhomogeneous anisotropic layered structure are studied.
The amplitude profiles of the Gaussian beam along the plane perpendicular
to the ray and along the plane perpendicular to the slowness vector are Gaussian.
The Gaussian profile is controlled by the 2×2 complex-valued matrix **M**
of the second derivatives of the travel-time field at any point of the ray.
The matrix **M** can be simply determined at any point of the ray if
the ray-propagator matrix along the ray is known and if the value of
**M** is specified at a selected point of the ray. The ray-propagator matrix can
be determined by dynamic ray tracing along the ray. In inhomogeneous anisotropic
medium, the dynamic ray tracing can be performed alternatively in several coordinate
systems: in global Cartesian coordinates, in ray-centred coordinates and in wavefront
orthonormal coordinates. In addition, also simplified dynamic ray tracing in global Cartesian coordinates
can be used, which reduces the number of equations of the dynamic ray tracing system.
The derived expressions for the Gaussian beams are applicable to general 3-D inhomogeneous
layered structures of arbitrary anisotropy (specified by upto 21 independent position-dependent
elastic moduli). Possible simplification of the procedure are outlined.

### Keywords

Paraxial travel times, Gaussian beams, dynamic ray tracing,
anisotropic heterogeneous medium.

### Whole paper

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In: Seismic Waves in Complex 3-D Structures, Report 19,
pp. 123-156, Dep. Geophys., Charles Univ., Prague, 2009.

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