## Green function as an integral superposition
of Gaussian beams in inhomogeneous anisotropic
layered structures in Cartesian coordinates

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

Integral superposition of Gaussian beams is a useful
generalization of the standard ray theory. It removes some
of the deficiencies of the ray theory like its failure to
describe properly behaviour of waves in caustic regions. It also
leads to a more efficient computation of seismic wavefields since
it does not require the time-consuming two-point ray tracing. We
present the Gaussian beam integral superposition of Green function
for inhomogeneous, isotropic or anisotropic, layered structures based
on the dynamic ray tracing (DRT) in Cartesian coordinates. For
the evaluation of the superposition formula, it is sufficient to
solve the DRT in Cartesian coordinates just for the point-source
initial conditions. Moreover, instead of seeking 3 × 3 paraxial
matrices, it is sufficient to seek just 3 × 2 parts of these
matrices. The presented formulae can be used for the computation of
wavefields generated by various types of point sources (explosive,
moment-tensor). Receivers may be situated at an arbitrary point of
the medium, including the ray-theory shadow regions. Arbitrary direct,
multiply reflected/transmitted, unconverted or converted elementary
waves, propagating independently, can be considered.

### Keywords

elastodynamic Green function, inhomogeneous anisotropic media, integral
superposition of Gaussian beams

### Whole paper

The paper is available in
PDF (137 kB).

*Seismic Waves in Complex 3-D Structures*, **26** (2016), 131-153.