## Single-frequency approximation of the coupling ray theory

**Ludek Klimes** and
**Petr Bulant**
### Summary

The coupling-ray-theory Green tensor is frequency dependent,
and is usually calculated for many frequencies. This frequency
dependence represents no problem for calculating the Green tensor,
but may represent a great problem when storing the Green tensor
at the nodes of dense grids, typical for applications such as seismic
migrations. This paper is devoted to the approximation of the
coupling-ray-theory Green tensor, which eliminates this frequency
dependence.

In the vicinity of a given prevailing frequency, we approximate the
frequency-domain coupling-ray-theory Green tensor by two Green tensors
corresponding to two S waves described by their travel times
and amplitudes. We refer to these travel times and amplitudes as
the coupling-ray-theory travel times and the coupling-ray-theory
amplitudes. This "single-frequency approximation" of the coupling ray
theory allows us to process the coupling-ray-theory wavefield in
the same way as the anisotropic-ray-theory wavefield. This simplification
may be decisive when storing the Green tensor at the nodes of dense grids,
which is typical for applications such as seismic migrations.

We test the accuracy of the proposed single-frequency approximation
of the coupling ray theory numerically in eight anisotropic velocity models.
The additional inaccuracy introduced by the single-frequency approximation
is smaller than the inaccuracy of the standard frequency-domain coupling
ray theory, and smaller than the additional inaccuracy introduced by many
other approximations of the coupling ray theory.

### Whole paper

The paper is available in
PDF (1813 kB).

In: Seismic Waves in Complex 3-D Structures, Report 22,
pp. 143-167, Dep. Geophys., Charles Univ., Prague, 2012.