## Prevailing-frequency approximation
of the coupling ray theory
for electromagnetic waves or elastic S waves

**Ludek Klimes**
&
**Petr Bulant**
### Summary

The coupling-ray-theory tensor Green function
for electromagnetic waves or elastic S waves is frequency dependent,
and is usually calculated for many frequencies.
This frequency dependence represents no problem
in calculating the Green function,
but may represent a great problem in storing
the Green function at the nodes of dense grids,
typical for applications such as the Born approximation.
This paper is devoted to the approximation
of the coupling-ray-theory tensor Green function,
which practically eliminates this frequency dependence
within a reasonably broad frequency band.

In the vicinity of a given prevailing frequency,
we approximate the frequency-dependent frequency-domain
coupling-ray-theory tensor Green function
by two dyadic Green functions corresponding to two waves
described by their travel times and amplitudes
calculated for the prevailing frequency.
We refer to these travel times and amplitudes
as the coupling-ray-theory travel times
and the coupling-ray-theory amplitudes.
This "prevailing-frequency approximation"
of the coupling ray theory
for electromagnetic waves or elastic S waves
allows us to process the coupling-ray-theory wave field
in the same way as the anisotropic-ray-theory wave field.
This simplification may be decisive when storing
the tensor Green function at the nodes of dense grids,
which is typical for applications such as the Born approximation.

We test the accuracy of the proposed
prevailing-frequency approximation
of the coupling ray theory numerically
using elastic S waves in eight anisotropic velocity models.
The additional inaccuracy
introduced by the prevailing-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.

### Keywords

Electromagnetic waves, elastic S waves,
wave coupling, tensor Green function, travel time, amplitude,
anisotropy, bianisotropy, heterogeneous media, prevailing frequency.

### Whole paper

The reprint is available in
PDF (1936 kB).

*Stud. geophys. geod.*, **60** (2016), 419-450.