## Interpolation of the coupling-ray-theory
Green function within ray cells

**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 pose a significant challenge in storing
the Green function at the nodes of dense grids,
typical for applications such as the Born approximation
or non-linear source determination.
Storing the Green function at the nodes of dense grids
for too many frequencies may be impractical or even unrealistic.
We have already proposed the approximation
of the coupling-ray-theory tensor Green function,
in the vicinity of a given prevailing frequency,
by two coupling-ray-theory dyadic Green functions
described by their coupling-ray-theory travel times
and their coupling-ray-theory amplitudes.
The above mentioned prevailing-frequency approximation
of the coupling ray theory enables us to interpolate
the coupling-ray-theory dyadic Green functions
within ray cells,
and to calculate them at the nodes of dense grids.
For the interpolation within ray cells,
we need to separate the pairs of
prevailing-frequency coupling-ray-theory
dyadic Green functions
so that both the first Green function and the second Green function
are continuous along rays and within ray cells.
We describe the current progress in this field and
outline the basic algorithms.
The proposed method is equally applicable
to both electromagnetic waves and elastic S waves.
We demonstrate the preliminary numerical results
using the coupling-ray-theory travel times of elastic S waves.

### Keywords

Wave propagation, elastic anisotropy, electromagnetic bianisotropy,
heterogeneous media, wave coupling,
travel time, amplitude, polarization.

### Whole paper

The reprint is available in
PDF (902 kB).

*Stud. geophys. geod.*, **61** (2017), 541-559.