Prevailing-frequency approximation of the coupling ray theory for S waves along the SH and SV reference rays
Abstract
The coupling-ray-theory tensor Green function for elastic S waves is frequency dependent, and is usually calculated for many frequencies. This frequency dependence represents no problem for calculating the Green function, but may be impractical or even unrealistic in storing the Green function at the nodes of dense grids, typical for applications such as Born approximation or non-linear source determination.
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 the 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. In this contribution, we describe the current progress in this field and outline the basic algorithms.
We also demonstrate the preliminary numerical results in several velocity models.