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

Abstract

Abstract 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.