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.
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