Transformation of spatial and perturbation derivatives of travel time at a curved interface between two arbitrary media

2018

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In an elastic medium, it was proved that the stiffness tensor is symmetric with respect to the exchange of the first pair of indices and the second pair of indices, but the proof does not apply to a viscoelastic medium. In order to indicate which phenomena could be observed in the wave field if the stiffness matrix were nonsymmetric, we propose the frequency-domain ray series for viscoelastic waves with a non-symmetric stiffness tensor in this paper.

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Section: Christoffel Equation and Eikonal Equationmentioning

confidence: 99%

Frequency-domain ray series for viscoelastic waves with a non-symmetric stiffness matrix

2018

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“…(2) i of the Christoffel matrix are usually approximated by various perturbation expansions along the reference rays (Klimeš, 2002(Klimeš, , 2010b(Klimeš, , 2016b. The perturbation approximation of the anisotropic-ray-theory travel times depends on the reference ray and on degree N of the perturbation Hamiltonian function homogeneous with respect to the slowness vector.…”

Section: 1 R E F E R E N C E a N D P E R T U R B A T I O N H A M mentioning

confidence: 99%

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

Bulant

2016

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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 frequencydependent 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-raytheory 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.K e y wo r d s :

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Tracing real-valued reference rays in anisotropic viscoelastic media

2022