Errors due to the anisotropic-common-ray approximation of the coupling ray theory

Klimeš, Luděk; Bulant, Petr

doi:10.1007/s11200-006-0029-5

Cited by 21 publications

(22 citation statements)

References 17 publications

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“…Quantities ∆ϕ k and ∆ε k are calculated according to Bulant and Klimeš (2002, Eqs 18 and 21), but often using the second-order perturbations of travel times instead of the first-order perturbations (Klimeš and Bulant, 2006 ). We obtain the algorithm of calculating the frequency derivative D of propagator matrix Π by differentiating algorithm (30)- (32) with respect to frequency ω:…”

Section: Numerical Algorithmmentioning

confidence: 99%

“…(1) and τ (2) in the coupling equation by the second-order perturbation expansion according to Klimeš and Bulant (2006). We approximate eigenvectors g (1) i and g (2) i of the Christoffel matrix by the unperturbed reference eigenvectors calculated using the Christoffel matrix with the unperturbed reference slowness vector.…”

Section: 2 N U M E R I C a L M E T H O D S B E I N G C O M P A R E Dmentioning

confidence: 99%

“…Moreover, there are many more or less accurate approximations of this coupling ray theory (Bulant and Klimeš, 2002 ;Pšenčík, 2008, 2010 ;Pšenčík et al, 2012 ). Note that the anisotropic-common-ray approximation (Klimeš, 2006 ;Klimeš and Bulant, 2006 ) usually preserves the accuracy of the coupling ray theory and simultaneously simplifies ray tracing considerably by eliminating the slowness surface singularities. However, in approximately uniaxial (approximately transversely isotropic) media (Klimeš, 2015(Klimeš, , 2016c, we may also use the reference ordinary (SH) and extraordinary (SV) rays (Klimeš and Bulant, 2015 ).…”

Section: Introductionmentioning

confidence: 99%

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

Klimeš

Bulant

2016

Stud Geophys Geod

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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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Section: Numerical Algorithmmentioning

confidence: 99%

Section: 2 N U M E R I C a L M E T H O D S B E I N G C O M P A R E Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Klimeš

Bulant

2016

Stud Geophys Geod

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“…Traveltime errors related to different approaches of the shearwave coupling problem are estimated by Klimes and Bulant (2006). Similar to ray theory, a quasi-isotropic WKBJ perturbation approach with the Langer approximation has been proposed by Maupin (1994) for layered structures.…”

Section: Ray Theorymentioning

confidence: 99%

Theory and Observations - Seismic Anisotropy

Maupin

Park

2015

Treatise on Geophysics

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“…In this paper, we assume that both prevailing-frequency coupling-ray-theory tensor Green functions are calculated along a single anisotropic common reference ray (Klimeš, 2006 ;Klimeš and Bulant, 2006 ;Bulant and Klimeš, 2008 ). The anisotropic common reference rays then determine the ray cells for interpolation according to Bulant and Klimeš (1999).…”

Section: Introductionmentioning

confidence: 99%

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

Klimeš

Bulant

2017

Stud Geophys Geod

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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 pose a significant challenge in storing the Green function at the nodes of dense grids, typical for applications such as the Born approximation or nonlinear 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 couplingray-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 prevailingfrequency 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-raytheory travel times of elastic S waves. K e y wo r d s :

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Errors due to the anisotropic-common-ray approximation of the coupling ray theory

Cited by 21 publications

References 17 publications

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

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

Theory and Observations - Seismic Anisotropy

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

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