Errors Due to the Common Ray Approximations of the Coupling Ray Theory

Klimeš, Luděk; Bulant, Petr

doi:10.1023/b:sgeg.0000015588.43488.8e

Cited by 28 publications

(33 citation statements)

References 14 publications

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“…The caustics cause triplications and strong energy focusing (Hurley & Wolfe 1985; Every 1986, 1988; Shuvalov & Every 1997; Wolfe 1998). The acoustic axes also pose complications in tracing rays (Vavryčuk 2001, 2003b; Farra 2005) and in modelling wavefields because of the coupling of waves (Chapman & Shearer 1989; Kravtsov & Orlov 1990; Coates & Chapman 1990; Rümpker & Thomson 1994; Pšenčík 1998; Bulant & Klimeš 2004; Klimeš & Bulant 2004).…”

Section: Introductionmentioning

confidence: 99%

Acoustic axes in weak triclinic anisotropy

Vavryčuk¹

2005

Geophysical Journal International

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S U M M A R YAcoustic axes can exist even under an infinitesimally weak anisotropy, and occur when slowness surfaces of the S1 and S2 waves touch or intersect. The maximum number of isolated acoustic axes in weak triclinic anisotropy is 16 as in strong triclinic anisotropy. The directions of acoustic axes are calculated by solving two coupled polynomial equations in two variables. The order of the equations is 6 under strong anisotropy and reduces to 5 under weak anisotropy. The weak anisotropy approximation is particularly useful, when calculating the acoustic axes under extremely weak anisotropy with anisotropy strength less than 0.1 per cent because the equations valid for strong anisotropy might become numerically unstable and their modification, which stabilizes them, is complicated. The weak anisotropy approximation can also find applications in inversions for anisotropy from the directions of acoustic axes.

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Section: Introductionmentioning

confidence: 99%

Acoustic axes in weak triclinic anisotropy

Vavryčuk¹

2005

Geophysical Journal International

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“…The same velocity model was used by Bulant and Klimeš (2002) and Klimeš and Bulant (2004) to demonstrate the coupling ray theory and its quasi-isotropic approximations. For a more detailed discussion and description of this velocity model refer to Pšenčík and Dellinger (2001).…”

Section: Elastic Numerical Examplesmentioning

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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“…The same velocity model has been used by Bulant and Klimeš (2002) and Klimeš and Bulant (2004) to demonstrate the coupling ray theory and its quasi-isotropic approximations. For comparison with the isotropic-ray-theory and anisotropic-ray-theory seismograms in velocity model QI and for a more detailed discussion and description of this velocity model refer to Pšenčík and Dellinger (2001).…”

Section: 3 a N I S O T R O P I C V E L O C I T Y M O D E L Smentioning

confidence: 99%

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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Errors Due to the Common Ray Approximations of the Coupling Ray Theory

Cited by 28 publications

References 14 publications

Acoustic axes in weak triclinic anisotropy

Acoustic axes in weak triclinic anisotropy

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

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

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