Ray-centred coordinate systems in anisotropic media

Klimeš, Luděk

doi:10.1007/s11200-006-0027-7

Cited by 19 publications

(37 citation statements)

References 8 publications

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“…The ray-centered coordinate system q = (q 1 ; q 2 ; q 3 ) q = (q 1 ; q 2 ; q 3 ) connected with reference ray Ð Ð, may be introduced in many ways, see Klimeš (2006). The most important property of these coordinates is that reference ray Ð Ð is the third coordinate axis of the system.…”

Section: Dynamic Ray Tracing In Ray-centered Coordinatesmentioning

confidence: 99%

“…See Klimeš (1994Klimeš ( , 2006 and Červený (2001, eqs. 4.2.77 and 4.2.78), where a detailed derivation can be found.…”

Section: Dynamic Ray Tracing In Ray-centered Coordinatesmentioning

confidence: 99%

“…The main properties of the raycentered coordinate system are: i) Reference ray Ð Ð represents the q 3 q 3 -axis of the coordinate system, ii) The coordinate system is, in general, curvilinear, nonorthogonal. Coordinate axes q 1 q 1 , q 2 q 2 may be chosen in various ways, see Hanyga (1982), Kendall et al (1992), Klimeš (1994Klimeš ( , 2006, Červený (2001, sec. 4.2.4/3), .…”

Section: Introductionmentioning

confidence: 99%

“…4.2.4/3), . For a particularly detailed treatment and for the comparison of several approaches see Klimeš (2006). In general, the dynamic ray tracing system in ray-centered coordinates q i consists of six equations.…”

Section: Introductionmentioning

confidence: 99%

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A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media

Červený

2007

Stud Geophys Geod

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Dynamic ray tracing plays an important role in paraxial ray methods. In this paper, dynamic ray tracing systems for inhomogeneous anisotropic media, consisting of four linear ordinary differential equations of the first order along the reference ray, are studied. The main attention is devoted to systems expressed in a particularly simple choice of ray-centered coordinates, here referred to as the standard ray-centered coordinates, and in wavefront orthonormal coordinates. These two systems, known from the literature, were derived independently and were given in different forms. In this paper it is proved that both systems are fully equivalent. Consequently, the dynamic ray tracing system, consisting of four equations in wavefront orthonormal coordinates, can also be used if we work in ray-centered coordinates, and vice versa.

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Section: Dynamic Ray Tracing In Ray-centered Coordinatesmentioning

confidence: 99%

“…See Klimeš (1994Klimeš ( , 2006 and Červený (2001, eqs. 4.2.77 and 4.2.78), where a detailed derivation can be found.…”

Section: Dynamic Ray Tracing In Ray-centered Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media

Červený

2007

Stud Geophys Geod

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“…For inhomogeneous anisotropic media, the DRT system in ray-centred coordinates was first derived by Hanyga (1982); see also Kendall et al (1992), Klimeš (1994Klimeš ( , 2006, Bakker (1996Bakker ( ), and Červený (2001Bakker ( , 2007. At present, the DRT in ray-centred coordinates in both isotropic and anisotropic inhomogeneous layered media, is a well-understood procedure.…”

Section: Introductionmentioning

confidence: 99%

Transformation relations for second-order derivatives of travel time in anisotropic media

Červený

Klimeš

2010

Stud Geophys Geod

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In the computation of paraxial travel times and Gaussian beams, the basic role is played by the second-order derivatives of the travel-time field at the reference ray. These derivatives can be determined by dynamic ray tracing (DRT) along the ray. Two basic DRT systems have been broadly used in applications: the DRT system in Cartesian coordinates and the DRT system in ray-centred coordinates. In this paper, the transformation relations between the second-order derivatives of the travel-time field in Cartesian and ray-centred coordinates are derived. These transformation relations can be used both in isotropic and anisotropic media, including computations of complex-valued travel times necessary for the evaluation of Gaussian beams.K e y w o r d s : paraxial travel times, paraxial approximation of the displacement vector, Gaussian beams, dynamic ray tracing, second-order travel-time derivatives

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Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium

Klimeš

2006

Stud Geophys Geod

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Ray-centred coordinate systems in anisotropic media

Cited by 19 publications

References 8 publications

A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media

A note on dynamic ray tracing in ray-centered coordinates in anisotropic inhomogeneous media

Transformation relations for second-order derivatives of travel time in anisotropic media

Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium

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