21. Analytic Description of <i>P</i>-Wave Ray Direction and Polarization in Orthorhombic Media

Rommel, B. E.; Tsvankin, Ilya

doi:10.1190/1.9781560801771.ch21

Cited by 7 publications

(6 citation statements)

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“…This result, valid only for weak anisotropy, follows from the identical form of the phase-velocity equation in any vertical plane of orthorhombic and VTI media (Tsvankin, 1997a(Tsvankin, , 2005. A more detailed discussion of the equivalence between VTI and orthorhombic media for out-of-plane propagation can be found in Rommel and Tsvankin (2000).…”

Section: Layer Above a Dipping Reflectormentioning

confidence: 64%

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Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Tsvankin¹,

Grechka²

2011

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180

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Section: Layer Above a Dipping Reflectormentioning

confidence: 64%

“…In the weak-anisotropy approximation, the definition of η (3) is symmetric in the sense that it does not change if x 2 is used as the symmetry axis of the equivalent VTI medium in the [x 1 , x 2 ]-plane(Rommel and Tsvankin, 2000).…”

mentioning

confidence: 99%

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Tsvankin¹,

Grechka²

2011

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180

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“…The calculation of the group velocity vector v g can be found, e.g., in Rommel and Tsvankin (2000) and Tsvankin (2001). If the propagation of the seismic wave is within symmetry planes of the anisotropic fabric, the group velocity and group angle can be given in compact form.…”

Section: Velocities In Orthorhombic Mediamentioning

confidence: 99%

Seismic wave propagation in anisotropic ice – Part 1: Elasticity tensor and derived quantities from ice-core properties

Diez

Eisen

2015

The Cryosphere

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Abstract.A preferred orientation of the anisotropic ice crystals influences the viscosity of the ice bulk and the dynamic behaviour of glaciers and ice sheets. Knowledge about the distribution of crystal anisotropy is mainly provided by crystal orientation fabric (COF) data from ice cores. However, the developed anisotropic fabric influences not only the flow behaviour of ice but also the propagation of seismic waves. Two effects are important: (i) sudden changes in COF lead to englacial reflections, and (ii) the anisotropic fabric induces an angle dependency on the seismic velocities and, thus, recorded travel times. A framework is presented here to connect COF data from ice cores with the elasticity tensor to determine seismic velocities and reflection coefficients for cone and girdle fabrics. We connect the microscopic anisotropy of the crystals with the macroscopic anisotropy of the ice mass, observable with seismic methods. Elasticity tensors for different fabrics are calculated and used to investigate the influence of the anisotropic ice fabric on seismic velocities and reflection coefficients, englacially as well as for the ice-bed contact. Hence, it is possible to remotely determine the bulk ice anisotropy.

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“…From these phase velocities we have to calculate the group velocities for the calculation of travel times. The calculation of the group velocity vector v g can be found, e.g., in Rommel and Tsvankin (2000) and Tsvankin (2001). If the propagation of the seismic wave is within symmetry planes of the anisotropic fabric, the group velocity and group angle can be given in compact form.…”

Section: Velocities In Orthorhombic Mediamentioning

confidence: 99%

Seismic wave propagation in anisotropic ice – Part 1: Elasticity tensor and derived quantities from ice-core properties

Diez¹,

Eisen²

2014

Preprint

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Abstract. A preferred orientation of the anisotropic ice crystals influences the viscosity of the ice bulk and the dynamic behaviour of glaciers and ice sheets. Knowledge about the distribution of crystal anisotropy, to understand its contribution to ice dynamics, is mainly provided by crystal orientation fabric (COF) data from ice cores. However, the developed anisotropic fabric does not only influence the flow behaviour of ice, but also the propagation of seismic waves. Two effects are important: (i) sudden changes in COF lead to englacial reflections and (ii) the anisotropic fabric induces an angle dependency on the seismic velocities and, thus, also recorded traveltimes. A framework is presented here to connect COF data with the elasticity tensor to determine seismic velocities and reflection coefficients for cone and girdle fabrics from ice-core data. We connect the microscopic anisotropy of the crystals with the macroscopic anisotropy of the ice mass, observable with seismic methods. Elasticity tensors for different fabrics are calculated and used to investigate the influence of the anisotropic ice fabric on seismic velocities and reflection coefficients, englacially as well as for the ice-bed contact. Our work, therefore, provides a contribution to remotely determine the state of bulk ice anisotropy.

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21. Analytic Description of P-Wave Ray Direction and Polarization in Orthorhombic Media

Cited by 7 publications

References 0 publications

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Seismology of Azimuthally Anisotropic Media and Seismic Fracture Characterization

Seismic wave propagation in anisotropic ice – Part 1: Elasticity tensor and derived quantities from ice-core properties

Seismic wave propagation in anisotropic ice – Part 1: Elasticity tensor and derived quantities from ice-core properties

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