Implications of general viscoelastic ray theory for anelastic geophysical models

The interaction of waves on deep water with spatially varying currents may be described by a ray theory, with the wave amplitudes determined by the principle of conservation of wave action (CWA). However, all previous deep water derivations of CWA are restricted to the case of an irrotational current. In this paper, both the ray theory and CWA are derived by a WKB method without the assumption of irrotationality. Also derived is a new equation for a spatially varying phase shift which is not predicted by the usual ray theory, and which, in general, displaces the positions of the wave crests by a distance on the order of a wavelength. This phase shift, which is caused by variations of the current velocity with depth, vanishes in the irrotational case, and so is in accord with the irrotational theory.

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Consequences of a Universal Cosmic-ray Theory for γ-ray Astronomy

Nature ◽

10.1038/241109b0 ◽

1973 ◽

Vol 241 (5385) ◽

pp. 109-110 ◽

Cited By ~ 25

Author(s):

A. W. STRONG ◽

A. W. WOLFENDALE ◽

J. WDOWCZYK

Keyword(s):

Cosmic Ray ◽

Ray Theory ◽

Γ Ray

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Dynamic properties of reflected and head waves near the critical point

Canadian Journal of Earth Sciences ◽

10.1139/e79-124 ◽

1979 ◽

Vol 16 (7) ◽

pp. 1388-1401 ◽

Cited By ~ 1

Author(s):

Larry W. Marks ◽

F. Hron

Keyword(s):

Exact Solution ◽

High Frequency ◽

Classical Problem ◽

Plane Boundary ◽

Head Wave ◽

Disk File ◽

Ray Theory ◽

Computational Point ◽

Spherical Waves ◽

Head Waves

The classical problem of the incidence of spherical waves on a plane boundary has been reformulated from the computational point of view by providing a high frequency approximation to the exact solution applicable to any seismic body wave, regardless of the number of conversions or reflections from the bottoming interface. In our final expressions the ray amplitude of the interference reflected-head wave is cast in terms of a Weber function, the numerical values of which can be conveniently stored on a computer disk file and retrieved via direct access during an actual run. Our formulation also accounts for the increase of energy carried by multiple head waves arising during multiple reflections of the reflected wave from the bottoming interface. In this form our high frequency expression for the ray amplitude of the interference reflected-head wave can represent a complementary technique to asymptotic ray theory in the vicinity of critical regions where the latter cannot be used. Since numerical tests indicate that our method produces results very close to those obtained by the numerical integration of the exact solution, its combination with asymptotic ray theory yields a powerful technique for the speedy computation of synthetic seismograms for plane homogeneous layers.

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