A new approach to the problem of the Rayleigh wave propagation along the boundary of a non-homogeneous elastic body

Babich, V. M.; Kirpichnikova, N. Ya.

doi:10.1016/j.wavemoti.2004.05.002

Cited by 22 publications

(22 citation statements)

References 13 publications

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“…Therefore it can be used when solving transport equations for Rayleigh wave amplitudes numerically with a (seismic) ray tracing program, say. Formulas for the amplitudes of Rayleigh waves were given by in [Babich and Kirpichnikova 2004].…”

Section: The Isotropic Subprincipal Symbolmentioning

confidence: 99%

Rayleigh-type surface quasimodes in general linear elasticity

Hansen

2011

APDE

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Rayleigh-type surface waves correspond to the characteristic variety, in the elliptic boundary region, of the displacement-to-traction map. In this paper, surface quasimodes are constructed for the reduced elastic wave equation, anisotropic in general, with traction-free boundary. Assuming a global variant of a condition of Barnett and Lothe, the construction is reduced to an eigenvalue problem for a selfadjoint scalar first order pseudodifferential operator on the boundary. The principal and the subprincipal symbol of this operator are computed. The formula for the subprincipal symbol seems to be new even in the isotropic case.

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Section: The Isotropic Subprincipal Symbolmentioning

confidence: 99%

Rayleigh-type surface quasimodes in general linear elasticity

Hansen

2011

APDE

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“…Even for some sort of soil, the material properties also change dramatically with the depth when the soil layer has large thickness . Based on the theory of elasticity for single‐phase continuous media, many investigations on the propagation characteristics of Rayleigh waves in inhomogeneous media have been presented . Therefore, how non‐homogeneity of the solid skeleton can affect the propagation of Rayleigh waves is an important problem to be investigated.…”

Section: Introductionmentioning

confidence: 99%

Propagation of Rayleigh waves in fluid‐saturated non‐homogeneous soils with the graded solid skeleton distribution

Zhou

2016

Num Anal Meth Geomechanics

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Summary The propagation characteristic of Rayleigh waves in a fluid‐saturated non‐homogeneous poroelastic half‐plane is addressed. Based on Biot's theory for fluid‐saturated media, which takes the inertia, fluid viscosity, mechanical coupling, compressibility of solid grains, and fluid into account, the dispersion equations of Rayleigh waves in fluid‐saturated non‐homogeneous soils/rocks are established. By considering the shear modulus of solid skeleton variation with depth exponentially, a small parameter, which reflects the relative change of shear modulus, is introduced. The asymptotic solution of the dispersion equation expressing the relationship between the phase velocity and wave number is obtained by using the perturbation method. In order to analyze the effects of non‐homogeneity on the propagation characteristic of Rayleigh waves, the variation of the phase velocity with the wave number is presented graphically and discussed through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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“…See [1] and the references therein, where assumptions are introduced to insure uniqueness and existence of free surface waves.…”

Section: Introductionmentioning

confidence: 99%