Love and Rayleigh waves in non-uniform media (original) (raw)
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Dispersion of love-type waves in a vertically inhomogeneous intermediate layer
Journal of Physics of the Earth, 1990
The problem of excitation of Love-type waves in an inhomogeneous layer lying between two half-spaces is studied. Using the Fourier transform and Green's function method, the dispersion relation for propagation of such waves is derived. Finally, the transmitted wave in the layer is presented.
Journal of Vibration and Control, 2014
The present paper deals with the effect of point source on the propagation of Love wave in a heterogeneous layer and inhomogeneous half-space. The upper heterogeneous layer is caused by consideration of exponential variation in rigidity and density. Also in half-space inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of Love wave has been obtained by using Green’s function technique. As a special case when the upper layer and lower half-space are homogeneous, our computed equation coincides with the general equation of Love wave. The propagation of Love waves are influenced by inhomogeneity parameters. The dimensionless phase velocity has been plotted against the dimensionless wave number for different values of inhomogeneity parameters. We have observed that the velocity of wave increases with the increase of inhomogeneity parameters.
Attenuation dispersion of Love waves in a two-layered half space
Wave Motion, 1995
The attenuation of dispersive Love waves in an anelastic two-layered half space and in a simple symmetric homogeneous three-layered model has been investigated by introducing the complex propagation functions into the known explicit dispersion relation. A frequency-dependent attenuation relation is explicitly given assuming that the media quality factors are constant. The resultant quality factor of Love waves depends not only on the frequency, but also on the layer depth, via media quality factors. The attenuation coefficient of the Love waves becomes therefore a non-linear function of the frequency. The result is consistent with the results given in the literature on seismology and in-seam seismics. It is known that the spectral ratio method can only be used to estimate the frequency-independent quality factor. Therefore, a modification of the spectral ratio method is presented to invert the frequency-dependent quality factor of Love-waves. The modification facilitates investigations of frequencydependent quality of the medium over previous methods.
Geophysical Journal International, 2015
The dispersion of interface waves is studied theoretically in a model consisting of a liquid layer of finite thickness overlying a transversely isotropic solid layer which is itself underlain by a transversely isotropic solid of dissimilar elastic properties. The method of potential functions and Hankel transformation was utilized to solve the equations of motion. Two frequency equations were developed: one for Love waves and the other for the remaining surface and interface waves. Numerical group and phase velocity dispersion curves were computed for four different classes of model, in which the substratum is stiffer or weaker than the overlying layer, and for various thickness combinations of the layers. Dispersion curves are presented for generalized Rayleigh, Scholte, Stoneley and Love waves, each of which are possible in all proposed models. They show the dependence of the velocity on layer thicknesses and material properties (elastic constants). Special cases involving zero thickness for the water layer or the solid layer, and/or isotropic material properties for the solid exhibit interesting features and agree favourably with previously published results for these simpler cases, thus validating the new formulation.
Dispersion of zero-frequency Rayleigh waves in an isotropic model ‘Layer over half-space’
Geophysical Journal International, 2008
A simple analytic formula for the derivative of the phase velocity of zero-frequency Rayleigh waves in a thin layer over a half-space is presented. It allows to classify the dispersion of these waves in a simple manner. The influence of the different elastic parameters is studied. These formulas may have practical applications in the laboratory and may be useful for theoretical considerations including the inversion of dispersion curves.
Dispersion of Love Waves in a Composite Layer Resting on Monoclinic Half-Space
Journal of Applied Mathematics, 2011
Dispersion of Love waves is studied in a fibre-reinforced layer resting on monoclinic half-space. The wave velocity equation has been obtained for a fiber-reinforced layer resting on monoclinic half space. Shear wave velocity ratio curve for Love waves has been shown graphically for fibre reinforced material layer resting on various monoclinic half-spaces. In a similar way, shear wave velocity ratio curve for Love waves has been plotted for an isotropic layer resting on various monoclinic half-spaces. From these curves, it has been observed that the curves are of similar type for a fibre reinforced layer resting on monoclinic half-spaces, and the shear wave velocity ratio ranges from 1.14 to 7.19, whereas for the case isotropic layer, this range varies from 1.0 to 2.19.
Travelling Waves in Nonconservative Media With Dispersion
this paper I will consider nonlinear wave phenomena in nonconservative media with dispersion. The keywords dispersion, nonlinearity, and force field will be emphasised. The dispersion effects are of importance when considering wave propagation in layered elastic media [1] or gravitational surface waves of water [2]. The main characteristic of a dispersive wave is that its velocity depends on its length. Wave process problems, where nonlinear effects can be neglected, are in principle always solvable by the linear theory. However, there are important physical phenomena, where nonlinear effects cannot be neglected. Characteristic in purely nonlinear wave phenomena is the occurrence of shock waves. When considering the dispersive and nonlinear effects together, solitary waves may occur. The most well-known example, modelling wave processes with dispersion and nonlinearity, i.e. in a conservative system, is the Korteweg-de Vries (KdV) equation
Applied Mathematics and Computation, 1999
In this paper, Love waves in a non-homogeneous orthotropic elastic medium under changeable initial stress has been studied. Fourier transform method has been applied to ®nd the dispersion equation. It has been shown that the velocity of Love waves lies between two quantities which are dependent on the non-homogeneities of two media. When the medium is isotropic and the initial stress is absent, the dispersion equation obtained is in agreement with the corresponding results. The eect of non-homogeneity and the initial stress are illustrated by ®gures.
International Journal of Solids and Structures, 2014
The paper investigates the existence of Love wave propagation in an initially stressed homogeneous layer over a porous half-space with irregular boundary surfaces. The method of separation of variables has been adopted to get an analytical solution for the dispersion equation and thus dispersion equations have been obtained in several particular cases. Propagation of Love wave is influenced by initial stress parameters, corrugation parameter and porosity of half-space. Velocity of Love waves have been plotted in several figures to study the effect of various parameters and found that the velocity of wave decreases with increases of non-dimensional wave number. It has been observed that the phase velocity decreases with increase of initial stress parameters and porosity of half-space.