Dispersion of love waves in a spherical earth with corrugated surface (original) (raw)
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On the frequency equation for love waves due to abrupt thickening of the crustal layer
Geofisica Pura e Applicata, 1962
The effect of thickening of the crustal layer in mountainous region Gn the dispersion curve of Love waves has been studied. Perturbation method has been applied to obtain the modified frequency equation for Love waves through the surface of separation between a semi-infinite material and a layer the thickness of which abruptly increases throughout a certain length of the path. The effect is to decrease the phase velocity of the waves particularly in the low period range. It has been pointed out that by proper study, the amount of thickening may be obtained.
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.
Torsional wave propagation in Earth’s crustal layer under the influence of imperfect interface
Journal of Vibration and Control, 2014
In this paper, we study the propagation of a torsional surface wave in a homogeneous crustal layer over an initially stressed mantle with linearly varying directional rigidities, density and initial stress under the effect of an imperfect interface. Twelve different types of imperfect interface have been considered using triangular, rectangular and parabolic shapes. A variable separable technique is adopted for the theoretical derivations and analytical solutions are obtained for the dispersion relation by means of Whittaker function and its derivative. Dispersion equations are in perfect agreement with the standard results when derived for a particular case. The graph is self-explanatory and reveals that the phase velocity of a torsional surface wave depends not only on the wave number, initial stress, inhomogeneity and depth of the irregularity but also on the layer structure.
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.
Effect of Gravity and Magnetism on Surface Wave Propagation in Heterogeneous Earth Crust
Procedia Engineering, 2016
This paper aims to study the propagation of surface wave in two initially stressed heterogeneous magnetoelastic transversely isotropic media lying over a transversely isotropic half-space under the action of gravity. Heterogeneities of both the layers are caused due to exponential variation in elastic parameters. Dispersion relation is obtained in closed form by using Whittaker's asymptotic expansion. Magnetoelastic coupling parameters, heterogeneity, horizontal compressive initial stress and gravity parameters have remarkable effect on the phase velocity of surface wave. The obtained dispersion relation is found to be in well agreement with the classical Love-wave equation. Comparative study and graphical illustration has been made to exhibit the outcomes.
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.
Love and Rayleigh waves in non-uniform media
Geophysical Journal International, 2002
This paper is concerned with the dispersion of Love and Rayleigh waves in multilayered models with smooth and weakly non-parallel boundaries. Perturbation formulae for the phase, frequency, wavenumber, phase velocity, group velocity and amplitude are derived from ¢rst-order perturbation theory of Whitham's equation for dispersive waves in non-uniform media. Derivation of the average Lagrangian for Love and Rayleigh waves is obtained as required by the perturbation formulae. Explicit formulae are given for Love waves in the long-wavelength limit and comparisons with related studies are made. In order to demonstrate the results, numerical calculations for the perturbation in frequency, wavenumber, amplitude and phase are performed. The models consist of non-uniform media of one and two layers over a half-space. The perturbed parameter is the layer depth, sampled at di¡erent locations.
Linear waves on the spheroidal Earth
Dynamics of Atmospheres and Oceans, 2012
The Linearized Shallow Water Equations (LSWE) are formulated on an oblate spheroid (ellipsoid of revolution) that approximates Earth's geopotential surface more accurately than a sphere. The application of a previously developed invariant theory (i.e. applied to an arbitrary smooth surface) to oblate spheroid yields exact equations for the meridional structure function of zonally propagating wave solutions such as Planetary (Rossby) waves and Inertia-Gravity (Poinacré) waves. Approximate equations (that are accurate to first order only of the spheroid's eccentricity) are derived for the meridional structure of Poincaré (Inertia-Gravity) and Rossby (Planetary) and the solutions of these equations yield expressions in terms of prolate spheroidal wave functions. The eigenvalues of the approximate equations provide explicit expressions for the dispersion relations of these waves. Comparing our expressions for the dispersion relations on a spheroid to the known solutions of the same problem on a sphere shows that the relative error in the dispersion relations on a sphere is of the order of the square of spheroid's eccentricity (i.e. about 0.006 for Earth) for both Poincaré and Rossby waves.
Impact of pre-stress, inhomogeneity and porosity on the propagation of Love wave
Acta Geophysica, 2018
This work presents a mathematical modelling of Love wave transference through a pre-stress influenced anisotropic medium with heterogeneity between a sandy medium and an initially stressed anisotropic porous medium. Variable separation method has been induced in order to derive the frequency relation. Using appropriate boundary conditions at two interfaces, the dispersion equation has been obtained in its closed form. Possible particular cases are considered, and the corresponding results are consonant with the classical cases. Numerical computations have been employed to demonstrate the role of inhomogeneity factors, initial stresses and porosity, and are depicted by means of graphs which substantiates that those parameters immensely affect the Love wave velocity. In mineral prospecting and exploring technique in earth, the method and the results of this problem may be applicable.
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.