Propagation of Torsional Surface Waves in a NonHomogeneous Crustal Layer over a Viscoelastic Mantle (original) (raw)
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Influence of rigid boundary on the propagation of torsional surface wave in an inhomogeneous layer
Journal of Earth System Science, 2015
The present work illustrates a theoretical study on the effect of rigid boundary for the propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. It is believed that the inhomogeneity in the half space arises due to hyperbolic variation in shear modulus and density whereas the layer has linear variation in shear modulus and density. The dispersion equation has been obtained in a closed form by using Whittaker's function, which shows the variation of phase velocity with corresponding wave number. Numerical results show the dispersion equations, which are discussed and presented by means of graphs. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close resemblance. It is also observed that, for a layer over a homogeneous half space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary, whereas it does at the free boundary. Graphical user interface (GUI) software has been developed using MATLAB 7.5 to generalize the effect of various parameter discussed.
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.
International Journal of Applied Mechanics and Engineering
The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.
Viscoelastic Waves in Layered Media
The Journal of the Acoustical Society of America, 2009
This book is a rigorous, self-contained exposition of the mathematical theory for wave propagation in layered media with arbitrary amounts of intrinsic absorption. The theory, previously not published in a book, provides solutions for fundamental wave-propagation problems in the general context of any media with a linear response (elastic or anelastic). It reveals physical characteristics for two-and three-dimensional anelastic body and surface waves, not predicted by commonly used models based on elasticity or one-dimensional anelasticity. It explains observed wave characteristics not explained by previous theories. This book may be used as a textbook for graduate-level courses and as a research reference in a variety of fields such as solid mechanics, seismology, civil and mechanical engineering, exploration geophysics, and acoustics. The theory and numerical results allow the classic subject of fundamental elastic wave propagation to be taught in the broader context of waves in any media with a linear response, without undue complications in the mathematics. They provide the basis to improve a variety of anelastic wave-propagation models, including those for the Earth's interior, metal impurities, petroleum reserves, polymers, soils, and ocean acoustics. The numerical examples and problems facilitate understanding by emphasizing important aspects of the theory for each chapter.
Latin American Journal of Solids and Structures
The present paper studies the Propagation of SH waves in a double non-homogeneous crustal layers lying over an isotropic homogeneous half-space, where upper layer ((i.e. rigidity and density varying trigonometrically with depth) and intermediate layer (i.e. rigidity and density varying parabolically with depth). The wave velocity equation has been obtained. Closed form solutions have been derived separately for the displacements in two non-homogeneous crustal layers and lower half-space. The dispersion curves are depicted by means of graphs for different values of non-homogeneity parameters and thickness ratio for layers.
Torsional surface waves in inhomogeneous elastic media
International Journal for Numerical and Analytical Methods in Geomechanics, 1984
The present work deals with torsional wave propagation in a linear gradient-elastic half-space. More specifically, we prove that torsional surface waves (i.e. waves with amplitudes exponentially decaying with distance from the free surface) do exist in a homogeneous gradient-elastic half-space. This finding is in contrast with the well-known result of the classical theory of linear elasticity that torsional surface waves do not exist in a homogeneous half-space. The weakness of the classical theory, at this point, is only circumvented by modeling the half-space as having material properties variable with depth (E.
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.
Procedia Engineering, 2017
The Present Paper devoted to investigate the effect of presence of rigid boundary on the propagation of torsional surface waves in a gravitating earth with a dry sandy medium under initial stress. The mathematical analysis of the problem has been dealt with the Whittaker function. Assuming the expansion of the Whittaker function up to linear term, it is concluded that the gravity field will always allow torsional waves to propagate in elastic and sandy medium under initial stress and rigid layer. Finally, it reveals that the sandy medium without support of a gravity field can not allow the propagation of torsional surface waves in presence of initial stress under rigid layer , where as the presence of a gravity field always supports the propagation of torsional surface waves regardless of whether the medium is elastic or dry sandy under rigid layer.
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.
Viscoelastic Love-Type Surface Waves
The general theoretical solution for Love-Type surface waves in viscoelastic media provides theoretical expressions for the physical characteristics of the waves in elastic as well as anelastic media with arbitrary amounts of intrinsic damping. The general solution yields dispersion and absorption-coefficient curves for the waves as a function of frequency and the amount of intrinsic damping for any chosen viscoelastic model. Numerical results valid for a variety of viscoelastic models provide quantitative estimates of the physical characteristics of the waves pertinent to models of Earth materials ranging from small amounts of damping in the Earth's crust to moderate and large amounts of damping in soft soils and water-saturated sediments. Numerical results, presented herein, are valid for a wide range of solids and applications.