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1

Impact of Inhomogeneity on SH-type Wave Propagation in an Initially Stressed Composite Structure

Saha S., Chattopadhyay A., Singh A. K.

Acta Geophysica

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2018

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Vol. 66, no. 1

1--19

EN

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

2

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

Kumari N., Chattopadhyay A., Singh A. K., Sahu S. A.

Acta Geophysica

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2017

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Vol. 65, no. 1

189--205

EN

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.

3

Effect of Corrugation and Reinforcement on the Dispersion of SH-wave Propagation in Corrugated Poroelastic Layer Lying over a Fibre-reinforced Half-space

Singh A. K., Das A., Lakshman A., Chattopadhyay A.

Acta Geophysica

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2016

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Vol. 64, no. 5

1340--1369

EN

The presence of porosity and reinforcement in a medium is an important factor affecting seismic wave propagation and plays vital role in many geophysical prospects. Also, the presence of salt and ore deposits, mountains, basins, mountain roots, etc. is responsible for the existence of corrugated boundary surfaces of constituent layers. Such facts brought motivation for the present paper which deals with the propagation of SHwave in a heterogeneous fluid-saturated poroelastic layer with corrugated boundaries lying over an initially stressed fibre-reinforced elastic halfspace. Closed form of dispersion relation has been obtained and is found in well agreement to classical Love wave equation for isotropic case. The effect of corrugation, wave number, undulation, position parameter, horizontal compressive/tensile initial stress and heterogeneity on phase velocity has been analysed through numerical computation and graphical illustration. Moreover, comparative study exploring the effect of presence and absence of reinforcement in half-space on dispersion curve is the major highlight of the current study.

4

Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

Chattopadhyay A., Gupta S., Kumari P., Sharma K.

Acta Geophysica

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2012

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Vol. 60, no. 1

119-139

EN

The present paper is concerned with the propagation of shear waves in a homogeneous viscoelastic isotropic layer lying over a semi-infinite heterogeneous viscoelastic isotropic half-space due to point source. The inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of shear waves has been obtained using Green's function technique. The dimensionless angular frequency has been plotted against dimensionless wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves. graphical user interface (GUI) software in MATLAB has been developed to show the effect of various inhomogeneity parameters on angular frequency. The topic can be of interest for geophysical applications in propagation of shear waves on the Earth’s crust.

5

Propagation of shear waves in viscoelastic medium at irregular boundaries

Chattopadhyay A., Gupta S., Sharma V.K., Kumari P.

Acta Geophysica

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2010

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Vol. 58, no. 2

196-214

EN

The aim of the paper is to study the shear wave propagation in a viscoelastic layer over a semi-infinite viscoelastic half space due to irregularity in the viscoelastic layer. It is of great interest to study the propaga-tion of shear waves in the assumed medium having a non planar boundary due to its similarity to most of the real situations. The perturbation method is applied to find the displacement field. The effect of complex wave number on dissipation factor is analysed. Finally, as an application, the result obtained has been used to get the reflected field in viscoelastic layer when the shear wave is incident on an irregular boundary in the shape of parabolic irregularity as well as triangular notch. It is observed that the amplitude of this reflected wave decreases with increasing length of the notch, and increases with increasing depth of the irregularity.

6

Comment on "calculation of reflection and transmission coefficients for qP waves incident on a planar interface between isotropic and triclinic media" by L. Li

Chattopadhyay A.

Acta Geophysica

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2008

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Vol. 56, no. 4

1202-1204

7

Reflection and refraction of waves at the interface of an isotropic medium over a highly anisotropic medium

Chattopadhyay A., Rajneesh H.

Acta Geophysica

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2006

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Vol. 54, no. 3

239-249

EN

In this paper, we have considered the reflection and refraction of a plane wave at an interface between two half-spaces. The lower half-spaces is composed of highly anisotropic triclinic crystalline material and the upper half-space is homogeneous and isotropic. It has been assumed that due to incidence of a plane quasi-P (qP) wave, three types of waves, namely, quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH), will be generated in the lower half space whereas P and S waves will be generated in the upper half space. The phase velocities of all the quasi waves have been calculated. It has been assumed that the direction of particle motion is neither parallel nor perpendicular to the direction of propagation. Some specific relations have been established between directions of motion and propagation, respectively. The expressions for reflection coefficients of qP, qSV, qSH and refracted coeffi-cients of P and SV waves are obtained. Results of reflection and refraction coeffi-cients are presented.

8

Reflection and refraction of quasi-SV waves at the interface of the monoclinic media

Chattopadhyay A., Saha S.

Acta Geophysica Polonica

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1999

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Vol. 47, nr 3

307-322

EN

Reflection and refraction phenomena of quasi-SV waves at a plane interface of two monoclinic half-spaces have been discussed. It has been pointed out that due to incident quasi-SV wave in a monoclinic medium, the three types of waves exist: quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH). The reflection and refraction coefficients for qP, qSV and qSH waves have been computed. The effects due to the crystalline nature of the medium have been distinctly marked. The results are presented graphically and compared with the isotropic case.