Propagation of Love-Type Wave in Porous Medium over an Orthotropic Semi-Infinite Medium with Rectangular Irregularity

Pramod Kumar Vaishnav,Anup Saha,Shishir Gupta,Santimoy Kundu

doi:10.1155/2016/2081505

Pramod Kumar Vaishnav, Anup Saha + Show 2 more

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https://doi.org/10.1155/2016/2081505

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Abstract

Propagation of Love-type wave in an initially stressed porous medium over a semi-infinite orthotropic medium with the irregular interface has been studied. The method of separation of variables has been adopted to get the dispersion relation of Love-type wave. The irregularity is assumed to be rectangular at the interface of the layer and half-space. Finally, the dispersion relation of Love wave has been obtained in classical form. The presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves in porous medium bounded below by an orthotropic half-space. The scientific effect of porosity, irregularity, and initial stress in the phase velocity of the Love-type wave propagation has been studied and shown graphically.

Highlights

The Earth contains fluid-saturated porous rocks on or below its surface in the form of sandstone and other sediments permeated by groundwater or oil; the diffusion of fluid and readjustment of fluid pressure have been acting as a triggering mechanism for earthquakes
It has been noticed that the presence of porosity, irregularity, and initial stress in the dispersion equation approves the significant effect of these parameters in the propagation of Love-type waves
We have considered a model consisting of initially stressed porous layer of finite thickness H overlying an orthotropic half-space with irregular interface

Summary

Introduction

The Earth contains fluid-saturated porous rocks on or below its surface in the form of sandstone and other sediments permeated by groundwater or oil; the diffusion of fluid and readjustment of fluid pressure have been acting as a triggering mechanism for earthquakes. The current work is concerned with the propagation of Love-type waves in initially stressed porous layer overlying semi-infinite orthotropic medium with irregular interface. Abo-Dahab et al [6] discussed the rotation and magnetic field effect on surface waves propagation in an elastic layer lying over a generalized thermoelastic diffusive half-space with imperfect boundary. Ahmed and Abo-Dahab [7] pointed out the propagation of Love waves in an orthotropic granular layer under initial stress overlying a semi-infinite granular medium. We use the porous medium (layer) over an orthotropic half-space with the effect of irregular interface in the propagation of Love-type waves. The main attention is paid to the influence of irregularity of interface, porosity, and initial stress on the propagation of Love-type waves in porous-orthotropic medium (Figure 1). It is useful for the study of seismic waves generated by artificial explosions

Mathematical Formulation of the Problem

Solution of the Initially Stressed Porous Layer

Solution of Orthotropic Half-Space

Particular Cases

Numerical Calculations and Discussions

Conclusions