Mathematics and Computer Science, Volume 2

9Propagation of Seismic Waves in Porous Thermoelastic Semi-Infinite Space with Impedance Boundary Conditions

Annu Rani and Dinesh Kumar Madan^⋆

Department of Mathematics, Chaudhary Bansi Lal University, Bhiwani, Haryana, India

Abstract

This work investigates the waves propagation in an isotropic saturated porous-thermoelastic medium. The incidence of a seismic wave is considered at the free surface of a thermoelastic semi-infinite space. The surface of semi-infinite space is taken as isothermal. Reflection ratios of waves for the incidence of longitudinal waves are derived for impedance boundary conditions. The graph depicts the effect of porosity on reflection ratios versus incident angle and impedance parameter. Graph plotting is done with the help of the MATLAB programming language. Results are presented for a particular model in this paper.

Keywords: Porous, thermoelastic, reflection, impedance, isothermal

9.1 Introduction

Thermoelasticity is the study of the change in shape and dimension of a solid object when the temperature of the object varies. With the theory of elasticity, Madan et al. [1] and Kumari and Madan [2] explore the propagation of waves. By extending the classical coupled theory of thermoelasticity by introducing relaxation time, Lord and Shulman [3] and Green and Lindsay [4] presented the generalized theory of thermoelasticity. A number of researchers [5–11] have discussed the phenomena of waves reflecting on a free surface. Rani and Madan [12] investigated ...