Table of Contents
ISRN Geophysics
Volume 2013, Article ID 258492, 10 pages
http://dx.doi.org/10.1155/2013/258492
Research Article

Propagation and Attenuation of Elastic Waves in a Double Porosity Medium

1Department of Mathematics, M.D. University, Rohtak 124001, India
2Department of Mathematics, Government College Kalka, Kalka 133302, India

Received 5 December 2012; Accepted 26 December 2012

Academic Editors: G. Casula, H. Perroud, and A. Streltsov

Copyright © 2013 J. S. Nandal and T. N. Saini. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study solves the mathematical model for the propagation of harmonic plane waves in a dissipative double porosity solid saturated by a viscous fluid. The existence of three dilatational waves is explained through three scalar potentials satisfying wave equations. Velocities of these waves are obtained from the roots of a cubic equation. Lone shear wave is identified through a vector potential satisfying a wave equation. The displacements of solid particles are expressed through these four potentials. The displacements of fluid particles in pores and fractures can also be expressed in terms of these potentials. A numerical example is solved to calculate the complex velocities of four waves in a dissipative double porosity solid. Each of the complex velocities is resolved to define the phase velocity and quality factor of attenuation for the corresponding wave. Effects of medium properties and wave frequency are analyzed numerically on the propagation characteristics of four attenuated waves. It seems that and S waves are not very sensitive to the pore/fluids characteristics, except the fracture porosity. Hence, the recovery and analysis of slower (, ) waves become more desired to understand the fluid-rock dynamism in crustal rocks.