Love-Type Wave Propagation in an Inhomogeneous Cracked Porous Medium Loaded by Heterogeneous Viscous Liquid Layer

Abstract

Love-type wave propagation through inhomogeneous dual porous layer has been investigated in this present article. The heterogeneous fluid-saturated dual porous stratum is bounded by a non-homogeneous viscous liquid layer and an isotropic half-space. Impacts of viscosity, inhomogeneity, matrix porosity along with fracture porosity have been calculated in detail. Navier–Stokes equation has been used to acquire the velocity component in heterogeneous viscous liquid layer. Separable variable method has been performed to convert partial differential equations into ordinary differential equations. Elimination of arbitrary constants from boundary conditions leads to complex dispersion relation of Love-type wave propagation. The complex equation consists of Whittaker functions and their derivatives which are expanded up to second term by approximating large parameters. Dispersion and attenuation equations of Love-type wave have been decoupled for implementing several graphs which illustrate reverberations of heterogeneity parameter, porosity, volume fraction of fractures, density on dispersive and damping nature of Love-type wave. Fundamental mode and higher modes of Love-type wave are observed through graphical execution. Effects of inhomogeneity parameters are also portrayed through surface plotting. Correlation of liquid layer and fractured porous layer in crustal region has been established both analytically and graphically which is also validated by applying particular conditions. Heterogeneity parameter, volume fraction of fractures, porosity, density have major impact on dispersion and attenuation of Love-type wave propagating in dual porous medium. This solid–liquid collaborative study unlocks a different area of future research.