Love-Type Wave Propagation in an Inhomogeneous Cracked Porous Medium Loaded by Heterogeneous Viscous Liquid Layer
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ORIGINAL PAPER
Love-Type Wave Propagation in an Inhomogeneous Cracked Porous Medium Loaded by Heterogeneous Viscous Liquid Layer Shishir Gupta1 • Rachaita Dutta1
•
Soumik Das1
Received: 5 March 2020 / Revised: 5 March 2020 / Accepted: 17 August 2020 Krishtel eMaging Solutions Private Limited 2020
Abstract Purpose 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. Methods 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. Results 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. Conclusions 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. Keywords Love-type wave Inhomogeneity Navier–Stokes equation Whittaker function Matrix porosity Fracture porosity
Introduction According to observational methodology, most of the rocks, earth materials and acoustic absorbent are often anisotropic, heterogeneous, porous and cracked. Due to earthquakes and heavy rainfall, the erosion process in mountains consisting of porous substances occurs. Those decayed rocks carried by rivers, waterfalls galvanise the creation of double porous layer above the Earth’s surface. & Rachaita Dutta [email protected] 1
Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, India
A dual porous rock basically inherits two types of porosities. One is primary or matrix porosity having low permeability. These matrix blocks cover a significant amount of total volume; whereas, the other type of porosity is named as fracture or secondary porosity with
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