Love-type wave propagation in a coated fluid-saturated fractured poro-viscoelastic layer with sliding contacts and point source effect

Abstract

The present paper studies Love-type wave propagation in a fluid-saturated fractured poro-viscoelastic layer sandwich between a coated elastic layer and a non-homogeneous anisotropic Voigt-type viscoelastic half-space. The interfaces between the layers and the half-space are considered as sliding contacts with two different sliding parameters. An impulsive point source is located at a varying depth in the intermediate poro-viscoelastic layer in the form of the Dirac-delta function. The vertical non-homogeneity in the half-space is assumed to be a combination of linear and exponential functions that vary with depth in the medium. Using the Fourier transforms and Green's functions, the equations of motion, in the form of partial differential equations, are solved analytically. An appropriate boundary condition is used to accomplish this. The closed form of the complex dispersion equation has been obtained by assuming that the wavenumber is in the form of a complex quantity. The validity of our model has been examined using several specific cases and compared to the classical Love wave equation. Numerical and graphical analyses of dispersion and displacement were performed using MATLAB software. It has been found that a single porous medium has a higher Love-type phase velocity than a double porous medium. Additionally, the sliding parameters increase the range of wavenumber when there is no phase velocity. An inverse relationship was found between the depth of the point source and the particle displacement in the coated layer. In addition to contributing to our understanding of geophysical phenomena and subsurface explosions, these findings may provide insight into the inner structure of the planet.