Love-type surface wave propagation due to interior impulsive point source in a homogeneous-coated anisotropic poroelastic layer over a non-homogeneous extended substance

Abstract

The paper is concerned with the effect of an impulsive point source on the Love-type surface wave propagation in an anisotropic poroelastic medium coated with an isotropic homogeneous thin layer over an infinite extent anisotropic non-homogeneous substance. The material properties of both the layer and extended medium are restricted on linear elasticity. Also, the transmissions of waves are considered as usually incidental transient. Infinitely extended medium is considered highly non-homogeneity with rigidity and density, which varies exponentially with depth. The closed-form equation of motion is formulated in each layered media depending on the conditional property of the surface seismic wave. Due to the presence of an impulsive point source at the interface of the intermediate layer and infinitely extended layer, a force density distribution function in the form of the Dirac-delta function is performed with the equations of motion. Green's function approach is demonstrated to obtain the closed-form dispersion relation of the Love-type wave. Attenuation analysis and numerical error analysis of the dispersive wave are performed for the complex quantity of the wavenumber and error percentage of the main dispersion. The validity of the Love-type dispersive wave is examined with the help of some particular cases. The theoretical prediction of phase and group velocities are illustrated numerically using MATLAB software. A short movie (link) of group velocity is created to show the changes of wave amplitude with porosity. It is observed that the phase/group velocity is highly affected by porosity, non-homogeneity, anisotropy, thickness of the layer, coated layer and attenuation coefficient. The derivation and analysis of the structural model bear the promise of having important applications in the field of seismology and civil engineering, particularly in the studies related to earthquakes and mechanical explosions on the near-surface of the Earth.