A comparative analysis (real-time data and theoretical results) for propagation of SH waves in a viscoelastic model influenced by a point source

Abstract

The propagation of SH waves in a heterogeneous viscoelastic layer lying over a heterogeneous viscoelastic half space from a point source is examined analytically. The significance of the heterogeneity of hyperbolic and exponential variations associated with rigidity, viscosity, and density is investigated mathematically. A dispersion equation and displacement components are computed in a compact form, considering the case that displacement and stress are continuous at the interface and stress vanishes on a free surface. The acquired dispersion equation signifies the relation between phase velocity and dimensionless wavenumber. The dispersion equation is highly influenced by heterogeneous parameters of both the layer and the half space. The dispersion equation is reduced to the classical equation of the Love wave after eliminating all the heterogeneous parameters, in agreement with pre-established results. The analysis uses the technique of Fourier transformation and Green’s function. The wavenumber is supposed to be complex, as the frequency is fixed in the viscoelastic model. Graphs are presented to demonstrate the effect of heterogeneous parameters on phase and damping velocity with respect to wavenumber.

Love‐like wave dispersion in a highly non‐homogeneous viscoelastic orthotropic layer under the effect of non‐local elasticity

“…Most of the above discussions and research publications are analyzed without any mentioned energy source, but the source of energy in the form of line or point sources also has been worked in seismic wave propagation. Alam et al [48] investigated Love-type wave dispersion in the magneto-viscoelastic layer; Kumhar et al [49], Kundu et al [50], Gupta et al [51], Chattopadhyay et al [52], and Manna et al [53] studied surface wave propagation due to an interior impulsive point source. In addition to the study of Love-type seismic surface waves, many authors have also explored Rayleigh-type seismic surface waves with the framework of non-local elasticity.…”