Theoretical Analysis of Torsional Wave Propagation in a Heterogeneous Aeolotropic Stratum over a Voigt-Type Viscoelastic Half-Space

Abstract

The aim of this paper was to study the analytical problem of torsional surface wave propagation in an initially stressed heterogeneous aeolotropic layer over a Voigt-type viscoelastic half-space. It is known that an elastic homogeneous medium does not allow torsional surface waves to pass through it, whereas a viscoelastic medium does allow this. The closed-form solutions of the dispersion equation were derived by solving the displacement equations subject to sufficient boundary conditions. The derived analytical expressions were computed by considering an illustrative example. The study revealed that the heterogeneity, initial stress, directional rigidities, and internal friction all had significant effects on torsional wave propagation in the medium. Using the computational results, dependence of phase velocity on the wave number and time period was investigated. The variations were presented graphically. The study revealed that, because the medium tended to be elastic as the viscoelastic parameter decreased, the propagation of torsional waves faced considerable hindrance in spreading further. The study bears the promise of having important applications in the field of geodynamics, particularly in studies related to earthquakes and mechanical explosions in the interior of the earth.