Abstract
A mathematical model is presented to explore the SH‐wave (horizontally polarized shear wave) propagation in a temperature‐dependent viscoelastic medium laid on a vertically heterogeneous elastic half‐space. Heterogeneity in the half‐space arises due to nth order depth variation in the elastic constants. Bessel's and Whittaker's functions have been used to derive the internal deformations. The expression of the complex frequency equation has been obtained with the aid of suitable boundary conditions. The decomposition of the complex frequency equation into real and imaginary parts provides dispersion and damping equations. These equations exhibited their reliance on the temperature ratio parameter, attenuation coefficient and dissipation factor due to viscoelasticity, heterogeneity and order of heterogeneity function. The impacts of the aforesaid parameters on the propagation of SH‐wave have been studied numerically and demonstrated by 2D/3D graphs.
A mathematical model is presented to explore the SH‐wave (horizontally polarized shear wave) propagation in a temperature‐dependent viscoelastic medium laid on a vertically heterogeneous elastic half‐space. Heterogeneity in the half‐space arises due to nth order depth variation in the elastic constants. Bessel's and Whittaker's functions have been used to derive the internal deformations. The expression of the complex frequency equation has been obtained with the aid of suitable boundary conditions.…