Vol.26, Special Issue B, 2026, pp. S27–S32
https://doi.org/10.69644/ivk-2026-siB-0027 

The present article investigates the propagation of torsional waves through a two-layer structured inhomogeneous elastic medium, where material parameters rigidity and depth parameter z change, and so does density. A case-wise study is conducted for the upper inhomogeneous layer. In the first case, the variation of parameters is governed by a power-law model, while in the second case, it follows the outcome of a polynomial power and an exponential term. For the space in the lower half, the variation is modelled using the result of multiplying an exponential function by a linear function. A mathematical model is formulated based on the elastic theory of wave propagation. The technique for separating variables is employed in both layers to obtain the displacement fields. Applying intrinsic boundary conditions yields a closed-form expression regarding the frequency equation. The study reveals a significant influence of density and stiffness profiles on the torque-related phase velocity of torsional waves. Visual illustrations are provided to validate and support the observations obtained from the relationship of dispersion. The study may be helpful in geophysical exploration, seismic interpretation, and in understating wave propagation in complex surface structures.

The analysis exhibits that the presence of inhomogeneity in the medium greatly affects the propagation behaviour of torsional waves. It is observed that variations in the elastic parameters and density distribution have a noticeable impact on the phase velocity. The dispersion relation governing the propagation of torsional waves is derived in a compact form by evaluating the determinant of the coefficient matrix. The result obtained in the present work provides a theoretical framework for understanding the propagation of torsional wave in a layered heterogeneous geological structure.

Keywords: • inhomogeneous • half-space • torsional wave • phase velocity • dispersion equation