Velocity-profile of torsional surface wave in a contorted watery-porous reservoir over a sand-dune deposit

•Velocity-profile of Torsional wave in a porous layer over sand-dune deposits have been found.•Single-step and double-step irregularity greatly influence phase velocity.•Heterogeneity varies as sinusoidal function, linear function, and cosine function of depth.•Biot's parameter, Initial stress in the layer, and the half-space affect the velocity marginally.•Higher magnitude velocity has been observed in RT irregularity compared to the RP interface. The current study aims to study the velocity profile of torsional surface waves in a three-layer model consisting of sand-dunes deposit sandwiched between the watery-porous layer and the orthotropic half-space. The top and the middle layers exhibit irregular interfaces employing various geometrical shapes such as parabolic, rectangular, and triangular notch. The main objective is to analyze the effect of these irregular interfaces on torsional wave propagation. Furthermore, the three-layer model involves inhomogeneity through gravity, initial stress, rigidity, and medium density. These inhomogeneity parameters, coupled with irregularity, bears a remarkable impact on the velocity-profile. The generalized dispersion relation has been derived, and one particular case has been deduced to validate the current work. Detailed numerical simulation has been performed to characterize the computations, and graphical illustrations have been exhibited to support the mathematical investigation.