Modeling of Love-type wave propagation in a fractional poro-viscoelastic layer over a viscoelastic-to-elastic half-space, induced by a Gaussian source

This study presents a mathematical model for the propagation of Love-type surface waves generated by a Gaussian distributed source in a poro-viscoelastic layer that lies above a viscoelastic-to-elastic half-space. The model incorporates memory-dependent fractional viscoelasticity using Riemann–Liouville derivatives to more accurately represent time-dependent mechanical behavior. The governing equations for wave motion are derived for both the layered and half-space media, taking into account poroelastic interactions and spatial variations in material properties. Using Fourier and Green’s function techniques, dispersion relations are derived and analyzed. Numerical simulations examine the influence of various parameters, including heterogeneity factors, fractional memory indices and the characteristics of the Gaussian source, on the dispersion characteristics of the Love-type waves. To extend these findings to structural implications, a single-degree-of-freedom oscillator model is employed and Monte Carlo simulations are carried out to compare oscillator responses excited by Gaussian versus point sources. The combined analysis of dispersion phenomenon and oscillator response highlights the dominant role of the fractional memory parameters of the top poro-viscoelastic layer in controlling the maximum amplitude and the vibration duration of the oscillator. By linking wave dispersion with oscillator dynamics, this framework bridges source–medium characterization and structural response, underscoring that explicit inclusion of fractional viscoelasticity is essential for accurate seismic hazard modeling and reliable estimation of structural demands.