Mathematical modeling and analysis of Love wave propagation in fluid-saturated continuum with spring-membrane interfacial foundations

Numerous scientific studies and industrial fields, including geology, geophysics, mining, etc., rely heavily on seismic waves. Seismic wave analysis provides information that helps us better manage and use natural resources by enhancing our understanding of their structure. With this objective, this study presents a comprehensive mathematical model for Love-type seismic wave propagation in a transversely isotropic fluid-saturated poroelastic (TIFSP) layer bonded to an elastic half-space through spring–membrane interfacial foundations. More precisely, Classical (CL), Spring (SPR), Membrane (MBR), and Combined (CB) elastic foundation models are discussed. Implementing analytical mathematical techniques and complex continuity conditions across the different interfaces, the hyperbolic boundary value problem is solved, and the closed-form expressions of dispersion relations for all four models are obtained. The obtained dispersion relations are also reduced as special cases and matched with the results in the literature. Noteworthy influences of prevalent parameters such as anisotropy, porosity, spring constant, surface/interface Lame and density constants, etc., on Love wave phase velocity are examined graphically and discussed. The results demonstrate that spring–membrane interfacial foundations provide an effective mechanism for tailoring Love-wave dispersion in fluid-saturated media, offering valuable insights for subsurface sensing, geophysical waveguides, and engineered layered composites with imperfect interfaces.