A COMPREHENSIVE THEORETICAL FRAMEWORK FOR SURFACE WAVE PROPAGATION IN LAYERED LIQUID–POROUS SYSTEMS WITH INCOMPRESSIBLE SATURATED CONSTITUENTS

Abstract

This investigation presents a comprehensive analysis of surface wave propagation in a multi-layered system consisting of a uniform liquid layer overlying a fluid-saturated incompressible porous half-space. The porous medium is modeled as a two-phase system using the theory of mixtures with incompressible constituents. A complex dispersion relation that connects phase velocity and attenuation coefficient with wave number is derived through rigorous mathematical formulation. Numerical simulations reveal distinct propagation characteristics across different modes, with the fundamental mode exhibiting minimal dispersion and attenuation while higher modes demonstrate strong dispersive behavior and significant energy dissipation. The presence of pore fluid is shown to substantially increase phase velocities compared to empty porous solids. Rayleigh-type surface waves at the
free surface are examined as a special case, demonstrating elliptical particle trajectories consistent with classical theory but modified by the two-phase nature of the medium. The results have a major bearing on geophysical exploration and nondestructive testing of saturated porous materials