Reflection and refraction of plane waves at the boundaries of a fractured porous solid layer saturated with two immiscible fluids underlying a fluid half-space and overlying a thermo-elastic solid substrate

Abstract The present study investigates reflection and refraction of plane waves in a fractured porous solid(FPS), saturated with two immiscible fluids, a layer between fluid half-space(FHS) and thermoelastic half-space(TEHS). This model represents an oceanic layered system in which seawater is modelled as the fluid half-space, the oceanic crust is idealised as a fractured porous solid saturated with two immiscible fluids, and the thermally active upper mantle is modelled as a thermoelastic half-space, thereby providing a physically consistent framework for analysing wave propagation in marine environments.To the best of the authors’ knowledge, no previous study has investigated wave reflection and refraction in a layered configuration of a fractured porous solid layer saturated with two immiscible fluids, bounded by a fluid half-space and a thermoelastic half-space.The governing equations for the FPS layer are derived using volume averaging theory.For the thermoelastic half-space, a generalised compact form of constitutive equations is presented to encompass different thermoelastic theories available in the literature. Appropriate boundary and continuity conditions are imposed at both the FHS–FPS and FPS–TEHS interfaces. At the FHS–FPS interface, both open and closed boundary conditions are considered.The reflection and refraction coefficients are evaluated by solving a system of algebraic equations, and the corresponding energy ratios of the reflected and refracted waves are determined analytically. The effects of frequency, angle of incidence, FPS layer thickness, fracture volume fraction, matrix and fracture permeabilities, and the thermoelastic coupling parameter on the energy ratios are examined. The impacts of these parameters on wave propagation characteristics are explored through numerical computations. The model is validated through comparison with earlier studies.The proposed model has applications in ocean engineering, particularly in marine seismic imaging and subsurface characterisation of fractured seabeds for hydrocarbon exploration. It also aids in the understanding wave propagation across fluid–seabed–mantle systems, with implications for seabed stability and offshore structures