Rayleigh-wave attenuation and shallow displacement response in saturated soils containing trapped nonwetting fluids: an oscillation-modified Biot framework

Rayleigh-wave attenuation, velocity dispersion, and shallow displacement response provide important information for geophysical characterization and dynamic-response assessment of fluid-bearing saturated porous formations. In multiphase subsurface media containing trapped nonwetting fluids, localized pore-throat-scale oscillations may introduce additional energy dissipation that is not explicitly captured by classical Biot-based Rayleigh-wave formulations, thereby limiting interpretation of dynamic responses in fluid-bearing formations relevant to geothermal energy and geological resource development. This study develops an oscillation-modified Biot framework to incorporate this mechanism into Rayleigh-wave analysis. A frequency-correction function derived from a pore-scale nonwetting-fluid oscillation model is introduced into the fluid-skeleton drag term of the Biot-type body-wave equations, from which the Rayleigh-wave dispersion equation for a saturated porous half-space is derived. The proposed formulation recovers the Rayleigh-wave solution derived from the classical Biot body-wave equations when localized oscillation effects are neglected. Numerical results show that trapped nonwetting-fluid oscillations affect Rayleigh-wave attenuation more strongly than phase velocity, especially in the medium-to-high-frequency range. Permeability, dissipation coefficient, and pore-throat geometry govern the locations and magnitudes of attenuation extrema, whereas nonwetting-fluid viscosity and density have secondary effects. Displacement analysis indicates that the oscillation-induced modification is mainly confined to the near-surface region. The framework establishes a mechanistic link between trapped-fluid oscillatory dissipation and Rayleigh-wave responses, enabling the analysis of attenuation, dispersion, and near-surface dynamics in fluid-bearing porous geomaterials relevant to geo-energy and subsurface resource development.