Wave propagation in unsaturated thermoporoelastic media based on a modified fractional Cole-Cole model

Accurate modeling of wave propagation in unsaturated thermoporoelastic media is essential for understanding seismic responses in heterogeneous reservoirs, geothermal exploration, and heavy oil recovery processes. Existing models based on the classical Lord-Shulman generalized thermoporoelastic theory employ a single relaxation mechanism, which cannot adequately describe broadband dispersion and attenuation caused by complex pore structures and multiphase fluid interactions. In this study, a modified fractional Cole-Cole model is introduced into the theoretical framework of unsaturated thermoporoelasticity to characterize frequency-dependent relaxation behavior. The governing equations of the unsaturated thermoporoelastic medium are first established by considering the coupled interactions among the solid skeleton, pore liquid, pore gas, and thermal field. Subsequently, numerical simulations are performed to examine the effects of fractional parameter, porosity, saturation, and permeability on wave dispersion and attenuation characteristics. Results demonstrate that the fractional Cole-Cole model provides a more accurate description of broadband relaxation behavior than the L-S model by capturing the heterogeneity of porous media. The fractional parameter controls the width and distribution of attenuation spectra, while porosity, saturation, and permeability significantly regulate the phase velocity and attenuation characteristics of different wave modes.