Abstract: In this study, a novel rock physics model is proposed to simulate the coupling effect of wave-induced ice viscosity and unfrozen water mobility, as well as temperature influences on physical properties in warm and ice-rich frozen soil, by combining the Burgers viscoelastic constitutive relation, the BISQ model, and thermodynamic theory. The analytical expressions of phase velocity and attenuation factor of fast P-waves, slow P-waves, and S-waves in this frozen soil are derived, which extend the description range of conventional elastic models. Through numerical examples, the basic response modes of phase velocities and attenuation factors for these three body waves are simulated and studied in the frequency domain. On this basis, the effects of model parameters such as soil porosity, ice viscosity, and temperature on wave propagation are analyzed and concluded. It is confirmed that the temperature can affect the velocity and attenuation of the fast P-wave on aspects of central frequencies and intensities; the slow P-wave has almost no temperature dependency; and the S-wave attenuation has a clear dependency at low frequencies. Under laboratory conditions, the applicability of new model is well verified by comparing the theory with the measured data of a warm, ice-rich, frozen soil sample.

Key words: frozen soil, viscoelastic porous media, elastic wave, dispersion and attenuation, temperature sensitivity