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.