Abstract: Based on the fluctuation theory of elastic medium, the fluctuation equation of thermoviscoelastic medium is established by using the Kelvin-Voigt viscoelastic model, the equation of motion of viscoelastic medium and the generalized thermoelasticity theory. This approach considers soil viscosity and thermal effects. Then the dispersive characteristic equation of the body wave in the thermoviscoelastic medium is derived by introducing the displacement potential function of the solid-phase medium. Numerical calculations were performed to analyze the influence of thermophysical parameters, such as thermal expansion coefficient, medium temperature and relaxation time on the wave velocity and attenuation coefficient of thermoelastic waves. The results indicate significant differences in the wave velocity and attenuation coefficient of thermal elastomer waves under the three theoretical models: elastic theory, thermoelastic theory, and thermoviscoelastic theory. For each 0.5×10⁻³ s increase in relaxation time, the P-wave speed and attenuation coefficient increased by up to 5.18% and 34.67%, respectively; the S-wave speed and attenuation coefficient increased by up to 9.27% and 34.6%, respectively; and the T-wave speed and attenuation coefficient decreased by up to 2.18% and 2.24%, respectively. As frequency increases, the wave velocity and attenuation coefficient of each thermoelastic wave gradually increase. An increase in medium temperature results in higher P-wave and T-wave speeds and a higher P-wave attenuation coefficient. Specifically, for every 20 K increase in temperature, the P-wave speed and attenuation coefficient increase by approximately 3% and 2%, respectively. However, temperature changes do not affect the S-wave propagation characteristics and the T-wave attenuation coefficient. An increase in the thermal expansion coefficient leads to an increase in P-wave velocity and a decrease in T-wave velocity, significantly affecting the attenuation coefficients of both P-wave and T-wave. Additionally, heat flux and the phase delay time of the temperature gradient significantly influence the wave velocity and attenuation coefficient of the T-wave.

Key words: viscoelastic media, thermal effects, bulk waves, wave velocity, attenuation coefficient