Acoustothermoelasticity for Joint Effects of Stress and Thermal Fields on Wave Dispersion and Attenuation

Abstract

AbstractThe stress field and thermal field are usually coupled in the Earth's subsurface. The mechanism of the joint effects of stress and thermal fields on wave propagation in rocks is not well understood. To fill this gap, this paper combines the acoustoelasticity theory with heat conduction theory to propose an acoustothermoelasticity mechanism to describe the joint effects of stress and thermal fields. The stress‐ and thermal‐dependent wave velocities and attenuation factors are formulated with 2‐D Fourier transform analysis for dynamic equations, which predict four wave modes of propagation including two longitudinal waves, namely, P wave and T (thermal) wave, and two shear waves, namely, fast S wave and second S wave. The stress‐induced anisotropy accounts for the S‐wave splitting phenomenon and T wave presents the thermal diffusive behavior, which depend on the magnitude and direction of stress and thermoelastic parameters. Stress and thermal effects on the wave velocity dispersion and attenuation are fully analyzed. Modeling results show that T wave is coupled with the P wave and fast S wave rather than the second S wave inducing the dissipation energy in the pre‐stressed thermoelastic rocks. The predicted wave velocities show reasonable agreement with ultrasonic laboratory measurements under uniaxial and triaxial stresses. Our model and results help to better understand mechanical properties and wave propagation in pre‐stressed thermoelastic rocks.