Classical third-order thermoelastic constants are generally formulated by the theory of small-amplitude acoustic waves in cubic crystals during heat treatments. Investigating higher-order thermoelastic constants for higher temperature is a challenging task because of more undetermined constants involved. However, even at low temperatures, these Taylor-type thermoelastic constants encounter divergence in characterizing the temperature-dependent velocity changes of elastic waves in solid rocks as a complete polycrystal compound of different mineral lithologies. Therefore, we propose third-order Padé-type thermoelastic constants derived by the approximation of Padé rational function to the total strain energy. The Padé thermoelastic constants are characteristics of a reasonable theoretical prediction for acoustic velocities of solid rocks even at high temperature. The results demonstrate that the third-order Padé thermoelasticity can characterize thermally induced velocity changes more accurately than the conventional third-order Taylor thermoelasticity, and have the same accuracy for the corresponding higher-order thermoelastic model. The Padé approximation could be considered a more versatile model for describing thermal velocity changes for polycrystals and solid rocks. The physics of the Padé coefficients is relevant to the thermal expansion mismatch and thermally induced deformation of microcracks. Introduction Temperature significantly changes the mechanical and physical properties of rocks, which becomes importance in many fields of earth sciences and geological engineering. Temperature-induced variations in elastic properties generally present strong nonlinearity even at low temperature because of the differential thermal expansion of multimineral rocks. The classical theory of thermoelasticity is formulated on account of the Taylor power series of the Helmholtz free energy functions (Dillon, 1962). The resulting second- and third-order thermoelastic constants have been widely used for crystals, but with certain insufficiencies in representing the temperature-dependent velocity changes of elastic waves for rocks like a completely polycrystal compound of varying mineral lithologies. The investigation of higher-order thermoelastic constants could be useful for understanding the nature of nonlinear behavior in heating rocks, but involves more undetermined constants and becomes a challenging task. As a more effective alternative, this article addresses a nonlinear thermoelasticity for solid rocks relied on the Padé approximation of Helmholtz free energy functions.

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Insight into wave propagation in prestressed media is of importance to geophysical applications such as monitoring changes in geopressure and tectonic stress. This issue can be approached by the theory of acoustoelasticity that accounts for nonlinear strain responses due to stresses of finite magnitude. In this study, a rotated staggered-grid finite-difference (RSG-FD) method with an unsplit convolutional perfectly matched layer (CPML) absorbing boundary is used to solve the relevant acoustoelastic equations with third-order elastic constants for elastic wave propagation in prestressed media. Numerical acoustoelasticity simulations for wave propagation in single- and double-layer models are performed under four states of prestresses, confining, uniaxial, pure-shear, and simple-shear. The results display the effective anisotropy of elastic wave propagation in acoustoelastic media, illustrating that the prestress-induced velocity anisotropy is of orthotropic features that are strongly related to the orientation of prestresses. These examples demonstrate the significant impact of prestress conditions on seismic responses in both phase and amplitude. Introduction The impact of prestressed zones on seismic waves is an important issue that affects the interpretation of the results by seismic imaging and inversion. It is well known that acoustic velocities in rocks are sensitive to prestresses. The theory of acoustoelasticity, as an extension of the classical theory of elasticity, is set up under the framework of hyperelasticity (Shams et al., 2011). The theory relates elastic moduli to prestresses (or residual stresses) in solids (Pao and Gamer, 1985), resulting in an effective anisotropy for wave propagation in acoustoelastic media. It has been used to account for stress-induced velocity variations in rocks (Johnson and Shankland, 1989), therefore perhaps providing the potential to understand the acoustic response to in-situ stresses (Sinha and Kostek, 1996; Huang et al., 2001) and, in turn, to monitor changes in geopressure and tectonic stress. Theoretical and experimental investigations of acoustoelasticity for wave propagation in prestressed rocks have made great signs of progress, but with limited literature on numerical simulations for acoustoelastic wave propagation. As a useful complement to the theoretical solutions of acoustoelastic equations, numerical acoustoelasticity simulations are thought to provide further insights into the stress-induced variations in velocity and anisotropy.