RESUMEN
Temperature-induced variations of elastic moduli in solid media are generally characterized by a strong nonlinear dependence on temperature associated with complex deformations under thermal treatments. Conventional thermoelasticity with third-order elastic constants for the one-order temperature dependence has been extensively studied for crystals, but encountering problems of divergent and limited velocity variations for rocks as a polycrystal mixture, especially at high temperatures. The extension of the theory beyond high-order elastic constants to solid media is addressed in this article to describe the nonlinear temperature dependence of both elastic constants and wave velocities. The total strain is divided into the background component associated with temperature variations and the infinitesimal component induced by propagating waves. A third-order temperature dependence of velocity variations is formulated by taking into account fourth-order elastic constants. Applications to solid rocks (sandstone, granite, and olivine) demonstrate an accurate description of temperature-induced variations, especially for high temperatures. Unlike crystals, the synthetic averaging elastic constants for a solid rock (as a polycrystal mixture) change less than 10% with temperatures. The thermal sensitivity of P-wave velocities is much more than that of S-wave velocities over the vast majority of temperatures examined.
RESUMEN
Stress-induced velocity variations for porous rocks are generally characterized by a strong nonlinear dependence on stress associated with complex deformations under loading. The classical theory of poro-acoustoelasticity with high-order elastic constants is based on the Taylor expansion of the strain energy function, encountering problems of divergence and limitless elastic wave velocities in describing stress-associated velocity variations, especially for high effective stresses. The extension of the theory beyond the high-order elastic constants based on the Padé approximation to the strain energy function is addressed in this article. The resultant acoustoelastic constants are characteristics of a reasonable theoretical limit in elastic wave velocities with increasing effective stresses, avoiding some of the problems associated with high-order elastic constants such as decreasing moduli with increasing effective pressure at high effective pressure, possibly implying the microstructural dependence of elastic constants. That is, the loading stress increases strain energy and wave velocity, but also induces frame-related attenuation, which in turn reduces stiffness and elastic constants. The Padé nonlinear constants can be reduced for low effective stresses to the conventional acoustoelastic constants based on the Taylor expansion. Theoretical results are compared with ultrasonic measurements for a perfectly elastic crystal, topaz (Al2SiO4F2), and a porous rock, demonstrating that the Padé-approximation-based acoustoelasticity gives a more accurate description of stress-associated velocity variations, especially for higher effective stresses.
