Effects of Induced Stress on Seismic Waves: Validation Based on Ab Initio Calculations

Abstract

When a continuum is subjected to an induced stress, the equations that govern seismic wave propagation are modified in two ways. First, the equation of conservation of linear momentum gains terms related to the induced deviatoric stress, and, second, the elastic constitutive relationship acquires terms linear in the induced stress. This continuum mechanics theory makes testable predictions with regard to stress‐induced changes in the elastic tensor. Specifically, it predicts that induced compression linearly affects the prestressed moduli with a slope determined by their local adiabatic pressure derivatives and that induced deviatoric stress produces anisotropic compressional and shear wave speeds. In this article we successfully compare such predictions against ab initio mineral physics calculations for NaCl and MgO.

On the stress dependence of the elastic tensor

“…Firstly, no matter its functional form, A 1 can be shown to possess all the classical elastic symmetries, as required by eq.(2.55). Secondly, given that it is explicitly linear in the stress-perturbation, this theory is superficially rather close to those of Dahlen (1972b), Dahlen & Tromp (1998), Tromp & Trampert (2018) and Tromp et al (2019), discussed in Section 1. There are some important differences, though.…”

“…Because the theories lead to distinct observable behaviour, mineral physics experiments or ab initio calculations have the potential to distinguish between them (e.g. Tromp et al 2019). Nonetheless, it is not clear to the present authors that the resolution of this issue lies simply in finding a correct choice for these constants.…”

“…The anisotropy displayed by A 1 does not divide neatly into the sum of 'anisotropy due to applied stress' and 'anisotropy due to crystal structure', as we noted when discussing the general linearised elastic tensor eq.(3.41). Of those discussed previously, only the elastic tensor of Tromp et al (2019) contains cross terms between 'inherent anisotropy' and applied stress, but it does not contain enough explicit free parameters to be consistent with eq.(4.39). The free parameters of eq.…”

“…where Γ ijkl denotes the pressure-derivative of Γ ijkl , τ 0 ij is the deviatoric part of T 0 ij as given above, and the elastic tensor Λ ijkl can be Tromp et al (2019). As above, we have taken an isotropic material (slowness surface shown faintly on each plot) and applied a given, small deviatoric stress to it according to the theories of the respective authors.…”

Determination of stress in the geological medium on the basis of well data using acoustoelastic correlations

“…The influence of initial stress on the nature of the propagation of elastic waves in rocks and sands has been experimentally studied [Li, Tao, 2015;Teachavorasinskun, Pongvithayapan, 2016]. Another interesting variant of study of effects of initial stress is suggested [Tromp et al, 2019]. The main linear and nonlinear physico-mechanical properties of the geological medium, the kinematic parameters of elastic waves, and the main components of the stress tensor are analytically related to each other in acousto-elastic correlations in the NLA.…”