Describing stress-dependent elasticity and wave propagation – new insights & connections between approaches

To establish a consistent framework for seismic wave propagation that honors the effects of stress changes, it is critical that we take into account different types of stress measures and their corresponding effects on seismic quantities (e.g., velocities) as dictated by continuum mechanics. Revisiting this theoretical foundation, we discuss connections among existing theories that describe the variation of elastic moduli with effective stress. We show that there is a direct connection between predicting stress-induced elastic changes with the well-known third-order elasticity tensor and the recently-proposed adiabatic pressure derivatives of elastic moduli. Each of these approaches, however, have different qualities and shortcomings both in terms of experimental validation as well as in their use in, e.g., waveform inversion. In addition, we investigate the connection with another general approach that relies on micromechanical structures (e.g., cracks and pores): while it can only be done algebraically, this connection remains unclear as to which type of stress measure and which corresponding constitutive relation should be considered in practical scenarios. We support our analysis with validations on previously published, benchmark experimental data.