A Pump-Probe Analysis of Nonlinear Elastic Behavior in Oklahoma

Fracture networks in the subsurface influence nearly every aspect of earthquakes and natural hazards. These aspects, including stress, permeability and material failure, and are important for hazard assessment. However, our ability to monitor fracture behavior in the Earth is insufficient for any type of decision-making regarding hazard avoidance. I propose a new method for probing the evolution of fracture networks in situ to inform public safety decisions and understand natural systems.

In heterogeneous, fractured materials, like those found in the Earth, the relationship between stress and strain is highly nonlinear. This nonlinearity in the upper crust is almost entirely due to fractures. By measuring to what extent Earth materials exhibit nonlinear elastic behavior, we can learn more information about them. Directly, measuring physical properties may be more useful than just detecting that fractures are present or how they are shaped and oriented. I measure nonlinearity by measuring the apparent modulus at different strains.

Currently, principal stress orientations are measured or modeled using earthquake focal mechanisms, or borehole based measurements. In this study I use a pump-probe analysis, which involves continuously probing velocity (as a proxy for modulus) while systematically straining the material. I use solid Earth tides as a strain pump and empirical Green's functions (EGF) as a velocity probe. I apply this analysis to north-central Oklahoma because the stress field is important to oil and gas operations and associated hazards. I find evidence that azimuthal behavior of nonlinear behavior is correlated with the principal stress orientations. Faults whose strikes are aligned with the maximum (compressive) horizontal stress have stronger nonlinear behavior than faults whose strikes are aligned with the minimum (compressive) horizontal stress. Principal stress orientations are important to understanding fracture generation and fault activation.