Numerical Simulation and Uncertainty Quantification of Models for Coseismic Damage and Healing of Rocks in 1D, 2D and 3D

The instantaneous weakening of rocks during the passage of seismic waves has first been observed in laboratory experiments. The change of elastic rock moduli during and after the dynamic perturbations typically includes three phases – a gradual drop of moduli, a dynamically steady state and the recovery over a time scale that is larger than that of the perturbations. Such changes have been referred to as slow dynamics (Johnson and Sutin, 2005). With the development of the long-term continuous monitoring of the velocity field inside the Earth using methods such as ambient noise interferometry, coseismic rock weakening and post-seismic recovery of rock strength have also been recorded in the field over the past two decades. The question that we want to answer is: how relevant is the non-classical nonlinearity observed in the lab to the coseismic velocity drop in the field? To this end, we aim to adapt an analytical model that explains the lab observations and apply it to field observations using numerical simulations. Our first step is to identify the appropriate nonlinear model(s). Most of the proposed physical models that explain the phenomenon contain many parameters and are hard to constrain. Moreover, most of the existing physical models are restricted to 1D analysis and are difficult to generalize to 2D or 3D modeling.

 

We apply two models within the framework of the continuum damage mechanics: (i) the internal variable model (Berjamin et al., 2017) and (ii) the continuum damage model that accounts for parallel micro-cracks oriented perpendicular to the maximum tension or compression (Lyakhovsky et al., 1997). Both models can generalize to 2D and 3D. We formulate both models as nonlinear hyperbolic partial differential equations (PDEs) and solve them with the arbitrary high-order discontinuous Galerkin method using ExaHyPE (Reinarz et al., 2020) in 2D and 3D. We show that both models successfully reproduce the three phases during and after dynamic perturbations observed in the laboratory. We find that the continuum damage model can explain the amplitude- and frequency-dependent damage with a good match against the lab measurements. We also compare the simulation results using both models quantitatively with the observations in a 2D copropagating acousto-elastic testing (Feng et al., 2018). Our sensitivity analysis of the model parameters using the Markov chain Monte Carlo method quantitatively estimates the uncertainties and correlations among the parameters of both models. We believe our work paves the way towards a model of nonlinear rock deformation with slow dynamics that can be used in large scale 2D and 3D seismic wave propagation simulations for direct analysis of field observations, such as the Tohoku earthquake, 2011 (Brenguier et al., 2014).