Dynamic perturbations reveal unconventional nonlinear behavior in rocks, as evidenced by field and laboratory studies. During the passage of seismic waves, rocks exhibit a decrease in elastic moduli, slowly recovering after. Yet, comprehensive physical models describing these moduli alterations remain sparse and insufficiently validated against observations. Here, we demonstrate the applicability of two physical damage models-the internal variable model (IVM) and the continuum damage model (CDM)-to provide quantitative descriptions of nonlinear co-seismic elastic wave propagation observations. While the IVM uses one internal variable to describe the evolution of elastic material moduli, the CDM damage variable is a mathematical representation of microscopic defects. We recast the IVM and CDM models as nonlinear hyperbolic partial differential equations and implement 1D and 2D numerical simulations using an arbitrary high-order discontinuous Galerkin method. We verify the modeling results with co-propagating acousto-elastic experimental measurements. Subsequently, we infer the parameters for these nonlinear models from laboratory experiments using probabilistic Bayesian inversion and 2D simulations. By adopting the Adaptive Metropolis Markov chain Monte Carlo method, we quantify the uncertainties of inferred parameters for both physical models, investigating their interplay in 70,000 simulations. We find that the damage variables can trade off with the stress-strain nonlinearity in discernible ways. We discuss physical interpretations of both damage models and that our CDM quantitatively captures an observed damage increase with perturbation frequency. Our results contribute to a more holistic understanding of co-seismic damage and post-seismic recovery after earthquakes bridging the worlds of theoretical analysis and laboratory findings. Rocks react to earthquakes by softening when seismic waves-the energy released by earthquakes-pass through them. Observations of such rock softening during the passage of seismic waves are common both in the laboratory and in the field. Interestingly, rocks gradually harden again once the shaking stops. Different physical mechanisms have been proposed to explain the observations. In this study, we put two existing theories to the test. One assumes that a term in the internal energy of the material increases with damage accumulation, while the other incorporates the opening and closing of micro-cracks. We implement them into a powerful simulation program called ExaHyPE. This allows us to model how nonlinear waves move through rocks. When we compare the computer simulation outcomes with real laboratory tests, we find that both models match what we see in reality. Studying thousands of simulations with different model parameters, we find some intriguing insights. For instance, the initial state of strain and the tiny cracks that open and close within the rock may be key to understanding the hardening and softening process. We hope to use these physical models in future earthquake simulations, offering more accurate predictions of how our Earth's crust reacts to earthquakes. We analyze two physical models suitable for simulations of nonlinear elastic wave propagation observed in the laboratoryThe experimentally observed co-seismic acoustic modulus drop can be explained with nonlinear damage modelsWe use the Markov chain Monte Carlo method to explore connections and uncertainties of nonlinear parameters
