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Dynamic perturbations reveal unconventional nonlinear behavior in rocks, asevidenced 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 sparseand insufficiently validated against observations. Here, we demonstrate theapplicability of two physical damage models - the internal variable model (IVM)and the continuum damage model (CDM) - to provide quantitative descriptions ofnonlinear co-seismic elastic wave propagation observations. We recast the IVMand CDM models as nonlinear hyperbolic partial differential equations andimplement 1D and 2D numerical simulations using an arbitrary high-orderdiscontinuous Galerkin method. We verify the modeling results withco-propagating acousto-elastic experimental measurements. We find that the IVMtime series of P-wave speed changes correlate slightly better withobservations, while the CDM better explains the peak damage delay relative topeak strain. Subsequently, we infer the parameters for these nonlinear modelsfrom laboratory experiments using probabilistic Bayesian inversion and 2Dsimulations. By adopting the Adaptive Metropolis Markov Chain Monte Carlomethod, we quantify the uncertainties of inferred parameters for both physicalmodels, investigating their interplay in 70,000 simulations. We find that thedamage variables can trade off with the stress-strain nonlinearity indiscernible ways. We discuss physical interpretations of both damage models andthat our CDM quantitatively captures an observed damage increase withperturbation frequency. Our results contribute to a more holistic understandingof non-classical non-linear damage with implications for co-seismic damage andpost-seismic recovery after earthquakes.

Modeling and Quantifying Parameter Uncertainty of Co-seismic Non-classical Nonlinearity in Rocks