  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. 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. We find that the IVM
time series of P-wave speed changes correlate slightly better with
observations, while the CDM better explains the peak damage delay relative to
peak strain. 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 non-classical non-linear damage with implications for co-seismic damage and
post-seismic recovery after earthquakes.
