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Abstract:
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.
