Bayesian Calibration of dynamic models of earthquake sequences using observations from past large earthquakes

Physics-based models of the earthquake cycle could be used for time-dependent hazard assessment. For such an application, their parameters must be calibrated so that simulated earthquake sequences reproduce the statistics of past earthquakes, including recurrence statistics and magnitudes. This is challenging because the dynamics are described by nonlinear partial differential equations, initial conditions are unknown, and records of past earthquakes are sparse, incomplete, and noisy. To address this challenge, we present a Bayesian inverse-problem framework to infer heterogeneous parameters in an earthquake-cycle model from observations of past large earthquakes. Rather than matching a time-series of individual events, we exploit ergodicity (long-term statistics independent of initial conditions) and invert for stationary, spatially distributed summary statistics of event timing and slip, including mean interevent times, coefficients of variation, burstiness, and average coseismic slip, which are quantities that can in principle be estimated from paleoseismic and historical records. Observational noise and event-detection thresholds are explicitly accounted for in the construction of these statistics. The inverse problem is solved using a derivative-free ensemble Kalman inversion method, and uncertainty quantification is enhanced by an emulate–sample strategy that leverages machine-learning for surrogate modeling, in which a Gaussian-process surrogate of the parameter-to-statistics map enables efficient MCMC sampling without further expensive forward simulations. Synthetic experiments with realistic data noise demonstrate that the model parameters can be inverted from statistical quantities observable from paleoseismology at a limited number of observation points. The framework provides a principled and computationally tractable method to calibrate earthquake-cycle models, providing a foundation for forecasting.