We develop a Bayesian framework for calibrating physics-based earthquake-cycle models using sparse and noisy records of past large earthquakes, such as those available from paleoseismic observations. Because earthquake-cycle models can be chaotic, matching the exact timing of historical events is generally unstable and strongly dependent on unknown initial conditions. Instead, we infer model parameters by comparing long-term statistical properties of simulated and observed earthquake sequences, including recurrence intervals, event variability, temporal clustering, and average coseismic slip. The inverse problem is solved using Ensemble Kalman Inversion, and posterior uncertainty is refined with an efficient emulate–sample strategy based on a Gaussian-process surrogate. Through synthetic experiments, we show that paleoseismic-style data can constrain key frictional and geometric properties of faults, while also revealing which parameters remain weakly identifiable. This work provides a statistically grounded and computationally feasible step toward calibrating earthquake-cycle models for physics-based forecasting and time-dependent seismic hazard assessment.
See the preprint here.