Data Assimilation in Reduced-order Model of Chaotic Earthquake Sequences

Realistic models of earthquake sequences can be simulated by assuming faults governed by rate-and-state friction embedded in an elastic medium. Exploring the possibility of using such models for earthquake forecasting is challenging due to the difficulty of integrating Partial Differential Equation (PDE) models with sparse, low-resolution observational data. This paper presents a machine-learning-based reduced-order model (ROM) for earthquake sequences that addresses this limitation. The proposed ROM captures the slow/fast chaotic dynamics of earthquake sequences using a low-dimensional representation, enabling computational efficiency and robustness to high-frequency noise in observational data. The ROM's efficiency facilitates effective data assimilation using the Ensemble Kalman Filter (EnKF), even with low-resolution, noisy observations. Results demonstrate the ROM's ability to replicate key scaling properties of the sequence and to estimate the distributions of fault slip rate and state variable, enabling predictions of large events in time and space with uncertainty quantification. These findings underscore the ROM's potential for forecasting and for addressing challenges in inverse problems for nonlinear geophysical systems.