Model-order reduction applied to rate-and-state friction earthquake cycle models uncovering the physics driving slow-slip events.

Over the past two decades, advancements in seismological and geodetic observations have uncovered a diverse range of aseismic fault slip behaviors occurring at various depths, significantly contributing to the seismic cycle moment budget. One notable phenomenon is Episodic Slow Slip Events (SSEs), which occur in many subduction zones, at depths greater than the coupled seismogenic zone and shallower than the creeping zone. Lasting from days to weeks, SSEs are detected by GNSS stations through a reversal in station velocity, with amplitudes reaching several centimeters. The small deformation signal, combined with the rapid decrease in resolvable fault information with depth, suggests that data-driven models have limited constraints on the physics governing these events. Forward modeling of SSEs using rate-and-state friction laws offers valuable insights, but it is computationally intensive and constrained by the fast oscillating processes inherent to the system, limiting exploration of the controlling physics. In this study, we employ a two-dimensional subduction fault model with laboratory-constrained rate-and-state friction parameters to simulate SSEs in a Cascadia-like setting. We apply a model-order reduction technique to alleviate computational demands, facilitating detailed parametric studies of SSEs dynamics.

To model slow slip events, we use the open-source seismic cycle and aseismic slip (SEAS) simulation framework, Tandem (Uphoff et al., 2023). The Cascadia subduction zone is represented as a 1D planar fault that dips at an angle of 10°. We introduce SSEs into the system by creating a zone of low effective normal stress (σ_n) in the region where the fault transitions from slip weakening (up dip) to slip strengthening (down dip). The ratio of this low effective normal stress zone (W) with the critical nucleation size (h*), were found to control both the occurrence and rate of SSEs (e.g., Liu & Rice, 2007,

2009) and is given by

,

where a, b, and D_c are friction parameters.

To rigorously explore the parametric space controlling SSEs (W - width, σ_n- normal stress, a, b, D_c - friction parameters), we utilize a non-intrusive, data-driven Reduced Order Model (ROM). First, we transform the spatial fault distribution of simulated slip-time trajectories (time history data) into a latent space vector representation through spline interpolation across the slip-rate to state variable domain. This process compresses the simulated slip-time history by 90% allowing for efficient interpolation between latent state vectors. Next, we employ Proper Orthogonal Decomposition ROM using Radial Basis Functions to interpolate the latent state vectors over the parameter space. This two-step model order reduction approach significantly reduces the computational cost of obtaining slip-time trajectories compared to a traditional SEAS simulation, decreasing the run-time from thousands of CPU hours to just seconds.

This study emphasizes the potential of ROMs to enhance our understanding of earthquake physics, particularly the mechanisms behind SSEs. This advancement paves the way for improved models of seismic cycle dynamics and hazard assessments in subduction zones. By combining computational efficiency with physical insight, ROMs offer unique opportunities to explore the complex interplay of physical parameters that govern subduction seismogenic.