Fault-valve behavior during slow slip cycles constrained using Bayesian data assimilation for a Cascadia subduction fault slip model

Independent lines of seismic evidence suggest that pore fluid pressure at the depth range of episodic slow slip events (SSEs) may undergo periodic fluctuations synced with the SSE slip cycles.  Here we develop a numerical simulation framework that integrates the SSE model governed by the rate- and state-dependent friction with Bayesian data assimilation to optimize time-variable fault friction parameters, using constraints from the northern Cascadia GNSS time series.  We first conduct synthetic experiments to calculate surface displacement time series from the rate-state SSE model generated fault slip history with imposed Gaussian noise. Both frictional parameters, effective normal stress (normal stress minus pore pressure) and characteristic slip distance, converge to their true values in 5-10 iterations from the initial guesses that are 10-20% off from the true values, demonstrating the feasibility of the data assimilation framework. We then apply this framework to 2009-2020 GNSS time series that encompasses SSE cycles recorded at ~ 30 stations along the northern Cascadia subduction zone.  We use a GNSS time series of 1000 days (~3 SSE cycles) in each inversion run to fully resolve the temporal changes in stress or friction; longer time series will cause inversion convergence issues due to the system nonlinearity. Within an inversion run, we choose a sliding time window of 9 months for each optimization epoch, which is a trade-off that on one hand includes sufficient information for the prediction of fault slip in the next time step and on the other hand allows temporal distinctions between the inter- versus intra-SSE time periods. Our inversion results show clear cyclic fluctuations in the optimized characteristic distance and effective normal stress values during SSE cycles. Specifically, effective normal stress increases (pore pressure drops) during the intra-SSE period; effective normal stress decreases (pore pressure increases) during the inter-SSE period.  The pore pressure oscillation pattern is independent of whether the characteristic slip distance is time-invariant during data assimilation, but the converse does not hold. Our results are thus consistent with the proposed pore pressure build-up and release processes, i.e., fault-valve model, at the SSE depth range.