Time series from a Lorenz 96 model and a Burridge-Knopoff model coupled with rate-and-state friction using the non-dimensional formulation of Erickson et al. 2011 (https://academic.oup.com/gji/article/187/1/178/560601). The time series of the 1-D Burridge-Knopoff model of 20 blocks includes the evolution of the shear stress, velocity, slip, and state theta. The time series of the Lorenz 96 model with 20 cells includes the evolution of the state x. The time series were used for the sensitivity analysis of the changes in the recurrence intervals for different values of the parameter epsilon (sensitivity of the velocity relaxation) in Chapter 2 (Numerical modeling of earthquakes), the perfect model experiments in Chapter 3 (Ensemble data assimilation methods), and the perfect model experiments on Chapter 5 (Non-Gaussian ensemble data assimilation methods for optimized earthquake forecasting) of the Ph.D. thesis "Ensemble data assimilation methods for estimating fault slip and future earthquake occurrences", and for the publication "Ensemble Kalman, Adaptive Gaussian Mixture, and Particle Flow Filters for Optimized Earthquake Forecasting" prepared for submission. The estimates of the perfect model experiment correspond to three different ensemble data assimilation methods, namely the Ensemble Kalman Filter (EnKF), the Adaptive Gaussian Mixture Filter (AGMF), and the Particle Flow Filter (PFF).

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