Data underlying the publication: Ensemble Kalman, Adaptive Gaussian Mixture, and Particle Flow Filters for Optimized Earthquake Forecasting

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).

本数据集包含基于Erickson等人2011年提出的无量纲化公式（https://academic.oup.com/gji/article/187/1/178/560601），由洛伦兹96模型（Lorenz 96 model）与耦合速率-状态摩擦（rate-and-state friction）的伯里奇-诺普夫模型（Burridge-Knopoff model）生成的时间序列。针对包含20个块体的一维伯里奇-诺普夫模型，其时间序列涵盖剪切应力、速度、滑移量以及状态变量θ的演化过程；针对包含20个单元的洛伦兹96模型，其时间序列涵盖状态变量x的演化过程。该时间序列已用于博士论文《用于估算断层滑移与未来地震发生的集合数据同化方法》（原英文标题：Ensemble data assimilation methods for estimating fault slip and future earthquake occurrences）的第2章（地震数值模拟）中针对不同参数ε（速度松弛敏感性）取值下复发间隔变化的敏感性分析、第3章（集合数据同化方法）及第5章（面向优化地震预报的非高斯集合数据同化方法）中的完美模型试验，同时也用于待投稿论文《用于优化地震预报的集合卡尔曼滤波、自适应高斯混合滤波与粒子流滤波器》（原英文标题：Ensemble Kalman, Adaptive Gaussian Mixture, and Particle Flow Filters for Optimized Earthquake Forecasting）的相关研究。本次完美模型试验的估计结果对应三种不同的集合数据同化方法，分别为集合卡尔曼滤波（Ensemble Kalman Filter, EnKF）、自适应高斯混合滤波（Adaptive Gaussian Mixture Filter, AGMF）以及粒子流滤波（Particle Flow Filter, PFF）。