Embracing Data Incompleteness for Better Earthquake Forecasting

Abstract: We propose two methods to calibrate the parameters of the epidemic-type aftershock sequence (ETAS) model based on expectation maximization (EM) while accounting for temporal variation of catalog completeness. The first method allows for model calibration on long-term earthquake catalogs with temporal variation of the completeness magnitude, $m_c$. This calibration technique is beneficial for long-term probabilistic seismic hazard assessment (PSHA), which is often based on a mixture of instrumental and historical catalogs. The second method generalizes the concept of $m_c$, considering rate- and magnitude-dependent detection probability, and allows for self-consistent estimation of ETAS parameters and high-frequency detection incompleteness. With this approach, we aim to address the potential biases in parameter calibration due to short-term aftershock incompleteness, embracing incompleteness instead of avoiding it. Using synthetic tests, we show that both methods can accurately invert the parameters of simulated catalogs. We then use them to estimate ETAS parameters for California using the earthquake catalog since 1932. To explore how model calibration, inclusion of small events, and accounting for short-term incompleteness affect earthquakes' predictability, we systematically compare variants of ETAS models based on the second approach in pseudo-prospective forecasting experiments for California. Our proposed model significantly outperforms the ETAS null model, with decreasing information gain for increasing target magnitude threshold. We find that the ability to include small earthquakes for simulation of future scenarios is the primary driver of the improvement and that accounting for incompleteness is necessary. Our results have significant implications for our understanding of earthquake interaction mechanisms and the future of seismicity forecasting.