Optimizing earthquake nowcasting with machine learning: The role of strain hardening in the earthquake cycle

Nowcasting is a term originating from economics, finance, and meteorology. It refers to the process of determining the uncertain state of the economy, markets or the weather at the current time by indirect means. In this paper, we describe a simple two-parameter data analysis that reveals hidden order in otherwise seemingly chaotic earthquake seismicity. One of these parameters relates to a mechanism of seismic quiescence arising from the physics of strain-hardening of the crust prior to major events. We observe an earthquake cycle associated with major earthquakes in California, similar to what has long been postulated. An estimate of the earthquake hazard revealed by this state variable time series can be optimized by the use of machine learning in the form of the Receiver Operating Characteristic skill score. The ROC skill is used here as a loss function in a supervised learning mode. Our analysis is conducted in the region of 5 degrees x 5 degrees in latitude-longitude centered on Los Angeles, a region which we used in previous papers to build similar time series using more involved methods (Rundle & Donnellan, 2020, https://doLoT/10.1029/2020EA001097; Rundle, Donnellan et al., 2021, https://doi.org/10.1029/2021EA001757; Rundle, Stein et al., 2021, https://doi.org/10.1088/13616633/abf893). Here we show that not only does the state variable time series have forecast skill, the associated spatial probability densities have skill as well. In addition, use of the standard ROC and Precision (PPV) metrics allow probabilities of current earthquake hazard to be defined in a simple, straightforward, and rigorous way. Plain Language Summary Earthquake nowcasting refers to the determination of hazard for major earthquakes at the present time, the recent past, and the near future. Nowcasting is an idea borrowed from economics, markets, and meteorology, where it has been frequently used. In this paper, we show that there is order hidden within chaotic earthquake seismicity using a very simple transformation of the data. Small earthquakes appear to transition from unstable stick-slip events that produce seismic waves, to stable sliding where no seismic waves are produced. Our hypothesis is that this transition is due to a material phenomenon called strain-hardening, that is frequently observed in laboratory rock mechanics experiments. The result is a state variable time series, computed over the last 51 years in California, that strongly resembles the long-anticipated cycle of stress accumulation and release. Using supervised machine learning techniques, we can optimize the two-parameter model. From that optimized model, we can rigorously calculate the probability of current hazard from major earthquakes. Extending these methods, we can also compute spatial hazard as well. The result is a new method for assessing earthquake hazard that may be useful for a variety of applications.