The earthquake cycle of stress accumulation and release is associated with the elastic rebound hypothesis proposed by H.F. Reid following the M7.9 San Francisco earthquake of 1906. However, observing details of the actual values of time- and space-dependent tectonic stress is not possible at the present time. In previous research, we have proposed two methods to image the earthquake cycle in California by means of proxy variables. These variables are based on correlations in patterns of small earthquakes that occur nearly continuously in time. One of these is based on the construction of a time series by the unsupervised detection of small earthquake clusters. The other is based on expanding earthquake seismicity in PCA-derived patterns, to construct a weighted correlation time series. The purpose of the present research is to compare these two methods by evaluating their information content using decision thresholds and Receiver Operating Characteristic methods together with Shannon information entropy. Using seismic data from 1940 to present in California, we find that both methods provide nearly equivalent information on the rise and fall of earthquake correlations associated with major earthquakes in the region. We conclude that the resulting time series can be viewed as proxies for the cycle of stress accumulation and release associated with major tectonic activity. The figure shows the PCA patterns of small earthquakes associated with 5 major M>7 earthquakes in California since 1950.

We propose a new machine learning-based method for nowcasting earthquakes to image the time-dependent earthquake cycle. The result is a timeseries which may correspond to the process of stress accumulation and release. The timeseries is constructed by using Principal Component Analysis of regional seismicity. The patterns are found as eigenvectors of the cross-correlation matrix of a collection of seismicity timeseries in a coarse grained regional spatial grid (pattern recognition via unsupervised machine learning). The eigenvalues of this matrix represent the relative importance of the various eigenpatterns. Using the eigenvectors and eigenvalues, we then compute the weighted correlation timeseries (WCT) of the regional seismicity. This timeseries has the property that the weighted correlation generally decreases prior to major earthquakes in the region, and increases suddenly just after a major earthquake occurs. As in a previous paper (Rundle and Donnellan, 2020), we find that this method produces a nowcasting timeseries that resembles the hypothesized regional stress accumulation and release process characterizing the earthquake cycle. We then address the problem of whether the timeseries contains information regarding future large earthquakes. For this we compute a Receiver Operating Characteristic and determine the decision thresholds for several future time periods of interest (optimization via supervised machine learning). We find that signals can be detected that can be used to characterize the information content of the timeseries. These signals may be useful in assessing present and near-future seismic hazard.