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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° × 5° 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://doi.org/10.1029/2020EA001097; Rundle, Donnellan et al., 2021, https://doi.org/10.1029/2021EA001757; Rundle, Stein et al., 2021, https://doi.org/10.1088/1361-6633/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.

Abstract: 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 two previous papers, we have proposed 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. The purpose of the present paper 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 timeseries can be viewed as proxies for the cycle of stress accumulation and release associated with major tectonic activity. Article Highlights: The current state of the earthquake cycle of tectonic stress accumulation and release is unobservableWe review two methods for visualizing the current state of the earthquake cycle from correlation in small earthquake patternsMachine learning techniques indicate that signals in a correlation time series corresponding to future large earthquakes can be detected

We propose a new machine learning-based method for nowcasting earthquakes to image the time-dependent earthquake cycle. The result is a timeseries that may correspond to the process of stress accumulation and release. The timeseries are 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 compute the weighted correlation timeseries 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 & Donnellan, 2020, https://doi.org/10.1029/2020ea001097), 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 contain 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 hazards.

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using stochastic simulations of earthquake catalogs. Our catalog simulations are computed using an Earthquake Rescaled Aftershock Seismicity ("ERAS") stochastic model. This model is similar in many ways to other stochastic seismicity simulations, but has the advantage that the model has only 2 free parameters to be set, one for the aftershock (Omori‐Utsu) time decay, and one for the aftershock spatial migration away from the epicenter. Generating a simulation catalog and fitting the two parameters to the observed catalog such as California takes only a few minutes of wall clock time. While clustering can arise from random, Poisson statistics, we show that significant information in the simulation catalogs arises from the "non‐Poisson" power‐law aftershock clustering, implying that the practice of de‐clustering observed catalogs may remove information that would otherwise be useful in forecasting and nowcasting. We also show that the nowcasting method provides similar results with the ERAS model as it does with observed seismicity. Plain Language Summary: Earthquake nowcasting was proposed as a means of tracking the change in the potential for large earthquakes in a seismically active area, using the record of small earthquakes. The method was developed using observed seismic data, in which probabilities of future large earthquakes can be computed using machine learning methods that were originally developed with the advent of radar in the 1940s. These methods are now being used in the development of machine learning and artificial intelligence models in a variety of applications. In recent times, methods to simulate earthquakes using the observed statistical laws of earthquake seismicity have been developed. One of the advantages of these stochastic models is that it can be used to analyze the various assumptions that are inherent in the analysis of seismic catalogs of earthquakes. In this paper, we analyze the importance of the space‐time clustering that is often observed in earthquake seismicity. We find that the clustering is the origin of information that makes the earthquake nowcasting methods possible. We also find that a common practice of "aftershock de‐clustering", often used in the analysis of these catalogs, removes information about future large earthquakes. Key Points: Earthquake nowcasting tracks the change in the potential for large earthquakes, using information contained in seismic catalogsWe analyze the information contained in the space‐time clustering that is observed in earthquake seismicityWe find that "aftershock de‐clustering" of catalogs removes information about future large earthquakes that the nowcasting method uses [ABSTRACT FROM AUTHOR]

Simple Summary: Earthquakes are a common occurrence at The Geysers geothermal field in California which, over the years, have led to general land sinking in the area. In our study, we explore the correlation of geothermal data and seismicity and find that the injection rate exhibits a high correlation with the number of earthquakes. Additionally, we rely on satellite imagery which measures the extent of the land subsidence and develop a machine learning model that predicts future land subsidence, finding that it has a relatively low error rate. Moreover, we incorporate geothermal data into this model and find that it performs even better. All in all, this encourages the use of machine learning models in hazard mitigation in order to minimize the potential impacts that land subsidence might bring. The Geysers geothermal field in California is experiencing land subsidence due to the seismic and geothermal activities taking place. This poses a risk not only to the underlying infrastructure but also to the groundwater level which would reduce the water availability for the local community. Because of this, it is crucial to monitor and assess the surface deformation occurring and adjust geothermal operations accordingly. In this study, we examine the correlation between the geothermal injection and production rates as well as the seismic activity in the area, and we show the high correlation between the injection rate and the number of earthquakes. This motivates the use of this data in a machine learning model that would predict future deformation maps. First, we build a model that uses interferometric synthetic aperture radar (InSAR) images that have been processed and turned into a deformation time series using LiCSBAS, an open-source InSAR time series package, and evaluate the performance against a linear baseline model. The model includes both convolutional neural network (CNN) layers as well as long short-term memory (LSTM) layers and is able to improve upon the baseline model based on a mean squared error metric. Then, after getting preprocessed, we incorporate the geothermal data by adding them as additional inputs to the model. This new model was able to outperform both the baseline and the previous version of the model that uses only InSAR data, motivating the use of machine learning models as well as geothermal data in assessing and predicting future deformation at The Geysers as part of hazard mitigation models which would then be used as fundamental tools for informed decision making when it comes to adjusting geothermal operations. [ABSTRACT FROM AUTHOR]

Yes Plain Language Summary: The question of whether earthquake occurrence is random in time, or perhaps chaotic with order hidden in the chaos, is of major importance to the determination of risk from these events. It was shown many years ago that if aftershocks are removed from the earthquake catalogs, what remains are apparently events that occur at random time intervals, and therefore not predictable in time. In the present work, we enlist machine learning methods using Receiver Operating Characteristic analysis. With these methods, probabilities of large events and their associated information value can be computed. Here information value is defined using Shannon entropy, shown by Claude Shannon to define the surprise value of a communication such as a string of computer bits. Random messages can be shown to have high entropy, surprise value, or uncertainty, whereas low entropy is associated with reduced uncertainty and high reliability. An earthquake nowcast probability associated with reduced uncertainty and greater reliability is most desirable. Examples of the latter could be the statements that there is a 90% probability of a major earthquake within 3 years, or a 5% chance of a major earthquake within 1 year. Despite the random intervals between major earthquakes, we find that it is possible to make low uncertainty, high reliability statements on current hazard by the use of machine learning methods using catalog data from 1970‐present. Key Points: Interval statistics have been used to conclude that major earthquakes are random events in time and cannot be anticipated or predictedMachine learning is a powerful new technique that enhances our ability to understand the information content of earthquake catalogsUsing small earthquake rates, we show that catalogs contain significant information on predictability of future large earthquakes [ABSTRACT FROM AUTHOR]

Simple Summary: Excessive use of groundwater resources in the Central Valley in California has led to major land sinking over the years. In this study, we rely on satellite imagery to monitor and assess the extent of this sinking. Specifically, we use images from a satellite that emits microwaves which allows us to directly obtain the deformation at a specific time. Then, we apply a machine learning algorithm to the resulting data in an attempt to effectively predict short-term future deformation. We find that the algorithm applied has a low error when compared to the actual data. This shows that machine learning algorithms could be incorporated into models that assess potential hazards associated with land sinking. Land subsidence caused by excessive groundwater pumping in Central Valley, California, is a major issue that has several negative impacts such as reduced aquifer storage and damaged infrastructures which, in turn, produce an economic loss due to the high reliance on crop production. This is why it is of utmost importance to routinely monitor and assess the surface deformation occurring. Two main goals that this paper attempts to accomplish are deformation characterization and deformation prediction. The first goal is realized through the use of Principal Component Analysis (PCA) applied to a series of Interferomtric Synthetic Aperture Radar (InSAR) images that produces eigenimages displaying the key characteristics of the subsidence. Water storage changes are also directly analyzed by the use of data from the Gravity Recovery and Climate Experiment (GRACE) twin satellites and the Global Land Data Assimilation System (GLDAS). The second goal is accomplished by building a Long Short-Term Memory (LSTM) model to predict short-term deformation after developing an InSAR time series using LiCSBAS, an open-source InSAR time series package. The model is applied to the city of Madera and produces better results than a baseline averaging model and a one dimensional convolutional neural network (CNN) based on a mean squared error metric showing the effectiveness of machine learning in deformation prediction as well as the potential for incorporation in hazard mitigation models. The model results can directly aid policy makers in determining the appropriate rate of groundwater withdrawal while maintaining the safety and well-being of the population as well as the aquifers' integrity. [ABSTRACT FROM AUTHOR]

Charles Richter's observation that 'only fools and charlatans predict earthquakes,' reflects the fact that despite more than 100 years of effort, seismologists remain unable to do so with reliable and accurate results. Meaningful prediction involves specifying the location, time, and size of an earthquake before it occurs to greater precision than expected purely by chance from the known statistics of earthquakes in an area. In this context, 'forecasting' implies a prediction with a specification of a probability of the time, location, and magnitude. Two general approaches have been used. In one, the rate of motion accumulating across faults and the amount of slip in past earthquakes is used to infer where and when future earthquakes will occur and the shaking that would be expected. Because the intervals between earthquakes are highly variable, these long-term forecasts are accurate to no better than a hundred years. They are thus valuable for earthquake hazard mitigation, given the long lives of structures, but have clear limitations. The second approach is to identify potentially observable changes in the Earth that precede earthquakes. Various precursors have been suggested, and may have been real in certain cases, but none have yet proved to be a general feature preceding all earthquakes or to stand out convincingly from the normal variability of the Earth's behavior. However, new types of data, models, and computational power may provide avenues for progress using machine learning that were not previously available. At present, it is unclear whether deterministic earthquake prediction is possible. The frustrations of this search have led to the observation that (echoing Yogi Berra) 'it is difficult to predict earthquakes, especially before they happen.' However, because success would be of enormous societal benefit, the search for methods of earthquake prediction and forecasting will likely continue. In this review, we note that the focus is on anticipating the earthquake rupture before it occurs, rather than characterizing it rapidly just after it occurs. The latter is the domain of earthquake early warning, which we do not treat in detail here, although we include a short discussion in the machine learning section at the end. [ABSTRACT FROM AUTHOR]

Seismic bursts in Southern California are sequences of small earthquakes strongly clustered in space and time and include seismic swarms and aftershock sequences. A readily observable property of these events, the radius of gyration (RG), allows us to connect the bursts to the temporal occurrence of the largest M ≥ 7 earthquakes in California since 1984. In the Southern California earthquake catalog, we identify hundreds of these potentially coherent space‐time structures in a region defined by a circle of radius 600 km around Los Angeles. We compute RG for each cluster then filter them to identify those bursts with large numbers of events closely clustered in space, which we call "compact" bursts. Our basic assumption is that these compact bursts reflect the dynamics associated with large earthquakes. Once we have filtered the burst catalog, we apply an exponential moving average to construct a time series for the Southern California region. We observe that the RG of these bursts systematically decreases prior to large earthquakes, in a process that we might term "radial localization." The RG then rapidly increases during an aftershock sequence, and a new cycle of "radial localization" then begins. These time series display cycles of recharge and discharge reminiscent of seismic stress accumulation and release in the elastic rebound process. The complex burst dynamics we observe are evidently a property of the region as a whole, rather than being associated with individual faults. This new method allows us to improve earthquake nowcasting, which is a technique to evaluate the current state of hazard in a seismically active region. Plain Language Summary: Earthquake nowcasting is a method to evaluate the current state of seismic hazard from large earthquakes. In this paper, we connect the temporal occurrence of the largest and most potentially destructive earthquakes in California since 1984 with a readily observable property of small earthquake seismicity in the region. Our method involves the calculation of the time history of the average radius (horizontal size or extent) of "bursts" of small earthquakes, in the time leading up to and following major earthquakes in the region. We observe that the radius systematically and gradually decreases leading up to major earthquakes, increasing suddenly and discontinuously following the event. This observable pattern resembles the long‐hypothesized cycle of regional tectonic stress buildup and release, or elastic rebound, associated with large destructive earthquakes. We propose that the radius of these bursts might be considered to be a proxy variable for the changing state of regional stress in Southern California. Key Points: A new nowcasting method using earthquake swarms and aftershocks reveals the hazard from large M ≥ 7 earthquakes in Southern CaliforniaMachine learning defines a time series of bursts using an exponential moving average filtered and optimized to reveal temporal structureCycles of recharge and discharge associated with M ≥ 7 earthquakes are revealed, reminiscent of stress accumulation and release [ABSTRACT FROM AUTHOR]