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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]

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]

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. 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. Key Points: "Chaotic" seismicity contains hidden structure in the form of state variable time seriesStandard data science methods can be used to convert the time series to probabilitiesBoth temporal and spatial probabilities can be computed [ABSTRACT FROM AUTHOR]

The period of heightened volcanic and seismic activity at Kīlauea volcano on the island of Hawai'i, USA from late spring through summer 2018 included a remarkable quasi‐periodic sequence of caldera collapse events. From mid‐May to early‐August, 62 collapse events, each releasing the seismic energy equivalent of a Mw 5.0 ± 0.4 earthquake, occurred about every 1–2 days with over 300 M ≥ 2.5 earthquakes between sequential collapses. This region, experiencing very high rates of seismicity and frequent large magnitude events, is a good candidate to apply a regional seismic hazard assessment. Nowcasting is a type of statistical analysis that uses small magnitude events to estimate the occurrence of large magnitude events. This is done utilizing the concept of natural time in which time is counted by small magnitude event occurrences between large magnitude events, not in clock time (days passed). This method has produced a "nowcasted" set of large earthquakes that are in good agreement with the actual cataloged events in prior studies analyzing non‐volcanic regions. Previously applied to tectonic earthquakes and induced seismicity over longer time frames, this is the first test of nowcasting large caldera collapse events in volcanic associated seismicity and on a relatively short time scale. The technique produced limited "success" nowcasting 37 collapse events that agreed with the catalog of actual events. A temporal dependence of successful nowcasting during the sequence was found that may correlate to previously identified and analyzed physical changes in the volcanic system. Key Points: We applied earthquake nowcasting to 37 caldera collapse events, yielding close agreement with the actual recorded set of collapse eventsKīlauea volcano saw a temporal change in the natural time relationship that can be related to changes in the physical systemThis nowcasting method revealed limited success in a volcanic setting compared to prior tectonic earthquake applications [ABSTRACT FROM AUTHOR]

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. Plain Language Summary: Major earthquakes on fault systems in a tectonically active region are thought to occur in approximately repetitive cycles as a result of the buildup and release of tectonic forces (stress). Nowcasting is a technique adopted from weather, finance, and other fields that use readily observable proxy data to represent the unobservable stress accumulation process of interest. This paper presents a method that computes a timeseries representing the weighted correlation of small earthquake activity in the California region from 1950 to 2020. Prior to major magnitude M > 7 earthquakes, the timeseries trends toward lower values. Just after the earthquake occurs, the timeseries increases suddenly in association with the earthquake, before resuming its gradual trend toward lower values. Plotting the timeseries on an inverted scale, one sees a cyclic behavior that strongly resembles the hypothesized earthquake cycle. In principle, we can therefore use this timeseries for nowcasting, as a proxy for stress accumulation and release. Using methods of signal detection first developed for radar by the British in the 1940's, we find that the timeseries contain information about future large earthquakes that can be used for hazard assessment. Key Points: The current state of the earthquake cycle of tectonic stress accumulation and release is unobservable with existing methodsWe show that readily observable small earthquake correlations can be used to nowcast the current state of the earthquake cycleMachine learning techniques indicate that signals corresponding to future large earthquakes can be detected in a correlation time series [ABSTRACT FROM AUTHOR]

Interferometric synthetic aperture radar (InSAR) interferograms contain valuable information about the fault systems hidden beneath the surface of the Earth. In a new approach, we aim to fit InSAR ground deformation data using a distribution of multiple seismic point sources whose parameters are found by a genetic algorithm. The resulting source distribution could provide another useful tool in solving the difficult problem of accurately mapping earthquake faults. We apply the algorithm to an ALOS‐2 InSAR interferogram and perform a multifractal analysis on the resulting distribution, finding that it exhibits multifractal properties. We report first results and discuss advantages and disadvantages of this approach. Key Points: Inversion for seismic moment of point source distributionMultifractal analysis of seismic moment distribution is performedSeismic moment distribution exhibits multifractal properties [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]

Following the Mw 6.9 Hawaiian earthquake on 4 May 2018, a remarkable quasiperiodic sequence of collapse events began at Halema'uma'u Crater at the summit of Kīlauea Volcano. The collapse events were associated with the drainage of magma from beneath the summit to the Lower East Rift Zone where fissure eruptions occurred. From 4 June 2018 to 2 August 2018 forty‐seven collapse events Mw 5.3 ± 0.1 occurred with the same temporal pattern of seismicity occurring between sequential pairs of collapse events. This paper focuses on this interevent seismicity pattern. Following a collapse event, there was a relatively quiescent period. This was followed by a sudden increase in seismicity, occurring at a nearly linear rate of 397 ± 96 earthquakes per day. These seismically active periods lasted until the next collapse event occurred. The pattern then repeated itself beginning again with postcollapse quiescence. We provide a statistical summary of this seismicity behavior by isolating the quiescent and active times to look at immediate precollapse and postcollapse activity. In mid‐June there were significant changes in the quiescent time lengths (decreased), the number of earthquakes during the interevent times (increased), and the rates of seismicity during the active times (increased). This type of interevent study could be conducted with other seismically well recorded, sequential caldera collapse events and also with other data types to look for potential physical explanations and an improved understanding of precollapse and postcollapse activity. Key Points: The same pattern of seismically quiescent and active periods occurred between every pair of collapse events at the summitThe active times had linear rates of seismicity, and the quiescent times had fewer earthquakesFollowing a large increase in June 2018, there was a general decrease in the active time seismicity rates until the end of the sequence [ABSTRACT FROM AUTHOR]

The Nonlinear Geophysics Technical Committee was formed in 1998 by a small group of AGU members to meet a growing interest in the analysis, modeling, and prediction of nonlinear behavior in geophysical processes. This paper provides a history as the technical committee, evolved into a focus group, and into a section, including officers, awards, prizes, named lectures, standing committees, and books written or edited by members on the subject of nonlinear geophysical patterns and processes. Key Point: This manuscript provides a history of the Nonlinear Section of AGU [ABSTRACT FROM AUTHOR]

Seismic nowcasting uses counts of small earthquakes as proxy data to estimate the current dynamical state of an earthquake fault system. The result is an earthquake potential score that characterizes the current state of progress of a defined geographic region through its nominal earthquake "cycle." The count of small earthquakes since the last large earthquake is the natural time that has elapsed since the last large earthquake (Varotsos et al., 2006, https://doi.org/10.1103/PhysRevE.74.021123). In addition to natural time, earthquake sequences can also be analyzed using Shannon information entropy ("information"), an idea that was pioneered by Shannon (1948, https://doi.org/10.1002/j.1538‐7305.1948.tb01338.x). As a first step to add seismic information entropy into the nowcasting method, we incorporate magnitude information into the natural time counts by using event self‐information. We find in this first application of seismic information entropy that the earthquake potential score values are similar to the values using only natural time. However, other characteristics of earthquake sequences, including the interevent time intervals, or the departure of higher magnitude events from the magnitude‐frequency scaling line, may contain additional information. Plain Language Summary: Earthquake nowcasting has been developed to determine the current level of earthquake risk for seismically active areas. Historically, statistical communication theory has been developed to analyze the information content of signals involved in telecommunications and computer systems. We combine these techniques to analyze the information contained in earthquake magnitudes for great earthquakes and mega‐tsunamis. Key Points: Nowcasting was previously used to analyze earthquake data to determine current seismic risk to global megacities for magnitudes M ≥ 6We extend the method to computing hazard from great earthquake and mega‐tsunami sources arising from earthquakes with magnitudes M > 7.9We also develop nowcasting methods using the information entropy of earthquake sequences [ABSTRACT FROM AUTHOR]

Parallelization strategies are presented for Virtual Quake, a numerical simulation code for earthquakes based on topologically realistic systems of interacting earthquake faults. One of the demands placed upon the simulation is the accurate reproduction of the observed earthquake statistics over three to four decades. This requires the use of a high-resolution fault model in computations, which demands computational power that is well beyond the scope of off-the-shelf multi-core CPU computers. However, the recent advances in general-purpose graphic processing units have the potential to address this problem at moderate cost increments. A functional decomposition of Virtual Quake is performed, and opportunities for parallelization are discussed in this work. Computationally intensive modules are identified, and these are implemented on graphics processing units, significantly speeding up earthquake simulations. In the current best case scenario, a computer with six graphics processing units can simulate 500 years of fault activity in California at 1.5 km × 1.5 km element resolution in less than 1 hour, whereas a single CPU requires more than 2 days to perform the same simulation. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: Tectonic motion across the Los Angeles region is distributed across an intricate network of strike‐slip and thrust faults that will be released in destructive earthquakes similar to or larger than the 1933 M6.4 Long Beach and 1994 M6.7 Northridge events. Here we show that Los Angeles regional thrust, strike‐slip, and oblique faults are connected and move concurrently with measurable surface deformation, even in moderate magnitude earthquakes, as part of a fault system that accommodates north‐south shortening and westerly tectonic escape of northern Los Angeles. The 28 March 2014 M5.1 La Habra earthquake occurred on a northeast striking, northwest dipping left‐lateral oblique thrust fault northeast of Los Angeles. We present crustal deformation observation spanning the earthquake showing that concurrent deformation occurred on several structures in the shallow crust. The seismic moment of the earthquake is 82% of the total geodetic moment released. Slip within the unconsolidated upper sedimentary layer may reflect shallow release of accumulated strain on still‐locked deeper structures. A future M6.1–6.3 earthquake would account for the accumulated strain. Such an event could occur on any one or several of these faults, which may not have been identified by geologic surface mapping. [ABSTRACT FROM AUTHOR]

Terra Nova, 23, 369-374, 2011 Abstract Seismic precursors revealed by statistical physics methods are important for earthquake forecasting and helpful for understanding fault behaviour. One of the precursors, earthquake migration, has been observed in simulated models and rock experiments, as well as anecdotal observations for large earthquakes along major fault zones. However, there has been no systematic methodology for investigating earthquake migration in nature, and only a small number of studies have observed earthquake migration at large scales. In this work, we show that migration of small earthquakes towards the epicentre before large earthquakes can be visualized. We present a method for detecting small earthquake migration in the spatiotemporal domain, and retrospectively apply it to two recent examples of major earthquakes in Taiwan. We observe that anomalous seismicity occurs increasingly close to the epicentre as the occurrence time is approached. At that point, the bulk of the seismicity concentrates on the epicentre, accumulating stress on the rupture zone and leading to the full rupture. Our findings imply a new type of large-scale pre-seismic earthquake migration pattern that is complementary to the well-studied patterns of source-region activation and quiescence. [ABSTRACT FROM AUTHOR]

We describe an application to interactively create and manipulate digital fault maps, either by tracing existing (paper) fault maps created from geological surveys, or by directly observing fault expressions and earthquake hypocenters in remote sensing data such as high-resolution (⩾100k × 100k elevation postings) digital elevation models with draped color imagery. Such fault maps serve as input data to finite-element-method simulations of fault interactions, and are crucial to understand regional tectonic processes causing earthquakes, and have tentatively been used to forecast future seismic events or to predict the shaking from likely future earthquakes. This fault editor is designed for immersive virtual reality environments such as CAVEs, and presents users with visualizations of scanned 2D fault maps and textured 3D terrain models, and a set of 3D editing tools to create or manipulate faults. We close with a case study performed by one of our geologist co-authors (Yikilmaz), which evaluates the use of our fault editor in creating a detailed digital fault model of the North Anatolian Fault in Turkey, one of the largest, seismically active strike-slip faults in the world. Yikilmaz, who was directly involved in program development, used our fault editor both in a CAVE and on a desktop computer, and compares it to the industry-standard software package ArcGIS. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The Virtual California simulation tool can be used to study fault and stress interaction scenarios for realistic California earthquakes and produces a large data set, which is ideally suited for statistical analysis. As with any complex system, it can produce emergent phenomena unexpected by its designers; these can be studied in order to gain insight into real world geophysical phenomena. We have developed a statistical method to analyze Virtual California data that enables us to determine the correlation relationships between the simulated fault elements. We present the results of this analysis of 40 000 years of data for 59 faults (639 elements). We focus on five specific cases that display noteworthy behavior that includes long-range fault interactions, activation–quiescence, and complex small-scale interactions. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]