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Number of M ≥ 6 earthquakes from the USGS worldwide catalog from 1900 to present. The catalog appears to be complete after 1 January 1950 about the time that nuclear testing began
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Nowcasting refers to the use of proxy data to estimate the current dynamic state of driven complex systems such as earthquakes, neural networks, or the financial markets. In previous papers, methods to nowcast earthquakes have been presented based on the natural time count of small earthquakes after the last large earthquake in a defined, seismical...
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Citations
... Nowcasting_(economics)(accessed 12/22/2022)). This idea uses state ("proxy") variables to infer the current state of the earthquake cycle (Pasari, 2019(Pasari, , 2020(Pasari, , 2022Pasari & Mehta, 2018;Pasari & Sharma, 2020;Rundle et al., 2016, Rundle, Luginbuhl, et al., 2019, Rundle, Luginbuhl, et al., 2020, Rundle, Ortez, et al., 2020, Rundle, Donnellan, Fox, Crutchfield, & Granat, 2021Rundle, Stein, et al., 2021;Luginbuhl et al., 2018). An approach such as this is needed since the cycle of stress accumulation and release is not observable , Rundle, Donnellan, Fox, Crutchfield, & Granat, 2021Scholz, 2019). ...
... A critical component of the current approach is that the information is encoded in the earthquake clusters or bursts, which are a series of events closely spaced in time Rundle, Luginbuhl, et al., 2020, Rundle, Ortez, et al., 2020. Bursts are a temporal clustering of highly correlated seismicity, typically in a small spatial region. ...
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.
... A new view of time, termed natural time χ has been introduced by the first three authors in 2001, see, e.g., [1]. It has been found to be useful in various disciplines, for example it has been employed by Rundle, Turcotte, and coworkers [2][3][4][5][6][7][8] as a basis for a new methodology to estimate the current level of seismic risk, termed Nowcasting Earthquakes (which was recently reviewed in [9][10][11]). In this new view, novel dynamical features hidden behind time series in complex systems can emerge but cannot when the analysis is carried out within the frame of conventional time. ...
This article is focused on a new procedure concerning a more accurate identification of the occurrence time of an impending major earthquake (EQ). Specifically, we first recapitulate that, as was recently shown [P. Varotsos et al., Communications in Nonlinear Science and Numerical Simulation 125 (2023) 107370], natural time analysis of seismicity supplemented with the non-additive Tsallis entropy Sq leads to a shortening of the time window of an impending major EQ. This has been shown for the Tohoku mega-EQ of magnitude M9 that occurred in Japan on 11 March 2011, which is the largest event ever recorded in Japan. Here, we also show that such a shortening of the time window of an impending mainshock can be achieved for major, but smaller EQs, of the order of M8 and M7. In particular, the following EQs are treated: the Chiapas M8.2 EQ, which is Mexico’s largest EQ for more than a century that took place on 7 September 2017 near the coast of Chiapas state in Mexico, the 19 September 2017 M7.1 EQ that occurred within the Mexican flat slab, and the M7.1 Ridgecrest EQ on 6 July 2019 in California.
... Nowcasting_(economics)(accessed 12/22/2022)). This idea uses state ("proxy") variables to infer the current state of the earthquake cycle (Pasari, 2019(Pasari, , 2020(Pasari, , 2022Pasari & Mehta, 2018;Pasari & Sharma, 2020;Rundle et al., 2016, Rundle, Luginbuhl, et al., 2019, Rundle, Luginbuhl, et al., 2020, Rundle, Ortez, et al., 2020, Rundle, Donnellan, Fox, Crutchfield, & Granat, 2021Rundle, Stein, et al., 2021;Luginbuhl et al., 2018). An approach such as this is needed since the cycle of stress accumulation and release is not observable , Rundle, Donnellan, Fox, Crutchfield, & Granat, 2021Scholz, 2019). ...
... A critical component of the current approach is that the information is encoded in the earthquake clusters or bursts, which are a series of events closely spaced in time Rundle, Luginbuhl, et al., 2020, Rundle, Ortez, et al., 2020. Bursts are a temporal clustering of highly correlated seismicity, typically in a small spatial region. ...
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.
... It's basic concepts have evolved within the field of economics ( e.g., Giannone et al., 2008 ) and has more recently been applied to assessing seismic hazard. Since it's initial development ( Rundle et al., 2016 ), it has been applied in multiple locations in the United States of America as well as other seismically active locations around the globe ( e.g., Donnellan et al., 2018;Luginbuhl, Rundle, Hawkins, & Turcotte, 2018;Luginbuhl et al., 2018aLuginbuhl et al., , 2018bLuginbuhl et al., , 2019Pasari, 2019;Pasari & Mehta, 2018;Pasari & Sharma, 2020;Pasari et al., 2021;Rundle et al., 2018;Rundle et al., 2019;Rundle et al., 2020;Varotsos et al., 2017 ). In earthquake application, it has been developed as a statistical approach to use as an indirect way of gaining insight into the changing stress state and seismic hazard of a region in the time between large seismic events. ...
Abstract 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.
... This methodology analyzes seismic catalogues by using the natural time introduced by Varotsos et al. [80,81], in the frame of which an order parameter has been defined, the study of the variability of which [82,83] has been also shown to lead to the estimation of the epicentral area [R6] of an impending major earthquake. Some applications of nowcasting method have been reported in [79,[84][85][86][87][88][89][90]. ...
After the M8.2 main-shock occurred on 7 September 2017 at the Isthmus of Tehuantepec, Mexico, the spatial distribution of seismicity has showed a clear clusterization of earthquakes along the collision region of the Tehuantepec Transform/Ridge with the Middle America Trench off Chiapas. Furthermore, nowadays, the temporal rate of occurrence in the number of earthquakes has also showed a pronounced increase. On the basis of this behavior, we studied the sequence of magnitudes of the earthquakes which occurred within the Isthmus of Tehuantepec in southern Mexico from 2010 to 2020. Since big earthquakes are considered as a phase transition, after the M8.2 main-shock, one must expect changes in the Tehuantepec ridge dynamics, which can be observed considering that the b-value in the Gutenberg–Richter law, has also showed changes in time. The goal of this paper is to characterize the behavior of the seismic activity by using the Gutenberg–Richter law, multifractal detrended fluctuation analysis, visibility graph and nowcasting method. Those methods have showed important parameters in order to assess risk, the multifractality and connectivity. Our findings indicate, first that b-value shows a dependency on time, which is clearly described by our analyses based on nowcasting method, multifractality and visibility graph.
... Earthquake nowcasting has been introduced by Rundle et al. [11] and allows the evaluation of the current state of seismic hazard for strong EQs by the number of smaller EQs that occur in the time interval between two strong ones. It has been applied for the estimation of seismic risk to global megacities [12,15] as well as of the risk of great earthquakes that may generate mega-tsunamis [74]. EN has also been applied for the estimation of induced seismicity [75,76] and offers unique possibilities for the estimation of the seismic risk worldwide through global sources of seismic catalogs, see, e.g., References [77][78][79][80], cf. ...
It has recently been shown in the Eastern Mediterranean that by combining natural time analysis of seismicity with earthquake networks based on similar activity patterns and earthquake nowcasting, an estimate of the epicenter location of a future strong earthquake can be obtained. This is based on the construction of average earthquake potential score maps. Here, we propose a method of obtaining such estimates for a highly seismically active area that includes Southern California, Mexico and part of Central America, i.e., the area N1035W80120. The study includes 28 strong earthquakes of magnitude M ≥7.0 that occurred during the time period from 1989 to 2020. The results indicate that there is a strong correlation between the epicenter of a future strong earthquake and the average earthquake potential score maps. Moreover, the method is also applied to the very recent 7 September 2021 Guerrero, Mexico, M7 earthquake as well as to the 22 September 2021 Jiquilillo, Nicaragua, M6.5 earthquake with successful results. We also show that in 28 out of the 29 strong M ≥7.0 EQs studied, their epicenters lie close to an estimated zone covering only 8.5% of the total area.
... It is the scope of the present paper to show that by combining the above two NTA results with the modern method of nowcasting EQs [33], an estimate of the epicenter of the impending EQ with M ≥ 7.1 in the eastern Mediterranean region is achieved. EQ nowcasting employs natural time, which is unique in its characteristics [116], to estimate seismic risk by means of an EQ potential score (EPS) and found many useful applications, both regionally and globally [33,[116][117][118][119][120][121][122][123][124][125][126]. EQ nowcasting [33] has, so far, focused on describing the current state of fault systems. ...
The variance κ1 of the natural time analysis of earthquake catalogs was proposed in 2005 as an order parameter for seismicity, whose fluctuations proved, in 2011, to be minimized a few months before the strongest mainshock when studying the earthquakes in a given area. After the introduction of earthquake networks based on similar activity patterns, in 2012, the study of their higher order cores revealed, in 2019, the selection of appropriate areas in which the precursory minima βmin of the fluctuations β of the seismicity order parameter κ1 could be observed up to six months before all strong earthquakes above a certain threshold. The eastern Mediterranean region was studied in 2019, where all earthquakes of magnitude M≥7.1 were found to be preceded by βmin without any false alarm. Combining these results with the method of nowcasting earthquakes, introduced in 2016, for seismic risk estimation, here, we show that the epicenter of an impending strong earthquake can be estimated. This is achieved by employing—at the time of observing the βmin—nowcasting earthquakes in a square lattice grid in the study area and by averaging, self-consistently, the results obtained for the earthquake potential score. This is understood in the following context: The minimum βmin is ascertained to almost coincide with the onset of Seismic Electric Signals activity, which is accompanied by the development of long range correlations between earthquake magnitudes in the area that is a candidate for a mainshock.
... Last decade a new nowcasting method has initially been developed in the fields of economics and finance (Banbura et al., 2011(Banbura et al., , 2013Soybilgen and Yazgan, 2021). Then it has been used in earthquake studies (Field et al., 2007;Holliday et al., 2005Holliday et al., , 2006Holliday et al., , 2016Holliday et al., , 2016Perez-Oregon et al., 2020;Rundle et al., 2003Rundle et al., , 2012Rundle et al., , 2016Rundle et al., , 2018Rundle et al., , 2020. In this domain, it uses a number of small events, e.g., small earthquakes, to determine the risk of large events, e.g., large earthquakes, using data analysis not in conventional time but in the so-called natural time (Varotsos et al., 2005a(Varotsos et al., ,b, 2011(Varotsos et al., , 2014Sarlis et al., 2015;Varotsos et al., 2020c,d). ...
The main objective of the present study is to develop a model for the prediction of the extreme events of air pollution in megacities using the concept of so-called "natural time" instead of the "conventional clock time". In particular, we develop a new nowcasting technique based on a statistically significant fit to the law of Gutenberg-Richter of the surface concentration of ozone (O3), particles of the size fraction less than 10 μm (PM-10) and nitrogen dioxide (NO2). Studying the air pollution over Athens, Greece during the period 2000–2018, we found that the average waiting time between successive extreme concentrations values varied between different atmospheric parameters accounted as 17 days in case of O3, 29 days in case of PM-10 and 28 days in case of NO2. This average waiting time depends on the upper threshold of the maximum extreme concentrations of air pollutants considered. For instance, considering the NO2 concentrations over Athens it was found that the average waiting time is 13 days for 130 μg/m³ and 2.4 years for 200 μg/m³. Remarkably, the same behaviour of obedience to the Guttenberg-Richter law characterizing the extreme values of the air pollution of a megacity was found earlier in other long-term ecological and paleoclimatic variables. It is a sign of self-similarity that is often observed in nature, which can be used in the development of more reliable nowcasting models of extreme events.
... Natural time analysis also uncovers unique dynamic features hidden behind the time series of complex systems and has found applications in diverse fields, including the Olami-Feder-Christensen (OFC) EQ model [28] (see also Section 2.2), such as the study of EQs [29,30] and the identification of the sudden cardiac death risk [31], compiled in Reference [24], see also References [32][33][34][35] for more recent applications. Natural time, which is unique in its characteristics [36], is currently considered to be the basis for a new methodology to estimate the seismic risk by Turcotte and coworkers [36][37][38][39][40][41][42][43] termed "nowcasting earthquakes". ...
... and is a measure of the level of current hazard. As mentioned in the Introduction, nowcasting EQs were found useful in many applications [36][37][38][39][40][41][42][43] including the highly important estimation of seismic risk to various cities of the world. In this application, EQs, reported as mentioned in a Global catalog, with depths smaller than a given value D within a large area are studied [38] in order to obtain the CDF of n i . ...
... E(µ) = 50%), respectively. Earthquake nowcasting [36][37][38][39][40][41][42][43] uses EPS as the basis to estimate the seismic risk, as already mentioned. Here, we will attempt to use the EPS statistics as a possible EQ prediction method that will be evaluated by means of the Receiver Operating Characteristics (ROC) technique (e.g., see Reference [95]). ...
Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.
... The goal of our work is to improve upon the methods of earthquake nowcasting (Rundle, Giguere, et al., 2019;Rundle, Luginbuhl, et al., 2019;Rundle et al., 2002Rundle et al., , 2016Rundle et al., , 2018, which can be used to define the current state of risk from large earthquakes. These methods have begun to be applied to India (Pasari, 2019), Japan (K. ...
... Our present results contribute to the development of seismic nowcasting methods that we have discussed earlier (Rundle et al., 2016(Rundle et al., , 2018Rundle, Giguere, et al., 2019;Rundle, Luginbuhl, et al., 2019). In the previous methods, elastic rebound is introduced as a constraint, by counting small earthquakes since the last large earthquake. ...
Abstract 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.
