In models of triggered seismicity and in their inversion with empirical data, the detection threshold m_d is commonly equated to the magnitude m_0 of the smallest triggering earthquake. This unjustified assumption neglects the possibility of shocks below the detection threshold triggering observable events. We introduce a formalism that distinguishes between the detection threshold m_d and the minimum triggering earthquake m_0 < m_d. By considering the branching structure of one complete cascade of triggered events, we derive the apparent branching ratio n_a (which is the apparent fraction of aftershocks in a given catalog) and the apparent background source S_a that are observed when only the structure above the detection threshold m_d is known due to the presence of smaller undetected events that are capable of triggering larger events. If earthquake triggering is controlled in large part by the smallest magnitudes as several recent analyses have shown, this implies that previous estimates of the clustering parameters may significantly underestimate the true values: for instance, an observed fraction of 55% of aftershocks is renormalized into a true value of 75% of triggered events.
Using the simple ETAS branching model of seismicity, which assumes that each earthquake can trigger other earthquakes, we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as the overall level of seismicity in the presence of a constant external seismicity source. We show that, in this model, the fraction of earthquakes in the population that are aftershocks is equal to the fraction of aftershocks that are indirectly triggered and is given by the average number of triggered events per earthquake. Previous observations that a sig…
We report precursory seismic patterns prior to the 2016 Kumamoto earthquakes, as measured by four different methods based on changes in seismicity that can be used for earthquake forecasting: the b-value method, two methods of seismic quiescence evaluation, and an analysis of seismicity density in space and time. The spatial extent of precursory patterns differs from one method to the other and ranges from local scales (typically, asperity size) to regional scales (e.g., 2 degree x 3 degree around the source zone). The earthquakes were preceded by periods of pronounced anomalies, which lasted …
Despite the enormous efforts towards searching for precursors, no precursors have exhibited real predictive power with respect to an earthquake thus far. Seismogenic locked segments that can accumulate adequate strain energy to cause major earthquakes are very heterogeneous and less brittle; progressive failures of the locked segments with these properties can produce an interesting seismic phenomenon: a characteristic earthquake and a sequence of smaller subsequent earthquakes (pre-shocks) always arise prior to another characteristic earthquake within a well-defined seismic zone and its curre…
Xu et al. [J. Asian Earth Sci. {\bf 77}, 59-65 (2013)] It has just been reported that approximately 2 months prior to the $M_w$9.0 Tohoku earthquake that occurred in Japan on 11 March 2011 anomalous variations of the geomagnetic field have been observed in the vertical component at a measuring station about 135 km from the epicenter for about 10 days (4 to 14 January 2011). Here, we show that this observation is in striking agreement with independent recent results obtained from natural time analysis of seismicity in Japan. In particular, this analysis has revealed that an unprecedented minimu…
It has been shown [Phys. Rev. E 84, 022101 (2011); Chaos 22, 023123 (2012)] that earthquakes of magnitude $M$ greater or equal to 7 are globally correlated. Such correlations were identified by studying the variance $κ_1$ of natural time which has been proposed as an order parameter for seismicity. Here, we study the fluctuations of this order parameter using the Global Centroid Moment Tensor catalog for a magnitude threshold $M_{thres}=5.0$ and focus on its behavior before major earthquakes. Natural time analysis reveals that distinct minima of the fluctuations of the order parameter of seism…
Crustal deformation due to the 2016 earthquake sequence in Kumamoto, Japan, that culminated in a preceding earthquake of magnitude M6.5 and a subsequent M7.3 earthquake 28 hours later, caused stress perturbation on and around the causative Futagawa-Hinagu fault zone. Monitoring changes in seismicity pattern along this zone plays a role in understanding the process before and after major earthquakes. For this purpose, stress-dependent laws in statistical seismology can be used: the Gutenberg-Richter frequency-size law and the Omori-Utsu aftershock-decay law. We review the results obtained by us…
The long-term erosion of steep landscapes is punctuated by dramatic erosional events that can remove significant amount of sediments within a time-scale shorter than a seismic cycle. However, the role of such large erosional events on seismicity is poorly understood. We use QDYN, a quasi-dynamic numerical model of earthquake cycles to investigate the effect of a large erosional event on seismicity. The progressive evacuation of landslide sediments is modelled by a transient normal stress decrease. We show that erosional events with a shorter duration compared with the duration of a seismic cyc…
Spatial and temporal data for earthquakes with magnitude M greater than or equal to 6.5 can provide crucial information about the seismic history and potential for large earthquakes in a region. We analyzed approximately 313,500 events that occurred in the Sunda-arc region during the last 56 years, from 1964 to 2020, reported by the International Seismological Center. We report a persistent increase in the annual number of the events with mb greater than or equal to 6.5. We tested this increase against the null hypothesis and discarded the possibility of the increase being due to random groupi…
In this paper we show, in terms of Fisher information and approximate entropy, that the two strong impulsive kHz electromagnetic (EM) bursts recorder prior to the Athens EQ (7 September 1999, magnitude 5.9) present compatibility to the radar interferometry data and the seismic data analysis, which indicate that two fault segments were activated during Athens EQ. The calculated Fisher information and approximate entropy content ratios closely follow the radar interferometry result that the main fault segment was responsible for 80% of the total energy released, while the secondary fault segment…
Using a catalog of seismicity for Southern California, we measure how the number of triggered earthquakes increases with the earthquake magnitude. The trade-off between this relation and the distribution of earthquake magnitudes controls the relative role of small compared to large earthquakes. We show that seismicity triggering is driven by the smallest earthquakes, which trigger fewer events than larger earthquakes, but which are much more numerous. We propose that the non-trivial scaling of the number of triggered earthquakes emerges from the fractal spatial distribution of seismicity.
This entry in the Encyclopedia of Complexity and Systems Science, Springer present a summary of some of the concepts and calculational tools that have been developed in attempts to apply statistical physics approaches to seismology. We summarize the leading theoretical physical models of the space-time organization of earthquakes. We present a general discussion and several examples of the new metrics proposed by statistical physicists, underlining their strengths and weaknesses. The entry concludes by briefly outlining future directions. The presentation is organized as follows. I Glossary II…
The aspect of self-affine nature of faulting and fracture is widely documented from the data analysis of both field observations and laboratory experiments. In this direction, Huang and Turcotte have stated that the statistics of regional seismicity could be merely a macroscopic reflection of the physical processes in earthquake source, namely, the activation of a single fault is a reduced self-affine image of regional seismicity. This work verifies the aforementioned proposal. More precisely we show that the population of: (i) the earthquakes that precede of a significant event and occur arou…
The observation of foreshocks preceding large earthquakes and the suggestion that foreshocks have specific properties that may be used to distinguish them from other earthquakes have raised the hope that large earthquakes may be predictable. Among proposed anomalous properties are the larger proportion than normal of large versus small foreshocks, the power law acceleration of seismicity rate as a function of time to the mainshock and the spatial migration of foreshocks toward the mainshock, when averaging over many sequences. Using Southern California seismicity, we show that these properties…
Any periodic variations of earthquake occurrence rates in response to small, known, periodic stress variations provide important opportunities to learn about the earthquake nucleation process. Yet, reliable detection of earthquake periodicity is complicated by the presence of earthquake clustering due to aftershocks and foreshocks. Existing methods for detecting periodicity in an earthquake catalogue typically require the prior removal of these clustered events. Declustering is a highly uncertain process, so declustering methods are inherently non-unique. Incorrect declustering may remove some…
Seasonal patterns associated with stress modulation, as evidenced by earthquake occurrence, have been detected in regions characterized by present day mountain building and glacial retreat in the Northern Hemisphere. In the Himalaya and the Alps, seismicity is peaking in spring and summer; opposite behaviour is observed in the Apennines. This diametrical behaviour, confirmed by recent strong earthquakes, well correlates with the dominant tectonic regime: peak in spring and summer in shortening areas, peak in fall and winter in extensional areas. The analysis of the seasonal effect is extended …
Seismotectonics and Slip Behavior of a Submarine Plate Boundary Fault from Seismicity Repeaters and Tomography using a high-resolution earthquake catalog from machine learning
The subsequent series of responses to big events may exhibit a synchronicity of event number, frequency and energy release in different fault zones. This synchronicity is a reliable source for probing non-intuitive geological structures, assessing regional seismicity hazard map and even predicting the next big events. The synchronicity of main faults in the eastern margin of the Qinghai-Tibetan Plateau is still unknown to us. We propose to examine the correlation of earthquake occurrence among different fault zones to indicate this synchronicity, and to obtain a preliminary understanding of ge…
The recent evolution of induced seismicity in Central United States calls for exhaustive catalogs to improve seismic hazard assessment. Over the last decades, the volume of seismic data has increased exponentially, creating a need for efficient algorithms to reliably detect and locate earthquakes. Today's most elaborate methods scan through the plethora of continuous seismic records, searching for repeating seismic signals. In this work, we leverage the recent advances in artificial intelligence and present ConvNetQuake, a highly scalable convolutional neural network for earthquake detection a…
The analysis of the earthquakes catalog of Greece for the period 1964 to 2010 indicates a continuously increasing no. of seismic events. A detailed determination of the cumulative seismic energy release, for specific earthquake magnitudes, revealed that for magnitudes up to Ms = 5.0R the Greek territory, considered as a unified seismogenic area, is at a state of accelerating deformation for almost the last 10 years. The background seismicity rate, considering constant cumulative seismic energy release for the entire study period, corresponds to a magnitude of Ms = 5.5R, while for earthquakes o…
The 2016 Kumamoto earthquakes started with a magnitude (M) 6.5 quake on Apr 14 on the Hinagu fault zone (FZ), followed by active seismicity including an M6.4 quake. Eventually, an M7.3 quake occurred on Apr 16 on the Futagawa FZ. We investigated if any sign indicative of the M7.3 quake could be found in the space-time changes of seismicity after the M6.5 quake. We determined in advance the threshold magnitude, above which all earthquakes are completely recorded. We then showed that the occurrence rate of relatively large (M >= 3) earthquakes significantly decreased 1 day before the M7.3 quake.…
Upon employing the analysis in a new time domain, termed natural time, it has been recently demonstrated that a remarkable change of seismicity emerges before major mainshocks in California. What constitutes this change is that the fluctuations of the order parameter of seismicity exhibit a clearly detectable minimum. This is identified by using a natural time window sliding event by event through the time series of the earthquakes in a wide area and comprising a number of events that would occur on the average within a few months or so. Here, we suggest a method to estimate the epicentral are…
Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $m_d$) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to investigate how the statistical properties of observable earthquakes differ from the statistics of all events. The ETAS (epidemic-type aftershock sequence) model assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence res…
The North Anatolian Fault experienced large earthquakes with 250-400 years recurrence time. In the Marmara Sea region, the 1999 (Mw = 7.4) and the 1912 (Mw = 7.4) earthquake ruptures bound the Central Marmara Sea fault segment. Using historical-instrumental seismicity catalogue and paleoseismic results (~2000-year database), the mapped fault segments, fault kinematic and GPS data, we compute the paleoseismic-seismic moment rate and geodetic moment rate. A clear discrepancy appears between the moment rates and implies a significant delay in the seismic slip along the fault in the Marmara Sea. T…
In their paper (Europhys. Lett., 71 (2005) 1036), Carbone, Sorriso-Valvo, Harabaglia and Guerra showed that "unified scaling law" for conventional waiting times of earthquakes claimed by Bak et al. (Phys. Rev. Lett., 88 (2002) 178501) is actually not universal. Here, instead of the conventional time, the concept of the internal time termed the event time is considered for seismicity. It is shown that, in contrast to the conventional waiting time, the waiting event time obeys a power law. This implies the existence of temporal long-range correlations in terms of the event time with no sharp dec…
In this work the data of the earthquake catalog of the NOAA, National Geophysical Data Center (NGDC) are processed in terms of global seismic energy release. The determined Global Cumulative Seismic Energy Release (GCSER) graph as a function of time, is analyzed in the magnitude domain (discrete energy windows). Characteristic components of the analyzed graph are: its accelerated deformation character observed for energy windows lower than the background seismicity (M = 7.0 - 7.5), its lock state that started on 1923 and long seismic quiescence periods that preceded recent mega - earthquakes. …
We present a model for estimating the probabilities of future earthquakes of magnitudes m > 4.95 in Italy. The model, a slightly modified version of the one proposed for California by Helmstetter et al. (2007) and Werner et al. (2010), approximates seismicity by a spatially heterogeneous, temporally homogeneous Poisson point process. The temporal, spatial and magnitude dimensions are entirely decoupled. Magnitudes are independently and identically distributed according to a tapered Gutenberg-Richter magnitude distribution. We estimated the spatial distribution of future seismicity by smoothing…
Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays
Currently, one of the best performing and most popular earthquake forecasting models rely on the working hypothesis that: "locations of past background earthquakes reveal the probable location of future seismicity". As an alternative, we present a class of smoothed seismicity models (SSMs) based on the principles of the Epidemic Type Aftershock Sequence (ETAS) model, which forecast the location, time and magnitude of all future earthquakes using the estimates of the background seismicity rate and the rates of future aftershocks of all generations. Using the Californian earthquake catalog, we f…
The 2018 rift zone eruption of K\=ılauea volcano was accompanied by a remarkable and episodic collapse of its summit. Between May-August the eruption and collapse sequence included over 70,000 earthquakes (M$\geq$0) and 54 major earthquakes (M$\geq$5). We analyzed the seismicity in the K\=ılauea summit region and estimated seismic full moment tensors with their uncertainties for the 54 M$\geq$5 events. These events occurred at almost daily intervals and were accompanied by intense seismicity which was concentrated between 0-3 km depths beneath the Halema`uma`u pit crater. The hypocenters revea…
The magnitude distribution of three seismic sequences occurred in Morocco were investigated by means of the Tsallis-based non-extensive analysis. The non-extensive parameters were estimated by means of the Levenberg-Marquadt nonlinear least square fitting method. It was found that the q value could be a good indicator of the complexity of seismic phenomena. Such findings could contribute in better understanding the dynamics of seismicity and suggesting a unifying view of earthquake occurrence.
Waiting-time statistics are generated from the Olami-Feder-Christensen model and shown to mimic some aspects of real seismicity. Preliminary analysis of the model data implies a recently proposed universal scaling law for the distribution in seismicity may be due to a mixing between aftershocks and uncorrelated event pairs, thus having limited application. Earthquake catalog data is also presented to support the argument.
Coulomb-stress theory has been used for years in seismology to understand how earthquakes trigger each other. Whenever an earthquake occurs, the stress field changes, and places with positive increases are brought closer to failure. Earthquake models that relate earthquake rates and Coulomb stress after a main event, such as the rate-and-state model, assume that the magnitude distribution of earthquakes is not affected by the change in the Coulomb stress. By using different slip models, we calculate the change in Coulomb stress in the fault plane for every aftershock after the Landers event (C…
We inquire the statistical nature and dynamics of shallow and deep seismogenesis along major plate margins of the NW Circum-Pacific Belt, by examining whether earthquakes are generated by Poisson processes and are independent (uncorrelated), or by Complex processes and are dependent (correlated). Analysis is based of Non Extensive Statistical Physics and the complete and homogeneous catalogue of the Japan Meteorological Agency for the period 2002-2016.5. Emphasis is given to background seismicity recovered by removing aftershocks with stochastic declustering. Long-term correlation and long-ran…
A recently proposed method of constructing seismic networks from 'record breaking events' from the earthquake catalog of California (Phy. Rev. E, 77 6,066104, 2008) was successfull in establishing causal features to seismicity and arrive at estimates for rupture length and its scaling with magnitude. The results of our implementation of this procedure on the earthquake catalog of Japan establishes the robustness of the procedure. Additionally, we find that the temporal distributions are able to detect heterogeneties in the seismicity of the region.
Starting in April 2004, unusual seismic activity was observed in the interior of the island of Tenerife (Canary Islands, Spain) with much evidence pointing to a reawakening of volcanic activity. This seismicity is now analyzed with techniques unprecedented in previous studies of this crisis. The 200 earthquakes located onshore during 2004 and 2005 have been classified by cross-correlation, resulting in a small number of significant families. The application of a relative location algorithm (hypoDD) revealed important features about the spatial distribution of the earthquakes. The seismic catal…
We propose and study a modified version of the Olami-Feder-Christiensen model of seismicity, that includes a mechanism of structural relaxation. We obtain realistic features of seismicity that are not obtained with the original version, mainly: aftershocks that obey the Omori law and cluster spatially around the slip surface of the main shock, and averaged frictional properties qualitatively similar to those observed in rock friction, in particular the velocity weakening effect.
We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark model of seismicity, which just assumes no difference in the physics of foreshocks, mainshocks and aftershocks. Our theoretical calculations provide good fits to the data and show that universality is only approximate. We conclude that the distributions of inter-event times do not reveal more information than what is already known from the Gutenberg-Richter and the Omori power laws. Our results reinforces the view t…
Spatio-temporal evolution of low-magnitude seismicity before the May 24, 2013, Sea of Okhotsk earthquake recovered by waveform cross correlation. Is it an earthquake prediction case?
A recent statistical analysis of the relationship between tides and seismic activity in Colombia has suggested the existence of correlation anomalies for the case of intermediate depth events in the Bucaramanga nest and the Cauca cluster (Moncayo et al., 2019). In this work, we explore in detail the hypothesis that tides may be triggering seismic activity in these regions and extend the analysis to two other seismic clusters in northern-central South America, specifically in the areas of El Puyo (Ecuador) and Pucallpa (Peru). For this purpose, we use the available focal mechanism information f…
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic catalogs while improving the access to the spatial information content of seismic catalogs. The PDFs of events are first ranked by decreasing location errors and then successively condensed onto better located and lower variance event PDFs. The obtained condensed catalog attributes different weights to each event, providing an optimal spatial representation w…
We show the capabilities of a downhole Distributed Acoustic Sensing (DAS) array in detecting, locating and characterizing low-magnitude earthquakes occurring in the vicinity of the Frontier Observatory for Research in Geothermal Energy (FORGE) site in Utah. 10.5 days of continuous data were acquired in a monitoring well at the FORGE geothermal site during the initial stimulation of an Enhanced Geothermal System in April-May 2019. Earthquake activity beneath Mineral Mountains, Utah also occurred within 10 km of the FORGE monitoring well. During the experiment, four events from those areas were …
By applying natural time analysis to the time series of earthquakes, we find that the order parameter of seismicity exhibits a unique change approximately at the date(s) at which Seismic Electric Signals (SES) activities have been reported to initiate. In particular, we show that the fluctuations of the order parameter of seismicity in Japan exhibits a clearly detectable minimum approximately at the time of the initiation of the SES activity observed almost two months before the onset of the Volcanic-seismic swarm activity in 2000 in the Izu Island region, Japan. To the best of our knowledge, …
I study a recently proposed statistical model of earthquake dynamics that incorporates aging as a fundamental ingredient. The model is known to generate earthquake sequences that quantitatively reproduce the spatial and temporal clustering of events observed in actual seismic patterns. The aim of the present work is to investigate if this model can give support to the empirical evidence that earthquakes can be triggered by transient small perturbations, particularly by the passing of seismic waves originated in events occurring in far geographical locations. The effect of seismic waves is inco…
The 2016 Mw 7.0 Kumamoto Earthquake Sequence, Japan revisited: Insights from Spatio-Temporal Analysis of Seismicity Parameters
Farhangian University（法尔干大学）；Ankara University（安卡拉大学）；University of Beira Interior（贝拉内陆大学）；Atmosphere and Ocean Research Institute (AORI), the University of Tokyo（东京大学大气海洋研究所）
