We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. Data pertaining to three different seismic regions, viz. California, Japan and Himalayas, are comparatively analyzed using such a network model. The distribution of recurrence lengths and recurrence times are two of the key features analyzed to draw conclusions about the universal aspects of such a network model. We find that the unimodal feature of recurrence length distribution, which helps to associate typical rupture lengths with different magnitude earthquakes, is robust across the different seismic regions. The out-degree of the networks shows a hub structure rooted on the large magnitude earthquakes. In-degree distribution is seen to be dependent on the density of events in the neighborhood. Power laws, with two regimes having different exponents, are obtained with recurrence time distribution. This is in agreement with the Omori law for aftershocks and extends it to spatial recurrences. The crossover to the second power law regime can be taken to be signalling the end of aftershock regime in an objective fashion.
Spatio-temporal correlations of earthquakes are studied numerically on the basis of the one-dimensional spring-block (Burridge-Knopoff) model. As large events approach, the frequency of smaller events gradually increases, while, just before the mainshock, it is dramatically suppressed in a close vicinity of the epicenter of the upcoming mainshock, a phenomenon closely resembling the ``Mogi doughnut''
Statistical properties of earthquakes are studied both by the analysis of real earthquake catalog of Japan and by numerical computer simulations of the spring-block model in both one and two dimensions. Particular attention is paid to the spatiotemporal correlations of earthquakes, e.g., the recurrence-time distribution or the time evolution before and after the mainshock of seismic distribution functions, including the magnitude distribution and the spatial seismic distribution. Certain eminent features of the spatiotemporal correlations, e.g., foreshocks, aftershocks, swarms and doughnut-lik…
The concept of proper time, which is different from universal time, has been introduced into the physics of earthquakes. The global activity of strong earthquakes was chosen as the object of study. We consider the sequence of earthquakes as a random process of the Poisson type. Comparatively weak earthquakes are used as the underground clock, the ticking of which marks the course of proper time. The Poisson distribution is compared with the distributions for two sequences of strong earthquakes. One of the sequences is ordered by calendar time, and the second by proper time. The result of the t…
Large earthquakes occurring worldwide have long been recognised to be non Poisson distributed, so involving some large scale correlation mechanism, which could be internal or external to the Earth. Till now, no statistically significant correlation of the global seismicity with one of the possible mechanisms has been demonstrated yet. In this paper, we analyse 20 years of proton density and velocity data, as reported by the ISC-GEM catalogue. We found clear correlation between proton density and the occurrence of large earthquakes (M>5.8), with a time shift of one day. The significance of such…
Spatiotemporal correlations of the two-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. The model is found to exhibit either ``subcritical'' or ``supercritical'' behavior, depending on the values of the model parameters. Transition between these regimes is either continuous or discontinuous. Seismic events in the ``subcritical'' regime and those in the ``supercritical'' regime at larger magnitudes exhibit universal scaling properties. In the ``supercritical'' regime, eminent spatiotemporal correlations, {\it e.…
A crucial point in the debate on feasibility of earthquake prediction is the dependence of an earthquake magnitude from past seismicity. Indeed, whilst clustering in time and space is widely accepted, much more questionable is the existence of magnitude correlations. The standard approach generally assumes that magnitudes are independent and therefore in principle unpredictable. Here we show the existence of clustering in magnitude: earthquakes occur with higher probability close in time, space and magnitude to previous events. More precisely, the next earthquake tends to have a magnitude simi…
A characteristic change of seismicity has been recently uncovered when the precursory Seismic Electric Signals activities initiate before an earthquake occurrence. In particular, the fluctuations of the order parameter of seismicity exhibit a simultaneous distinct minimum upon analyzing the seismic catalogue in a new time domain termed natural time and employing a sliding natural time window comprising a number of events that would occur in a few months. Here, we focus on the minima preceding all earthquakes of magnitude 8 (and 9) class that occurred in Japanese area from 1 January 1984 to 11 …
Recent observation studies have revealed that earthquakes are classified into several different categories. Each category might be characterized by the unique statistical feature in the time series, but the present understanding is still limited due to their nonlinear and nonstationary nature. Here we utilize complex network theory to shed new light on the statistical properties of earthquake time series. We investigate two kinds of time series, which are magnitude and inter-event time (IET), for three different categories of earthquakes: regular earthquakes, earthquake swarms, and tectonic tr…
We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of earthquakes is constructed, which is time ordered and with links between the more correlated ones. Data pertaining to the California region has been used in the study. Recurrences to earthquakes are identified employing correlation thresholds to demarcate the most meaningful ones in each cluster. The distribution of recurrence lengths and recurrence times are analy…
Spatio-temporal correlations of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes are extensively studied by means of numerical computer simulations. Particular attention is paid to clarifying how the statistical properties of earthquakes depend on the frictional and elastic properties of earthquake faults. It is found that, as the velocity-weakening tendency of the friction force gets weaker, the system tends to be more critical, while, as the velocity-weakening tendency gets stronger, the system tends to be more off-critical with enhanced features of a characteristic e…
In the present paper we have conducted studies on seismological properties using worldwide data of deep earthquakes (depth larger than 70 km), considering events with magnitude $m \geq 4.5$. We have addressed the problem under the perspective of complex networks, using a time window model to build the networks for deep earthquakes, which present scale-free and small-world features. This work is an extension of a previous study using a similar approach, for shallow events. Our results for deep events corroborate with those found for the shallow ones, since the connectivity distribution for deep…
We assess the level of cross correlation between P-waves generated by earthquakes in the Atlantic Ocean and measured by 22 array stations of the International Monitoring System (IMS). There are 931 events with 6,411 arrivals in 2011 and 2012. Station TORD was the most sensitive and detected 868 from 931 events. We constructed several 931 by 931 matrices of cross correlation coefficients (CCs) for individual stations and also for average and cumulative CCs. These matrices characterize the detection performance of the involved stations and the IMS. Sixty earthquakes located in the northern hemis…
Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade process, each event produces aftershocks. A definitive method to assess any connection between two earthquakes separated in time and distance does not exist. Here we propose a novel method of data analysis that, based on the space-time combined generalization of the correlation integral leads to a self-consistent visualization and analysis of both spatial and tem…
We propose a new type of earthquake precursor based on the analysis of correlation dynamics between geophysical signals of different nature. The precursor is found using a two-parameter cross-correlation function introduced within the framework of flicker-noise spectroscopy, a general statistical physics approach to the analysis of time series. We consider an example of cross-correlation analysis for water salinity time series, an integral characteristic of the chemical composition of groundwater, and geoacoustic emissions recorded at the G-1 borehole on the Kamchatka peninsula in the time fra…
It has been observed that the earthquake events possess short-term memory, i.e. that events occurring in a particular location are dependent on the short history of that location. We conduct an analysis to see whether real-time earthquake data also possess long-term memory and, if so, whether such autocorrelations depend on the size of earthquakes within close spatiotemporal proximity. We analyze the seismic waveform database recorded by 64 stations in Japan, including the 2011 "Great East Japan Earthquake", one of the five most powerful earthquakes ever recorded which resulted in a tsunami an…
The method of waveforms cross correlation (WCC) is used to detect signals from aftershocks of the August 14, 2016 earthquake within Sakhalin Island, which had local magnitude ML = 6.1. Arrivals of regular P- and S-waves detected by the WCC method with various master events at 6 regional stations are associated into a set of seismic events called the cross correlation standard event list (XSEL). We compare the XSEL with the bulletin for the same aftershock sequence compiled in routine seismological processing. The principal advantage of the XSEL is expressed in the increasing number of found se…
We revisit the work of Kilston and Knopoff (1983) to study the correlation of earthquakes with the main lunisolar tidal components in the limited zone of the Southern California region, with a considerably bigger amount of data. By adopting the same methodology as these authors, we confirm their results, i.e. that strong earthquakes with M >= 6 show a statistically significant correlation with half day and precession cycles, with respective periods 12 hr. and 18.6 y., while weaker earthquakes show a correlation with the annual cycle. Moreover we extended the study to the analysis of bi-modal p…
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?
The time dependence of the parameter of the Gutenberg-Richter (GR) magnitude distribution is computed for foreshock sequences of earthquakes, correlated with the main shock, by using the geometric-growth model of earthquake focus, the magnitude distribution of correlated earthquakes and the time-magnitude correlations, derived recently. It is shown that this parameter decreases in time in the foreshock sequence, from the background values down to the main shock. If correlations are present, this time dependence and the time-magnitude correlations provide a tool of monitoring the foreshock seis…
Spatiotemporal correlations of the two-dimensional spring-block (Burridge-Knopoff) models of earthquakes with the long-range inter-block interactions are extensively studied by means of numerical computer simulations. The long-range interaction derived from an elasticd theory, which takes account of the effect of the elastic body adjacent to the fault plane, falls off with distance r as 1/r^3. Comparison is made with the properties of the corresponding short-range models studied earlier. Seismic spatiotemporal correlations of the long-range models generally tend to be weaker than those of the …
Low-magnitude seismic activity between the Kamchatka July 20 and July 29, 2025, earthquakes. Spatio-temporal evolution recovered using waveform cross-correlation
From 23 - 27 July 2001 in the Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia was held a seminar under the title: "Possible correlations between electromagnetic earth fields and future earthquakes" organized by the Institute's Department of "Astrophysical Objects and Environment". As a main result of the first two days seminar work was the prediction of the direction and the day of the Skyros, Greece earthquake, that was confirned in the next day: Aeg. Sea, 07/26 00:21:37, 39.06N 24.34E, Depth 19 km, Mag 6.3- http://www.noa.gr/English/home-en.html. Analog…
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…
There are different kinds of intensity measures to characterize the main properties of the earthquake records. This paper proposes a simulation-based approach to compute correlation coefficients of motion duration and intensity measures of the earthquake ground motions. This method is used to investigate the influence of the ground motion data set selection in resulting duration-intensity correlation coefficients. The simulation procedure is used to tackle the problem of inadequate available ground motions with specific parameters. Correlation coefficients are investigated in three different c…
The concept of seismic interferometry embraces the construction of waves traveling between receivers or sources with cross-correlation techniques. In the present study cross-correlations of coda waves are used to measure travel times of shear waves between earthquake locations for five event clusters of the 2018 West Bohemia earthquake swarm. With the help of a high quality earthquake catalog, I was able to determine the shear wave velocity in the region of the five clusters separately. The shear wave velocities range between 3.5 km/s and 4.2 km/s. The resolution of this novel method is given …
Earthquake hypocenters form the basis for a wide array of seismological analyses. Pick-based earthquake location workflows rely on the accuracy of phase pickers and may be biased when dealing with complex earthquake sequences in heterogeneous media. Time-reversal imaging of passive seismic sources with the cross-correlation imaging condition has potential for earthquake location with high accuracy and high resolution, but carries a large computational cost. Here we present an alternative deep-learning approach for earthquake location by combining the benefits of neural operators for wave propa…
Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays
We study the spatial distribution of clusters associated to the aftershocks of the megathrust Maule earthquake MW 8.8 of 27 February 2010. We used a recent clustering method which hinges on a nonparametric estimation of the underlying probability density function to detect subsets of points forming clusters associated with high density areas. In addition, we estimate the probability density function using a nonparametric kernel method for each of these clusters. This allows us to identify a set of regions where there is an association between frequency of events and coseismic slip. Our results…
Earthquakes are a complex spatiotemporal phenomenon, the underlying mechanism for which is still not fully understood despite decades of research and analysis. We propose and develop a network approach to earthquake events. In this network, a node represents a spatial location while a link between two nodes represents similar activity patterns in the two different locations. The strength of a link is proportional to the strength of the cross-correlation in activities of two nodes joined by the link. We apply our network approach to a Japanese earthquake catalog spanning the 14-year period 1985…
We propose that the widely observed and universal Gutenberg-Richter relation is a mathematical consequence of the critical branching nature of earthquake process in a brittle fracture environment. These arguments, though preliminary, are confirmed by recent investigations of the seismic moment distribution in global earthquake catalogs and by the results on the distribution in crystals of dislocation avalanche sizes. We consider possible systematic and random errors in determining earthquake size, especially its seismic moment. These effects increase the estimate of the parameter beta of the p…
We invoke a metric to quantify the correlation between any two earthquakes. This provides a simple and straightforward alternative to using space-time windows to detect aftershock sequences and obviates the need to distinguish main shocks from aftershocks. Directed networks of earthquakes are constructed by placing a link, directed from the past to the future, between pairs of events that are strongly correlated. Each link has a weight giving the relative strength of correlation such that the sum over the incoming links to any node equals unity for aftershocks, or zero if the event had no corr…
A comparative study is performed on volcanic seismicities at Icelandic volcano, Eyjafjallajökull, and Mt. Etna in Sicily from the viewpoint of complex systems science, and the discovery of remarkable similarities between them is reported. In these seismicities as point processes, the jump probability distributions of earthquakes (i.e., distributions of the distance between the hypocenters of two successive events) are found to obey the exponential law, whereas the waiting-time distributions (i.e., distributions of inter-occurrence time of two successive events) follow the power law. A careful …
The imminent WHEN earthquake predictions are based on the correlation between geomagnetic quakes and the incoming minimum (or maximum) of tidal gravitational potential. The probability time window for the incoming earthquake is for the tidal minimum approximately one day and for the maximum- two days. The statistic evidence for reliability is based on of distributions of the time difference between occurred and predicted earthquakes for the period 2002- 2005 for Sofia region and 2004- 2005 for Skopje. The project for complex Balkan- Black Sea region NETWORK for earthquake prediction by using t…
Recovery of low-magnitude seismic events before the July 29, 2025, Kamchatka megathrust earthquake using waveform cross-correlation enhanced by the addition of stochastic noise
Motivated by the fact that empirical time series of earthquakes exhibit long-range correlations in space and time and the Gutenberg-Richter distribution of magnitudes, we propose a simple fault model that can account for these types of scale-invariance. It is an avalanching process that displays power-laws in the event sizes, in the epicenter distances as well as in the waiting-time distributions, and also aftershock rates obeying a generalized Omori law. We thus confirm that there is a relation between temporal and spatial clustering of the activity in this kind of models. The fluctuating bou…
A measure of the correlation between two earthquakes is used to link events to their aftershocks, generating a growing network structure. In this framework one can quantify whether an aftershock is close or far, from main shocks of all magnitudes. We find that simple network motifs involving links to far aftershocks appear frequently before the three biggest earthquakes of the last 16 years in Southern California. Hence, networks could be useful to detect symptoms typically preceding major events.
Self-similarity may stem from two origins: the process' increments infinite variance and/or process' memory. The $b$-value of the Gutenberg-Richter law comes from the first origin. In the frame of natural time analysis of earthquake data, a fall of the b-value observed before large earthquakes reflects an increase of the order parameter fluctuations upon approaching the critical point (mainshock). The increase of these fluctuations, however, is also influenced from the second origin of self-similarity, i.e., temporal correlations between earthquake magnitudes. This is supported by observations…
Earthquakes can be detected by matching spatial patterns or phase properties from 1-D seismic waves. Current earthquake detection methods, such as waveform correlation and template matching, have difficulty detecting anomalous earthquakes that are not similar to other earthquakes. In recent years, machine-learning techniques for earthquake detection have been emerging as a new active research direction. In this paper, we develop a novel earthquake detection method based on dictionary learning. Our detection method first generates rich features via signal processing and statistical methods and …
We study experimentally the fluctuations of deformation along a shear fault naturally emerging within a compressed frictional granular medium. Using laser interferometry, we show that the deformation inside this granular gouge occurs as a succession of localized micro-slips distributed along the fault. The associated distributions of released seismic moments, the memory effects in strain fluctuations, as well as the time correlations between successive events, follow exactly the empirical laws of natural earthquakes. Using a methodology initially developed in seismology and social science, we …
The empirical Bath's law is derived from the magnitude-difference statistical distribution of earthquake pairs. The pair distribution related to earthquake correlations is presented. The single-event distribution of dynamically correlated earthquakes is derived, by means of the geometric-growth model of energy accumulation in the focal region. The dynamical correlations may account, at least partially, for the roll-off effect in the Gutenberg-Richter distributions. The seismic activity which accompanies a main shock, including both the aftershocks and the foreshocks, can be viewed as fluctuati…
Extraction of information in the form of oscillations from noisy data of natural phenomena such as sounds, earthquakes, ionospheric and brain activity, and various emissions from cosmic objects is extremely difficult. As a method for finding periodicity in such challenging data sets, the 2D Hybrid approach, which employs wavelets, is presented. Our technique produces a wavelet transform correlation intensity contour map for two (or one) time series on a period plane defined by two independent period axes. Notably, by spreading peaks across the second dimension, our method improves apparent res…
We report remarkable similarities in the output signal of two distinct out-of- equilibrium physical systems - earthquakes and the intermittent acoustic noise emitted by crum- pled plastic sheets - Biaxially Oriented Polypropylene (BOPP) films. We show that both signals share several statistical properties including the distribution of energy, distribution of energy in- crements for distinct time scales, distribution of return intervals and correlations in the magnitude and sign of energy increments. This analogy is consistent with the concept of universality in com- plex systems and could prov…
It is given an attempt for statistical estimation of when earthquake prediction for Balkan- Black Sea region using the geomagnetic field signal. The preliminary test of the approach for England (Hartland), Turkey (Kandilli) and India (Alibag) regions is presented. The research step by step program for creating when, where and how earthquake prediction region Network system on the basis of the experimental data for geomagnetic field, electro-potential distribution in the Earth crust and atmosphere, temperature Earth crust distribution, gravitational anomaly map, season and day independent tempe…
Effects of stochastic and natural seismic noise on the performance of waveform cross-correlation used to recover low-magnitude seismicity prior to the July 29, 2025, Kamchatka earthquake
Research on the earthquake occurrences using a statistical methodology based on point processes has mainly focused on the data featuring earthquake catalogs which ignores the effect of environmental variables. In this paper, we introduce inhomogeneous versions of the Cox process models which are able to quantify the effect of geological factors such as subduction zone, fault, and volcano on the major earthquake distribution in Sulawesi and Maluku, Indonesia. In particular, we compare Thomas, Cauchy, variance-Gamma, and log-Gaussian Cox models and consider parametric intensity and pair correlat…
In this paper we show that the simple analysis of the local geomagnetic field behaviour can serve as reliable imminent precursor for regional seismic activity increasing. As the first step the problem was investigated using one- component Dubna fluxgate magnetometer. The result of 2001-2004 Sofia monitoring confirmed many old papers for connection between Earth tide (Sun- Moon tides as earthquakes trigger) and jump (Geomagnetic quake) of daily averaged one minute standart deviation of the geomagnetic field. The second step (2004-present), which included analisys of three-component Danish fluxg…
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…
A multicomponent random process used as a model for the problem of space-time earthquake prediction; this allows us to develop consistent estimation for conditional probabilities of large earthquakes if the values of the predictor characterizing the seismicity prehistory are known. We introduce tools for assessing prediction efficiency, including a separate determination of efficiency for "time prediction" and "location prediction": a generalized correlation coefficient and the density of information gain. We suggest a technique for testing the predictor to decide whether the hypothesis of no …
The phenomenon of aftershocks is studied in view of science of complexity. In particular, three different concepts are examined: (i) the complex-network representation of seismicity, (ii) the event-event correlations, and (iii) the effects of long-range memory. Regarding (i), it is shown the clustering coefficient of the complex earthquake network exhibits a peculiar behavior at and after main shocks. Regarding (ii), it is found that aftershocks experience aging, and the associated scaling holds. And regarding (iii), the scaling relation to be satisfied by a class of singular Markovian process…
We can observe the changes of Total Electron Content, TEC, in ionosphere by analyzing the data from GNSS satellites. There are many reports about TEC anomalies after earthquakes, i.e. large earthquakes often disturb the ionosphere. Up to now, preseismic TEC anomalies have been reported in several papers. However, they are not so clear as coseismic TEC anomalies, and their analysis methods have some problems for practical earthquake prediction. One factor making it difficult to detect TEC anomalies is large noises in TEC data. Non-negligible TEC disturbances are caused by many natural mechanism…
We perform a new analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears the Probability Density Functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape. This behaviour does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. Such a result can be analytically understood if the sizes (released energies) of the avalanches (earthquakes) have no correlations. Our findings s…
