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 analyzed subsequently to extract information about the complex dynamics. We find that the unimodal feature of recurrence lengths helps to associate typical rupture lengths with different magnitude earthquakes. The out-degree of the network 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 are also obtained with recurrence time distribution agreeing with the Omori law.
We investigate the sequence of great earthquakes over the past century. To examine whether the earthquake record includes temporal clustering, we identify aftershocks and remove those from the record. We focus on the recurrence time, defined as the time between two consecutive earthquakes. We study the variance in the recurrence time and the maximal recurrence time. Using these quantities, we compare the earthquake record with sequences of random events, generated by numerical simulations, while systematically varying the minimal earthquake magnitude Mmin. Our analysis shows that the earthquak…
We study the statistics of the recurrence times between earthquakes above a certain magnitude M$ in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time $τ_0$. As a consequence, the conditional mean recurrence time $\hat τ(τ_0)$ between two events increases monotonically with $τ_0$. For $τ_0$ well below the average recurrence time $\ovτ, \hatτ(τ_0)$ is smaller than $\ovτ$, while for $τ_0>\ovτ$, $\hatτ(τ_0)$ is greater than $\ovτ$. Also the mean residual time until the next earthquake does not depend only on the elapsed time, but als…
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 …
This paper presents an explanation of a possible mechanism underlying the shape of the universal curve of Scaling Law for Earthquake Recurrence Time Distributions. The presented simple stochastic cellular automaton model is reproducing the gamma distribution fit with the proper value of the parameter $γ$ characterizing Earth's seismicity and also imitates a deviation from the fit at the short interevent times, as observed in real data. Thus the model suggests an explanation of the universal pattern of rescaled Earthquake Recurrence Time Distributions in terms of combinatorial rules for accumul…
Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp $δ$-function-like peak corresponding to rhythmic recurrence of events with a fixed ``period'' uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology.
Extending the central concept of recurrence times for a point process to recurrent events in space-time allows us to characterize seismicity as a record breaking process using only spatiotemporal relations among events. Linking record breaking events with edges between nodes in a graph generates a complex dynamical network isolated from any length, time or magnitude scales set by the observer. For Southern California, the network of recurrences reveals new statistical features of seismicity with robust scaling laws. The rupture length and its scaling with magnitude emerges as a generic measure…
The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multiple regions (Bak et al.,2002). These unified scaling laws are characterized by intermediate power law asymptotics. On the other hand, Molchan (2005) has presented a mathematical proof that, if such a universal law exists, it is necessarily an exponential, in obvious contradiction with the data. First, we generalize Molchan's argument to show that an approximate unified law can be found which is compatible with the em…
We develop an efficient numerical scheme to solve accurately the set of nonlinear integral equations derived previously in (Saichev and Sornette, 2007), which describes the distribution of inter-event times in the framework of a general model of earthquake clustering with long memory. Detailed comparisons between the linear and nonlinear versions of the theory and direct synthetic catalogs show that the nonlinear theory provides an excellent fit to the synthetic catalogs, while there are significant biases resulting from the use of the linear approximation. We then address the suggestions prop…
In order to clarify how the statistical properties of earthquakes depend on the constitutive law characterizing the stick-slip dynamics, we make an extensive numerical simulation of the one-dimensional spring-block model with the rate- and state-dependent friction law. Both the magnitude distribution and the recurrence-time distribution are studied with varying the constitutive parameters characterizing the model. While a continuous spectrum of seismic events from smaller to larger magnitudes is obtained, earthquakes described by this model turn out to possess pronounced ``characteristic'' fea…
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 district of southern California and Japan are divided into small cubic cells, each of which is regarded as a vertex of a graph if earthquakes occur therein. Two successive earthquakes define an edge and a loop, which replace the complex fault-fault interaction. In this way, the seismic data are mapped to a random graph. It is discovered that an evolving random graph associated with earthquakes behaves as a scale-free network of the Barabasi-Albert type. The distributions of connectivities in the graphs thus constructed are found to decay as a power law, showing a novel feature of earthquak…
The North Anatolian Fault (NAF) has produced numerous major earthquakes. After decades of quiescence, the $\rm{M_w}$ 6.8 Elazığ earthquake (January 24, 2020) has recently reminded us that the East Anatolian Fault (EAF) is also capable of producing significant earthquakes. To better estimate the seismic hazard associated with these two faults, we jointly invert Interferometric Synthetic Aperture Radar (InSAR) and GPS data to image the spatial distribution of interseismic coupling along the eastern part of both the North and East Anatolian Faults. We perform the inversion in a Bayesian framework…
Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays
The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamental. A general form for the distribution is derived imposing only the self-similarity of the process, which also yields a scaling relation between the Gutenberg-Richter b-value, the exponent characterizing the correlations, and the recurrence-time exponent. This a…
We report on an extensive characterization of the cracking noise produced by charcoal samples when dampened with ethanol. We argue that the evaporation of ethanol causes transient and irregularly distributed internal stresses that promote the fragmentation of the samples and mimic some situations found in mining processes. The results show that, in general, the most fundamental seismic laws ruling earthquakes (Gutenberg-Richter law, unified scaling law for the recurrence times, Omori's law, productivity law and Bath's law) hold under the conditions of the experiment. Some discrepancies were al…
University of British Columbia（不列颠哥伦比亚大学）；GD Goenka University（GD戈恩卡大学）
Earthquake prediction has been a challenging research area for many decades, where the future occurrence of this highly uncertain calamity is predicted. In this paper, several parametric and non-parametric features were calculated, where the non-parametric features were calculated using the parametric features. $8$ seismic features were calculated using Gutenberg-Richter law, the total recurrence, and the seismic energy release. Additionally, criterions such as Maximum Relevance and Maximum Redundancy were applied to choose the pertinent features. These features along with others were used as …
Statistical properties of the one-dimensional spring-block (Burridge-Knopoff) model of earthquakes obeying the rate and state dependent friction law are studied by extensive computer simulations. The quantities computed include the magnitude distribution, the rupture-length distribution, the mainshock recurrence-time distribution, the seismic time correlations before and after the mainshock, the mean slip amount, and the mean stress drop at the mainshock, etc. Events of the model can be classified into two distinct categories. One tends to be unilateral with its epicenter located at the rim of…
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
Statistical similarities between earthquakes and other systems that emit cracking noises have been explored in diverse contexts, ranging from materials science to financial and social systems. Such analogies give promise of a unified and universal theory for describing the complex responses of those systems. There are, however, very few attempts to simultaneously characterize the most fundamental seismic laws in such systems. Here we present a complete description of the Gutenberg-Richter law, the recurrence times, Omori's law, the productivity law, and Bath's law for the acoustic emissions th…
We propose a method to search for signs of causal structure in spatiotemporal data making minimal a priori assumptions about the underlying dynamics. To this end, we generalize the elementary concept of recurrence for a point process in time to recurrent events in space and time. An event is defined to be a recurrence of any previous event if it is closer to it in space than all the intervening events. As such, each sequence of recurrences for a given event is a record breaking process. This definition provides a strictly data driven technique to search for structure. Defining events to be nod…
The occurrence of the September 28, 2004 Mw=6.0 mainshock at Parkfield, California, has significantly increased the mean and aperiodicity of the series of time intervals between mainshocks in this segment of the San Andreas fault. We use five different statistical distributions as renewal models to fit this new series and to estimate the time-dependent probability of the next Parkfield mainshock. Three of these distributions (lognormal, gamma and Weibull) are frequently used in reliability and time-to-failure problems. The other two come from physically-based models of earthquake recurrence (t…
