Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maximal magnitudes. We find the remarkable result that the magnitude difference between the largest and second largest event in the future temporal cluster is distributed according to the regular Gutenberg-Richer law that controls the unconditional distribution of earthquake magnitudes. For earthquakes obeying the Omori-Utsu law for the distribution of waiting times between triggering and triggered events, we show that the distribution of the durations of temporal clusters of events of magnitudes above some detection threshold νhas a power law tail that is fatter in the non-critical regime $n<1$ than in the critical case n=1. This paradoxical behavior can be rationalised from the fact that generations of all orders cascade very fast in the critical regime and accelerate the temporal decay of the cluster dynamics.
This paper aims to investigate the effects of motion duration on the structural seismic demands, seeking potential correlations between motion durations and structural responses at several seismic intensity levels. Three seismic intensity levels with 100years, 475years, and 2475years earthquake return periods (RPs) are first considered for correlation computations. Spectrally matched ground motions are employed to isolate the contribution of duration from the effects of ground motion amplitudes and response spectral shape. Four single degree of freedom systems derived from four real reinforced…
This study proposes a new approach to incorporate motion duration in incremental dynamic assessments. In the proposed methodology, at each intensity level, a simulation-based approach, which is verified with actual data, is employed to determine the median duration and the median acceleration spectra of ground motions expected to occur at the site. Afterward, at each intensity level, artificial or spectrally matched motions are produced based on the median acceleration spectra and the median duration, indicating that different intensity levels are directly covered by the generated artificial o…
Over the past decades, the Groningen Gas Field (GGF) has been increasingly faced by induced earthquakes resulting from gas production. The seismic monitoring network at Groningen has been recently densified to improve the seismic network performance, resulting in increasing amounts of seismic data. Although traditional automated event detection techniques generally are successful in detecting events from continuous data, its detection success is challenged in cases of lower signal-to-noise ratios. The data stream coming from these networks has initiated specific interest in neural networks for…
The biggest risk to operations in Polish copper is high-energy seismic tremors where hypocenters are located within the main roof strata. These phenomena occur often in the areas which are virtually free of tectonic disturbances. They are extremely difficult to both predict and analyze due to their short duration and unpredictable time of occurrence. The objective of the presented analysis was to determine the overall stress/deformation states within the considered mining panel prior to the selected archival seismic event and afterwards to judge how the progress of mining could affect the occu…
We report the analysis of the statistics of the phase fluctuations in the coda of earthquakes recorded during a temporary experiment deployed at Pinyon Flats Observatory, California. The practical measurement of the phase is discussed and the main pitfalls are underlined. For large values, the experimental distributions of the phase first, second and third derivatives obey universal power-law decays whose exponents are remarkably well predicted by circular Gaussian statistics. For small values, these distributions are flat. The details of the transition between the plateau and the power-law be…
Time-history deformation analyses of upstream-raised tailings dams use seismic records as input data. Such records must be representative of the in-situ seismicity in terms of a wide range of intensity measures (IMs) including peak ground acceleration (PGA), Arias intensity (AI), cumulative absolute velocity (CAV), source-to-site distance, duration, among others. No single IM is a sufficient descriptor of a given seismic demand (e.g. crest settlement) because different records, all of them compliant with any IM, can produce a very wide range of results from insignificant damage to global failu…
Continuous GPS and broadband seismic monitoring have revealed a variety of disparate slip patterns especially in shallow dipping subduction zones, among which regular earthquakes, slow slip events and silent quakes1,2. Slow slip events are sometimes accompanied by Non Volcanic Tremors (NVT), which origin remains unclear3, either related to fluid migration or to friction. The present understanding of the whole menagerie of slip patterns is based upon numerical simulations imposing ad hoc values of the rate and state parameters a and b4-6 derived from the temperature dependence of a and b of a w…
The discovery of gas in Groningen in 1959 has been a massive boon to the Dutch economy. From the 1990s onwards though, gas production has led to induced seismicity. In this paper, we carry out a comprehensive exploratory analysis of the spatio-temporal earthquake catalogue. We develop a non-parametric adaptive kernel smoothing technique to estimate the spatio-temporal hazard map and to interpolate monthly well-based gas production statistics. Second- and higher-order inhomogeneous summary statistics are used to show that the state of the art rate-and-state models for the prediction of seismic …
Fireballs are infrequently recorded by seismic sensors on the ground. If recorded, they are usually reported as one-off events. This study is the first seismic bulk analysis of the largest single fireball data set, observed by the Desert Fireball Network (DFN) in Australia in the period 2014-2019. The DFN typically observes fireballs from cm-m scale impactors. We identified 25 fireballs in seismic time series data recorded by the Australian National Seismograph Network (ANSN). This corresponds to 1.8% of surveyed fireballs, at the kinetic energy range of 10$^6$ to 10$^{10}$ J. The peaks observ…
We introduce a new approach for ground motion relations (GMR) in the probabilistic seismic hazard analysis (PSHA), being influenced by the extreme value theory of mathematical statistics. Therein, we understand a GMR as a random function. We derive mathematically the principle of area-equivalence; wherein two alternative GMRs have an equivalent influence on the hazard if these GMRs have equivalent area functions. This includes local biases. An interpretation of the difference between these GMRs (an actual and a modeled one) as a random component leads to a general overestimation of residual va…
We analyse the statistical pattern of seismicity before a 1-2 103 m3 chalk cliff collapse on the Normandie ocean shore, Western France. We show that a power law acceleration of seismicity rate and energy in both 40 Hz-1.5 kHz and 2 Hz-10kHz frequency range, is defined on 3 order of magnitude, within 2 hours from the collapse time. Simultaneously, the average size of the seismic events increases toward the time to failure. These in-situ results are derived from the only station located within one rupture length distance from the rock fall rupture plane. They mimic the "critical point" like beha…
A new non-parametric statistic is introduced for the characterization of deviations from power laws. It is tested on the distribution of seismic energies given by the Gutenberg-Richter law. Based on the two first statistical log-moments, it evaluates quantitatively the deviations of the distribution of scalar seismic moments from a power-like (Pareto) law. This statistic is close to zero for the Pareto law with arbitrary power index, and deviates from zero for any non-Pareto distribution. A version of this statistic for discrete distribution of quantified magnitudes is also given. A methodolog…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches: The non homogeneous Poissonian and the non Poissonian one. In all cases we obtain either a power law or a power law damped by an exponential factor behaviour. This feature of the distribution makes impossible any prediction of earthquakes occurrence. Nevertheless it suggests the interpretation of the earthquake occurrence phenomenon as due to some non-linear d…
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 Tucunduba Dam is about 290 km West of Fortaleza, Ceará state. The seismic monitoring of the area, with a local network, has began on June 11, 1997, soon after the occurrence of the event with magnitude 3.2 $m_b$ on June 09, 1997. The monitoring was done with one the analogical station (used for magnitude duration measurement and statistical control activity) and seven digital stations. The digital stations, with three components each, were operated from June to November 1997. In this work, the data collected during digital monitoring was analyzed to determine hypocenters and focal mechanis…
Physics-based and statistic-based models for describing seismic occurrence are two sides of the same coin. In this article we compare the temporal organization of events obtained in a spring-block model for the seismic fault with the one predicted by probabilistic models for seismic occurrence. Thanks to the optimization of the parameters, by means of a Maximum Likelihood Estimation, it is possible to identify the statistical model which fits better the physical one. The results show that the best statistical model must take into account the non trivial interplay between temporal clustering, r…
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 reliable statistical characterization of the spatial and temporal properties of large earthquakes occurrence is one of the most debated issues in seismic hazard assessment, due to the unavoidably limited observations from past events. We show that pattern recognition techniques, which are designed in a formal and testable way, may provide significant space-time constraints about impending strong earthquakes. This information, when combined with physically sound methods for ground shaking computation, like the neo-deterministic approach (NDSHA), may produce effectively preventive seismic ha…
The distribution of seismic moment is of capital interest to evaluate earthquake hazard, in particular regarding the most extreme events. We make use of likelihood-ratio tests to compare the simple Gutenberg-Richter power-law distribution with two statistical models that incorporate an exponential tail: the so-called tapered Gutenberg-Richter and the truncated gamma, when fitted to the global CMT earthquake catalog. The outcome is that the truncated gamma model outperforms the other two models. If simulated samples of the truncated gamma are reshuffled in order to mimic the time occurrence of …
We treat the case of a flat stress-free surface (i.e., the ground in seismological applications) separating air from a homogeneous, isotropic, solid substratum overlain by a homogeneous, isotropic, solid layer (in contact with the ground) solicited by a SH plane body wave incident in the substratum. The analysis is first carried out in the frequency domain and subsequently in the time domain. The frequency domain response is {\it normal} in that no resonances are excited (a resonance is here understood to be a situation in which the response is infinite in the absence of dissipation). The tran…
The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a spatially independent, time-homogenized version of Bak et al's procedure, which seems to …
The interpretation of seismic images faces challenges due to the presence of several uncertainty sources. Uncertainties exist in data measurements, source positioning, and subsurface geophysical properties. Understanding uncertainties' role and how they influence the outcome is an essential part of the decision-making process in the oil and gas industry. Geophysical imaging is time-consuming. When we add uncertainty quantification, it becomes both time and data-intensive. In this work, we propose a workflow for seismic imaging with quantified uncertainty. We build the workflow upon Bayesian to…
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 demonstrate the efficacy of a Bayesian statistical inversion framework for reconstructing the likely characteristics of large pre-instrumentation earthquakes from historical records of tsunami observations. Our framework is designed and implemented for the estimation of the location and magnitude of seismic events from anecdotal accounts of tsunamis including shoreline wave arrival times, heights, and inundation lengths over a variety of spatially separated observation locations. As an initial test case we use our framework to reconstruct the great 1852 earthquake and tsunami of eastern Ind…
Mazzarella and Scafetta (2016) showed that the seismic activity recorded at the Bunker-East (BKE) Vesuvian station from 1999 to 2014 suggests a higher nocturnal seismic activity. However, this station is located at about 50 m from the main road to the volcano's crater and since 2009 its seismograms also record a significant diurnal cultural noise due mostly to tourist tours to Mt. Vesuvius. Herein, we investigate whether the different seismic frequency between day and night times could be an artifact of the peculiar cultural noise that affects this station mostly from 9:00 am to 5:00 pm from s…
Geodetic earthquake early warning (EEW) algorithms complement point-source seismic systems by estimating fault-finiteness and unsaturated moment magnitude for the largest, most damaging earthquakes. Because such earthquakes are rare, it has been difficult to demonstrate that geodetic warnings improve ground motion estimation significantly. Here, we quantify and compare timeliness and accuracy of magnitude and ground motion estimates in simulated real time from seismic and geodetic observations for a suite of globally-distributed, large earthquakes. Magnitude solutions saturate for the seismic …
In this paper we present an approach for forecasting the imminent regional seismic activity by using geomagnetic data and Earth tide data. The time periods of seismic activity are the time periods around the Sun-Moon extreme of the diurnal average value of the tide vector module. For analyzing the geomagnetic data behaviour we use diurnal standard deviation of geomagnetic vector components F for calculating the time variance Geomag Signal. The Sun storm influence is avoided by using data for daily A-indexes (published by NOAA). The precursor signal for forecasting the incoming regional seismic…
The analysis of satellite thermal images of the Earth's surface within the spectral range of 10.5-11.3 mkm has shown that over some linear structures of the Middle-Asian seismically active region there is observed a stable in time and space increasing intensity of the outgoing radiation flux as compared to contiguous blocks. A retrospective analysis of a continuous series of observations of the outgoing IR radiation flux has shown that in certain individual zones of some major tectonic dislocations there appear from time to time positive anomalies of IR radiation, for instance at the point of …
The distribution of the magnitudes of seismic events is generally assumed to be independent on past seismicity. However, by considering events in causal relation, for example mother-daughter, it seems natural to assume that the magnitude of a daughter event is conditionally dependent on the one of the corresponding mother event. In order to find experimental evidence supporting this hypothesis, we analyze different catalogs, both real and simulated, in two different ways. From each catalog, we obtain the law of triggered events' magnitude by kernel density. The results obtained show that the d…
Machine Learning (ML) methods have demonstrated exceptional performance in recent years when applied to the task of seismic event detection. With numerous ML techniques now available for detecting seismicity, applying these methods in practice can help further highlight their advantages over more traditional approaches. Constructing such workflows also enables benchmarking comparisons of the latest algorithms on practical data. We combine the latest methods in seismic event detection to analyse an 18-day period of aftershock seismicity for the $M_{w}$ 6.4 2019 Durrës earthquake in Albania. We …
We introduce the first fully self-consistent model combining the seismic micro-ruptures occurring within a generalized Burridge-Knopoff spring-block model with the nucleation and propagation of electric charge pulses within a coupled mechano-electrokinetic system. This model provides a general theoretical framework for modeling and analyzing geoelectric precursors to earthquakes. In particular, it can reproduce the unipolar pulses that have often been reported before large seismic events, as well as various observed anomalies in the statistical moments of the ambient electric fields and the po…
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
The inter-event time, IET, is sometimes used as a basis for prediction of large earthquakes. It is the case when theoretical analysis of prediction is possible. Quite recently a specific IET- model was suggested for dynamic probabilistic prediction of M > 5.5 events in Italy . In this study we analyze both some aspects of the statistical estimation of the model and its predictive ability. We find that more or less effective prediction is possible within 4 out of 34 seismotectonic zones where seismicity rate or clustering of events is relatively high. We show that, in the framework of the model…
We modify the new method for the statistical estimation of the tail distribution of earthquake seismic moments introduced by Pisarenko et al. [2009] and apply it to the earthquake catalog of Japan (1923-2007). The method is based on the two main limit theorems of the theory of extreme values and on the derived duality between the Generalized Pareto Distribution (GPD) and Generalized Extreme Value distribution (GEV). We obtain the distribution of maximum earthquake magnitudes in future time intervals of arbitrary duration tau. This distribution can be characterized by its quantile Qq(tau) at an…
Scaling analysis reveals striking regularities in earthquake occurrence. The time between any one earthquake and that following it is random, but it is described by the same universal-probability distribution for any spatial region and magnitude range considered. When time is expressed in rescaled units, set by the averaged seismic activity, the self-similar nature of the process becomes apparent. The form of the probability distribution reveals that earthquakes tend to cluster in time, beyond the duration of aftershock sequences. Furthermore, if aftershock sequences are analysed in an analogo…
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…
The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO$_2$) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brit…
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.
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete and of unequal variance. In general, the observed number in any given magnitude range is described by a binomial distribution which, given a large total number of events of all magnitudes, approximates to a Poisson distribution for a sufficiently small probability associated with that range. In this paper, we examine four earthquake catalogues: New Zealand (…
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…
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…
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…
Based on several empirical evidence, a series of papers has advocated the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative Benioff strain (BS) increases as a power-law time-to-failure before the final event. This power law reflects a kind of scale invariance with respect to the distance to the critical point. A few years ago, on the basis of a fit of the cumulative BS released prior to the 1989 Loma Prieta earthquake, Sornette and Sammis [1995] proposed that this scale invaria…
Indian Institute of Science Education and Research Pune（印度科学教育研究所浦那分校）；Observatoire de la Côte d’Azur, Université Côte d’Azur（蔚蓝海岸天文台，蔚蓝海岸大学）；CNRS, IRD, Géoazur（法国国家科学研究中心、海外发展研究院、Géoazur）；University of California, Riverside（加州大学河滨分校）
Brittle fractures of inhomogeneous materials like rocks, concrete, or ceramics are of two types: Nominally brittle and driven by the propagation of a single dominant crack or quasi-brittle and resulting from the accumulation of many microcracks. The latter goes along with acoustic noise, whose analysis has revealed that events form aftershock sequences obeying characteristic laws reminiscent of those in seismology. Yet, their origin lacks explanation. Here we show that such a statistical organization is not only specific to the multi-cracking situations of quasi-brittle failure and seismology,…
