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 dynamics to be further investigated.
This paper illustrated the possible relationship between the occurrences of the earthquake and the anomalous line-of-sight propagations in the very high frequency band by the fast Fourier transform spectral analysis. Despite many anomalous propagations appear in the different very high frequency band during the earthquake occurrences, the majority of these abnormal signals contain similar frequency distributions in the frequency domain. For the 31 anomalous propagation spectral distributions, 30 of them present the same curve peaks, within a frequency range of (0-0.5)Hz. Furthermore, for the f…
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…
The theory about the brittle failures of multiple locked patches in a seismogenic fault system developed by us since 2010 is introduced in the present study. It is stated by the theory that the progressive failures of locked patch result in the occurrence of earthquakes due to fault movement, where the major earthquakes occurred at its volume expansion and peak strength points are referred to as characteristic ones. We analyze the seismogenic law of characteristic earthquakes in the Islamabad-Kathmandu seismic zone that extends along Himalayan seismic belt, and assess the seismicity trend of t…
One of the main interests in seismology is the formulation of models able to describe the clustering in time occurrence of earthquakes. Analysis of the Southern California Catalog shows magnitude clustering in correspondence to temporal clustering. Here we propose a dynamical scaling hypothesis in which time is rescaled in terms of magnitude. This hypothesis is introduced in the context of a generalized trigger model and gives account for clustering in time and magnitude for earthquake occurrence. The model is able to generate a synthetic catalog reproducing magnitude and inter-even time distr…
The roughness of the subduction interface is thought to influence seismogenic behavior in subduction zones, but a detailed understanding of how such roughness affects the state of stress along the subduction megathrust is still debated. Here, we use seismotectonic analogue models to investigate the effect of subduction interface roughness on seismicity in subduction zones. We compared analogue earthquake source parameters and slip distributions for two roughness endmembers. Models characterized by a very rough interface have lower interface frictional strength and lower interseismic coupling t…
The relation between seismic moment and fractured area is crucial to earthquake hazard analysis. Experimental catalogs show multiple scaling behaviors, with some controversy concerning the exponent value in the large earthquake regime. Here, we show that the original Olami, Feder, and Christensen model does not capture experimental findings. Taking into account heterogeneous friction, the visco elastic nature of faults together with finite-size effects, we are able to reproduce the different scaling regimes of field observations. We provide an explanation for the origin of the two crossovers b…
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 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 earthquake of Skyros Island in Greece (26/7/2001, Ms = 6.1 R) was announced three days before its occurrence in a meeting organized by the Bulgarian Academy of Sciences, Sofia on 2001. In this work a review is made on the results of the methodologies which were used for the analysis of the available data in order to utilize the specific prognosis. Of particular interest is the fact that the determined time of occurrence deviated for less than an hour (actually it was 41 minutes) from the actual occurrence time of the specific EQ. A similar example of another large EQ (Kythira, Greece, Ms =…
Active faults release elastic strain energy via a whole continuum of modes of slip, ranging from devastating earthquakes to Slow Slip Events and persistent creep. Understanding the mechanisms controlling the occurrence of rapid, dynamic slip radiating seismic waves (i.e. earthquakes) or slow, silent slip (i.e. SSEs) is a fundamental point in the estimation of seismic hazard along subduction zones. On top of showing slower rupture propagation velocity than earthquakes, SSEs exhibit different scaling relationships, which could reflect either different physical mechanisms or an intriguing lack of…
The Earth's electric field, recorded by two different and distant monitoring sites located in Greece, is analyzed in terms of monochromatic signals (T=24h). The analysis is based on the mapping procedures borrowed from the study of non-linear dynamic systems and chaos. The specific analysis applied on the electric field recorded for some weeks before the occurrence of 3 large EQs which occurred in Greece shows some very interesting results. Long before the EQ occurrence the phase map generated by the uncorrelated each other signals recorded by a pair of distant monitoring sites is characterize…
The Andravida EQ, Greece (8/6/2008, Ms=7.0R) seismic parameters: location, time of occurrence and magnitude were determined "a posteriori" in an attempt to verify the predictability of the large EQs. The Earth's electric field, after its processing by de-noising techniques, was used, in conjunction with appropriate physical models, for the determination of the epicenter by triangulation. The time of occurrence was determined in very short-term mode by the use of the tidal waves (M1, K1) and the "strange attractor like" seismic electric precursor, while its magnitude was calculated by the appli…
The time of occurrence of the large EQ that occurred recently in Japan (March 11th, 2011, Mw = 8.9) is compared to the time of peak amplitude occurrence of the M1 and K1 tidal components. It is shown that the specific EQ occurred on the peak of the M1 tidal component, and deviates for only 45 minutes from the corresponding K1 tidal peak. Therefore, the specific seismic event complies quite well with the earlier proposed physical mechanism (lithospheric oscillation) that causes triggering of large EQs.
In analyzing synthetic earthquake catalogs created by a two-dimensional Burridge-Knopoff model, we have found that a probability distribution of the interoccurrence times, the time intervals between successive events, can be described clearly by the superposition of the Weibull distribution and the log-Weibull distribution. In addition, the interoccurrence time statistics depend on frictional properties and stiffness of a fault and exhibit the Weibull - log Weibull transition, which states that the distribution function changes from the log-Weibull regime to the Weibull regime when the thresho…
The Epidemic Type Aftershock Sequence (ETAS) model is one of the most widely-used approaches to seismic forecasting. However most studies of ETAS use point estimates for the model parameters, which ignores the inherent uncertainty that arises from estimating these from historical earthquake catalogs, resulting in misleadingly optimistic forecasts. In contrast, Bayesian statistics allows parameter uncertainty to be explicitly represented, and fed into the forecast distribution. Despite its growing popularity in seismology, the application of Bayesian statistics to the ETAS model has been limite…
The normalized raw data of the Earth's electric field, monitored at PYR, ATH, HIO monitoring sites in Greece, are studied as far as it concerns the presence of electric seismic precursors. Electric preseismic pulses, plateau-like anomalous electric field and Very Long Period (VLP) anomalies were detected prior to the occurrence of the July 1st, 2009 large (Ms = 6.3R) EQ in Greece. Further processing of the same data revealed the true form of the generated preseimic potential thus providing an indirect estimation of the time window of the occurrence of the large EQ. Finally, by correlating, at …
The Neo-Deterministic Seismic Hazard Assessment (NDSHA) method reliably and realistically simulates the suite of earthquake ground motions that may impact civil populations as well as their heritage buildings. The modeling technique is developed from comprehensive physical knowledge of the seismic source process, the propagation of earthquake waves and their combined interactions with site effects. NDSHA effectively accounts for the tensor nature of earthquake ground motions formally described as the tensor product of the earthquake source functions and the Green Functions of the pathway. NDSH…
In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this paper, we describe a fractional differential equation that governs the earthquake intensity rate of the pure temporal ETAS model by using the Caputo fractional derivative and we solve it analytically. We highlight that the tools and special functions of fractional calculus simplify the classical methods employed to obtain the intensity rate and let us describe…
Unfortunately, working scientists sometimes reflexively continue to use "buzz phrases" grounded in once prevalent paradigms that have been subsequently refuted. This can impede both earthquake research and hazard mitigation. Well-worn seismological buzz phrases include "earthquake cycle," "seismic cycle," "seismic gap," and "characteristic earthquake." They all assume that there are sequences of earthquakes that are nearly identical except for the times of their occurrence. If so, the complex process of earthquake occurrence could be reduced to a description of one "characteristic" earthquake …
We have found that about two months after creating a new radiation belt in the inner magnetosphere due to a geomagnetic storm, an increasing seismic activity may occur near the magnetic field lines' footprint of a newly created radiation belt. The Combined Release and Radiation Effects Satellite (CRRES) detected a new radiation belt after a geomagnetic storm on March 24, 1991. Shortly after that, on May 30, 1991, a strong M7.0 earthquake occurred in Alaska in the footprint of geomagnetic line L~2.69. Additionally, on October 28, 2012, a strong M7.8 earthquake occurred in Canada near the footpr…
The electric field of the Earth registered by three monitoring sites (ATH, PYR, HIO) located in Greece, is investigated and analyzed after the occurrence of the Methoni EQ (14th of February, 2008, Ms =6.7R). The period of analysis is performed for 2 days (21st-22nd of February) and 7 days after the occurrence of the main seismic event. The obtained results suggest that the seismogenic area generates electrical signals denoting a specific epicentral area. This area coincides with the already seismically activated area. An estimate for the time of occurrence of this EQ is made by the application…
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.…
We have found that about two months after creating a new radiation belt in the inner magnetosphere due to a geomagnetic storm, an increasing seismic activity may occur near the magnetic field lines' footprint of a newly created radiation belt. The Combined Release and Radiation Effects Satellite (CRRES) detected a new radiation belt after a geomagnetic storm on March 24, 1991. Shortly after that, on May 30, 1991, a strong M7.0 earthquake occurred in Alaska in the footprint of geomagnetic line L~2.69. Additionally, on October 28, 2012, a strong M7.8 earth-quake occurred in Canada near the footp…
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''
Low-magnitude seismic activity between the Kamchatka July 20 and July 29, 2025, earthquakes. Spatio-temporal evolution recovered using waveform cross-correlation
The $b$-value in the Gutenberg-Richter (GR) law contains information that is essential for evaluating earthquake hazard and predicting the occurrence of large earthquakes. Estimates of $b$ are often based on seismic events whose magnitude exceed a certain threshold, the so called magnitude of completeness. Such estimates are sensitive to the choice of threshold and often ignore a substantial portion of available data. We present a general model for the distribution of observable earthquake magnitudes and an estimation procedure that takes all measurements into account. The model is obtained by…
We discuss various statistical distributions of earthquake numbers. Previously we derived several discrete distributions to describe earthquake numbers for the branching model of earthquake occurrence: these distributions are the Poisson, geometric, logarithmic, and the negative binomial (NBD). The theoretical model is the `birth and immigration' population process. The first three distributions above can be considered special cases of the NBD. In particular, a point branching process along the magnitude (or log seismic moment) axis with independent events (immigrants) explains the magnitude/m…
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 …
Applying Detrended Fluctuation Analysis (DFA) to the geomagnetic data recorded at three measuring stations in Japan, Rong et al. in 2012 reported that anomalous magnetic field variations were identified well before the occurrence of the disastrous Tohoku $M_w$9.0 earthquake that occurred on 11 March 2011 in Japan exhibiting increased "non-uniform" scaling behavior. Here, we provide an explanation for the appearance of this increase of "non-uniform" scaling on the following grounds: These magnetic field variations are the ones that accompany the electric field variations termed Seismic Electric…
It has recently been found that the evolution of the preparation of a strong earthquake (EQ), as it is monitored through fracture-induced electromagnetic emissions (EME) in the MHz band, presents striking similarity with the evolution of a thermal system as temperature drops, since distinct steps of the evolution of the phenomenon of spontaneous symmetry breaking (SSB) can be identified. Here, the study of fracture-induced EME in the MHz band in analogy to thermal systems is extended to the phase of local fracture structures that follow after the SSB (and the occurrence of the main EQ). By com…
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 …
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 study the structural similarity of earthquake networks constructed from seismic catalogs of different geographical regions. A hierarchical clustering of underlying undirected earthquake networks is shown using Jensen-Shannon divergence in graph spectra. The directed nature of links indicates that each earthquake network is strongly connected, which motivates us to study the directed version statistically. Our statistical analysis of each earthquake region identifies the hub regions. We calculate the conditional probability of the forthcoming occurrences of earthquakes in each region. The co…
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 …
The number of earthquakes as a function of magnitude decays as a power law. This trend is usually justified using spring-block models, where slips with the appropriate global statistics have been numerically observed. However, prominent spatial and temporal clustering features of earthquakes are not reproduced by this kind of modeling. We show that when a spring-block model is complemented with a mechanism allowing for structural relaxation, realistic earthquake patterns are obtained. The proposed model does not need to include a phenomenological velocity weakening friction law, as traditional…
The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features have been questioned and some criticisms have been raised. We investigate the existence of universal scaling properties by analyzing a Californian catalog and by means of numerical simulations of an epidemic-type model. We show that the interevent time distribution exhibits a universal behavior over the entire temporal range if four characteristic times are …
Forecasts of the focal mechanisms of future earthquakes are important for seismic hazard estimates and Coulomb stress and other models of earthquake occurrence. Here we report on a high-resolution global forecast of earthquake rate density as a function of location, magnitude, and focal mechanism. In previous publications we reported forecasts of 0.5 degree spatial resolution, covering the latitude range magnitude, and focal mechanism. In previous publications we reported forecasts of 0.5 degree spatial resolution, covering the latitude range from -75 to +75 degrees, based on the Global Centra…
A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence. The fluctuations of the rate, characterizing the non-stationarity of the process, show a doubly power-law distribution and are fundamental to determine the overall behavior, described by a double power law as well.
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?
For historical buildings and monuments, i.e. when considering time intervals of about a million year (we do not want to loose cultural heritage), the applicability of standard estimates of seismic hazard is really questionable. A viable alternative is represented by the use of the scenario earthquakes, characterized at least in terms of magnitude, distance and faulting style, and by the treatment of complex source processes. Scenario-based seismic hazard maps are purely based on geophysical and seismotectonic features of a region and take into account the occurrence frequency of earthquakes on…
Time Series Foundation Models and Deep Learning Architectures for Earthquake Temporal and Spatial Nowcasting
University of Virginia（弗吉尼亚大学）；University of California, Davis（加州大学戴维斯分校）；Santa Fe Institute（圣达菲研究所）；Jet Propulsion Laboratory（喷气推进实验室）；California Institute of Technology（加州理工学院）；University of California, Irvine（加州大学欧文分校）
Aftershocks of the 2012 Off-Coast of Sumatra Earthquake Sequence exhibit a complex and diffuse spatial distribution. The first-order complexity in aftershock distribution is clear and well beyond the influence of typical earthquake location uncertainty. The sequence included rupture of multiple fault segments, spatially separated. We use surface-wave based relative centroid locations to examine whether, at the small scale, the distribution of the aftershocks was influenced by location errors. Surface-wave based relative location has delineated precise oceanic transform fault earthquake locatio…
Earthquakes rank among the most destructive manifestations of the Earth's dynamics. Can they be predicted? This is often the first question students ask. To answer that right away: no, at present it is not possible to anticipate the date, site and magnitude of future seismic events. However, there does exist a general framework to describe observations related to earthquakes and understand the processes that lead to their occurrence: the seismic cycle. This chapter introduces the reader to the friction laws from a historical to state of the art perspective. It then deals with mechanical modell…
The MyShake project aims to build a global smartphone seismic network to facilitate large-scale earthquake early warning and other applications by leveraging the power of crowdsourcing. The MyShake mobile application first detects earthquake shaking on a single phone. The earthquake is then confirmed on the MyShake servers using a "network detection" algorithm that is activated by multiple single-phone detections. In this part one of the two paper series, we present a network detection algorithm and a simulation platform to test earthquake scenarios at various locations around the world. The p…
