Using a catalog of seismicity for Southern California, we measure how the number of triggered earthquakes increases with the earthquake magnitude. The trade-off between this relation and the distribution of earthquake magnitudes controls the relative role of small compared to large earthquakes. We show that seismicity triggering is driven by the smallest earthquakes, which trigger fewer events than larger earthquakes, but which are much more numerous. We propose that the non-trivial scaling of the number of triggered earthquakes emerges from the fractal spatial distribution of seismicity.
We estimate the relative importance of small and large earthquakes for static stress changes and for earthquake triggering, assuming that earthquakes are triggered by static stress changes and that earthquakes are located on a fractal network of dimension D. This model predicts that both the number of events triggered by an earthquake of magnitude m and the stress change induced by this earthquake at the location of other earthquakes increase with m as \~10^(Dm/2). The stronger the spatial clustering, the larger the influence of small earthquakes on stress changes at the location of a future e…
The physics of earthquake triggering together with simple assumptions of self-similarity impose the existence of a minimum magnitude m0 below which earthquakes do not trigger other earthquakes. Noting that the magnitude md of completeness of seismic catalogs has no reason to be the same as the magnitude m0 of the smallest triggering earthquake, we use quantitative fits and maximum likelihood inversions of observed aftershock sequences as well as Baath's law, compare with ETAS model predictions and thereby constrain the value of m0. We show that the branching ratio $n$ (average number of trigge…
There is evidence of tremor triggering by seismic waves emanating from distant large earthquakes. The frequency content of both triggered and ambient tremor are largely identical, suggesting that this property does not depend directly on the nature of the source. We show here that the model of plate dynamics developed earlier by us is an appropriate tool for describing tremor triggering. In the framework of this model, tremor is an internal response of a fault to a failure triggered by external disturbances. The model predicts generation of radiation in a frequency range defined by the fault p…
Evidence for the triggering of earthquakes by tides has been largely lacking for the continents but detectable in the oceans where the tides are larger. By far the strongest tidal triggering signals are in volcanic areas of mid-ocean ridges. These areas offer the most promise for the study of this process, but even the most basic mechanism of tidal triggering at the ridges has been elusive. The triggering occurs at low tides, but as the earthquakes are of the normal faulting type, low tides should inhibit rather than encourage faulting. Here, treating the most well documented case, Axial Volca…
Fundamentally related to the UV divergence problem in Physics, conventional wisdom in seismology is that the smallest earthquakes, which are numerous and often go undetected, dominate the triggering of major earthquakes, making the prediction of the latter difficult if not inherently impossible. By developing a rigorous validation procedure, we show that, in fact, large earthquakes (above magnitude 6.3 in California) are preferentially triggered by large events. Because of the magnitude correlations intrinsic in the validated model, we further rationalize the existence of earthquake doublets. …
The aftershock sequence of the devastating Japan earthquake of March 2011 is analyzed for the presence of periodicities at the Earth tide periods. We use spectral analysis as well as a time-domain method KORRECT developed earlier to detect presence of diurnal and semi-diurnal periodicities in the sequence of aftershocks (M \geq 4). This suggests that large aftershocks in the fault zone of the Japan 2011 earthquake were strongly influenced by Earth tides.
Finite-Horizon Triggering Cores of Earthquake Sequences
Institute of Risk Analysis, Prediction and Management (Risks-X), Academy for Advanced Interdisciplinary Studies, Southern University of Science and Technology（南方科技大学前沿交叉学科研究院风险分析、预测与管理研究所）；CNRS, ENS de Lyon, LPENSL, UMR 5672（法国国家科学研究中心里昂高等师范学院物理实验室）
In models of triggered seismicity and in their inversion with empirical data, the detection threshold m_d is commonly equated to the magnitude m_0 of the smallest triggering earthquake. This unjustified assumption neglects the possibility of shocks below the detection threshold triggering observable events. We introduce a formalism that distinguishes between the detection threshold m_d and the minimum triggering earthquake m_0 < m_d. By considering the branching structure of one complete cascade of triggered events, we derive the apparent branching ratio n_a (which is the apparent fraction of …
A fundamental mystery in earthquake physics is ``how can an earthquake be triggered by distant seismic sources?'' Here, we use discrete element method simulations of a granular layer, during stick-slip, that is subject to transient vibrational excitation to gain further insight into the physics of dynamic earthquake triggering. Using Coulomb friction law for grains interaction, we observe delayed triggering of slip in the granular gouge. We find that at a critical vibrational amplitude (strain) there is an abrupt transition from negligible time-advanced slip (clock advance) to full clock advan…
``Remote triggering" refers to the inducement of earthquakes by weak perturbations that emanate from far away sources, typically intense earthquakes that happen at much larger distances than their nearby aftershocks, sometimes even around the globe. Here, we propose a mechanism for this phenomenon; the proposed mechanism is generic, resulting from the breaking of Hamiltonian symmetry due to the existence of friction. We allow a transition from static to dynamic friction. {\em Linearly stable} stressed systems display giant sensitivity to small perturbations of arbitrary frequency (without a ne…
A likely source of earthquake clustering is static stress transfer between individual events. Previous attempts to quantify the role of static stress for earthquake triggering generally considered only the stress changes caused by large events, and often discarded data uncertainties. We conducted a robust two-fold empirical test of the static stress change hypothesis by accounting for all events of magnitude M>=2.5 and their location and focal mechanism uncertainties provided by catalogs for Southern California between 1981 and 2010, first after resolving the focal plane ambiguity and second a…
This paper has evolved out of our previous work on static stress transfer, where we used the full-space elastostatic Green's tensor to compute the Coulomb stress transfer impact of the Landers earthquake on the Hector Mine event. In this work, we use the elastostatic Green's tensor for an arbitrary layered Earth model with free-surface boundary conditions to study the impact of elastic heterogeneity as well as source-fault slip and geometry on the stress transfer mechanism. Slip distribution and fault geometry of the source have a significant impact on the stress transfer, especially in case o…
This paper brings space weather prediction close to earthquake (EQ) prediction research. The results of this paper support conclusions of previously presented statistical studies that solar activity influences the seismic activity, this influence is mediated through rapid geomagnetic disturbances and the geomagnetic disturbances are related with increases of solar wind speed. Our study concern an example of 40 days with direct response of a series of 7 strong-to-giant (M=6.8-9.3) EQs (including the Andaman-Sumatra EQ) to solar wind speed increases and subsequent geomagnetic fast disturbances. …
By using the maximum entropy principle with Tsallis entropy and under the assumption that the gouge plays an active role in the triggering of earthquakes, we obtain a functional dependence for energy distribution function for earthquakes which fits very well with observations in the region of small energies. This distribution function is related to the size distribution function of fragments in the gouge.
The driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered earthquakes. In nearly all generalizations of the ETAS model, the magnitudes of the background and the triggered earthquakes are assumed to follow Gutenberg-Richter law with the same exponent (\b{eta}-value). Furthermore, the magnitudes of the triggered earthquakes are always assumed to be independent of the magnitude of the triggering earthquake. Using an EM algor…
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…
By analyzing a southern California earthquake catalog, Davidsen and Paczuski [Phys. Rev. Lett. 94, 048501 (2005)] claim to have found evidence contradicting the theory of aftershock zone scaling in favor of scale-free statistics. We present four elements showing that Davidsen and Paczuski's results may be insensitive to the existence of physical length scales associated with aftershock zones or mainshock rupture lengths, so that their claim is unsubstantiated. (i) Their exponent smaller than 1 for a pdf implies that the power law statistics they report is at best an intermediate asymptotic; (i…
The Multifractal Stress-Activated (MSA) model is a statistical model of triggered seismicity based on mechanical and thermodynamic principles. It predicts that, above a triggering magnitude cut-off $M_0$, the exponent $p$ of the Omori law for the seismic decay of aftershocks is a linear increasing function $p(M) =a M+b$ of the main shock magnitude $M$. We previously reported empirical support for this prediction, using the Southern California SCEC catalog. Here, we confirm this law using an updated, longer version of the same catalog, as well as new methods to estimate $p$. One of this methods…
Theoretical constraints on tidal triggering of slow earthquakes
Ecole Normale Supérieure, CNRS-UMR 8538, PSL Research University（巴黎高等师范学院）；Bureau de Recherches Géologiques et Miniéres (BRGM)（法国地质矿产调查局）；Department of Earth and Planetary Science, The University of Tokyo（东京大学地球行星科学系）
The observation of foreshocks preceding large earthquakes and the suggestion that foreshocks have specific properties that may be used to distinguish them from other earthquakes have raised the hope that large earthquakes may be predictable. Among proposed anomalous properties are the larger proportion than normal of large versus small foreshocks, the power law acceleration of seismicity rate as a function of time to the mainshock and the spatial migration of foreshocks toward the mainshock, when averaging over many sequences. Using Southern California seismicity, we show that these properties…
We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark model of seismicity, which just assumes no difference in the physics of foreshocks, mainshocks and aftershocks. Our theoretical calculations provide good fits to the data and show that universality is only approximate. We conclude that the distributions of inter-event times do not reveal more information than what is already known from the Gutenberg-Richter and the Omori power laws. Our results reinforces the view t…
Spatiotemporal clustering of earthquake events is a generally-established fact, and is important for designing models and assessment techniques in seismicity. Here, we investigate how this behavior can manifest in the statistical distributions of inter-event distances and times between earthquakes from different regional catalogs. We complement the analysis of previous authors (Touati et al., PRL 102, 168501 (2009)) and observe histograms best described by a superposition of two component distributions for "short" and "long" distances and times. Our results quantify the spatiotemporal clusteri…
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 unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at t…
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 consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (``productivity'' or ``fertility''), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of f…
The long-term erosion of steep landscapes is punctuated by dramatic erosional events that can remove significant amount of sediments within a time-scale shorter than a seismic cycle. However, the role of such large erosional events on seismicity is poorly understood. We use QDYN, a quasi-dynamic numerical model of earthquake cycles to investigate the effect of a large erosional event on seismicity. The progressive evacuation of landslide sediments is modelled by a transient normal stress decrease. We show that erosional events with a shorter duration compared with the duration of a seismic cyc…
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…
Coupled Transient Processes Govern Intraplate Earthquake Swarm Evolution: Insights from the 2019-2020 Palghar Sequence
National Institute of Science Education and Research（国家科学教育与研究中心）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Geosciences Division, Space Applications Centre, Indian Space Research Organisation（印度空间研究组织太空应用中心地球科学部）；Laboratoire de Géologie, École Normale Supérieure, CNRS UMR 8538, PSL Research University（法国国家科研中心8538联合实验室，巴黎高等师范学院，PSL研究大学地质实验室）；Wadia Institute of Himalayan Geology（瓦迪亚喜马拉雅地质研究所）；CSIR–National Geophysical Research Institute（印度科学工业研究理事会国家地球物理研究所）
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic catalogs while improving the access to the spatial information content of seismic catalogs. The PDFs of events are first ranked by decreasing location errors and then successively condensed onto better located and lower variance event PDFs. The obtained condensed catalog attributes different weights to each event, providing an optimal spatial representation w…
Predicting earthquakes is of the utmost importance, especially to those countries of high risk, and although much effort has been made, it has yet to be realised. Nevertheless, there is a paucity of statistical approaches in seismic studies to the extent that an old theory is believed without verification. Seismic records of time and magnitude in Japan were analysed by exploratory data analysis (EDA). EDA is a parametric statistical approach based on the characteristics of data and is suitable for data-driven investigations. The distribution style of each dataset was determined, and the import…
Is the Number of Foreshocks Underestimated? The Role of Declustering Symmetry
University of Campania “L. Vanvitelli”（坎帕尼亚卢多维科范维泰利大学）；GFZ German Research Centre for Geosciences（德国地球科学研究中心）；CNRS, ENS de Lyon, LPENSL, UMR5672（法国国家科学研究中心、里昂高等师范学校、LPENSL联合研究实验室）；Asian School of the Environment, Nanyang Technological University（南洋理工大学亚洲环境学院）；Earth Observatory of Singapore, Nanyang Technological University（南洋理工大学新加坡地球观测站）
There is evidence of triggering of tremor by seismic waves emanating from distant large earthquakes. The frequency contents of triggered and ambient tremor are largely identical, suggesting that tremor does not depend directly on the nature of the source. We show here that the model of plate dynamics developed earlier by us is an appropriate tool for describing the onset of tremor. In the framework of this model, tremor is an internal response of a fault to a failure triggered by external disturbances. The model predicts generation of radiation in a frequency range defined by the fault paramet…
Joint Analysis of Shannon and Tsallis Entropy and GRACE-FO driven Equivalent Water Height Anomalies for Pre- and Post-Rupture Monitoring: An Example of the 2023 Mw = 7.8 Kahramanmaraş Earthquake, Türkiye
Farhangian University（法尔干大学）；The University of Tokyo（东京大学）；Arak University of Technology（阿拉克理工大学）
Seeing the Earth crust as crisscrossed by faults filled with fluid at close to lithostatic pressures, we develop a model in which its elastic modulii are different in net tension versus compression. In constrast with standard nonlinear effects, this ``threshold nonlinearity'' is non-perturbative and occurs for infinitesimal perturbations around the lithostatic pressure taken as the reference. For a given earthquake source, such nonlinear elasticity is shown to (i) rotate, widen or narrow the different lobes of stress transfer, (ii) to modify the $1/r^2$ 2D-decay of elastic stress Green functio…
Numerical simulations have shown that certain driven nonlinear systems can be characterized by mean-field statistical properties often associated with ergodic dynamics [C.D. Ferguson, W. Klein, and J.B. Rundle, Phys. Rev. E 60, 1359 (1999); D. Egolf, Science 287, 101 (2000)]. These driven mean-field threshold systems feature long-range interactions and can be treated as equilibrium-like systems with dynamics that are statistically stationary over long time intervals. Recently the equilibrium property of ergodicity was identified in an earthquake fault system, a natural driven threshold system,…
We present the first systematic exploration of earth tides-seismicity correlation in northwestern South America, with a special emphasis in Colombia. For this purpose, we use a dataset of ~167,000 earthquakes, gathered by the Colombian Seismological Network between 1993 and 2017. Most of the events are intermediate-depth earthquakes from the Bucaramanga seismic nest and the Cauca seismic cluster. For this purpose, we implemented a novel approach for the calculation of tidal phases that considers the relative positions of the Earth-Moon-Sun system at the time of the events. After applying the s…
Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.
The aim of this paper is to propose a 2D computational algorithm for modeling of the trigger and the propagation of shallow landslides caused by rainfall. We used a Molecular Dynamics (MD) inspired model, similar to discrete element method (DEM), that is suitable to model granular material and to observe the trajectory of single particle, so to identify its dynamical properties. We consider that the triggering of shallow landslides is caused by the decrease of the static friction along the sliding surface due to water infiltration by rainfall. Thence the triggering is caused by two following c…
Text analytics based on supervised machine learning classifiers has shown great promise in a multitude of domains, but has yet to be applied to Seismology. We test various standard models (Naive Bayes, k-Nearest Neighbors, Support Vector Machines, and Random Forests) on a seismological corpus of 100 articles related to the topic of precursory accelerating seismicity, spanning from 1988 to 2010. This corpus was labelled in Mignan (2011) with the precursor whether explained by critical processes (i.e., cascade triggering) or by other processes (such as signature of main fault loading). We invest…
The development of new earthquake forecasting models is often motivated by one of the following complementary goals: to gain new insights into the governing physics and to produce improved forecasts quantified by objective metrics. Often, one comes at the cost of the other. Here, we propose a question-driven ensemble (QDE) modeling approach to address both goals. We first describe flexible ETAS models in which we relax the assumptions of parametrically defined aftershock productivity and background earthquake rates during model calibration. Instead, both productivity and background rates are c…
Simple models of earthquake faults are important for understanding the mechanisms for their observed behavior, such as Gutenberg-Richter scaling and the relation between large and small events, which is the basis for various forecasting methods. Although cellular automaton models have been studied extensively in the long-range stress transfer limit, this limit has not been studied for the Burridge-Knopoff model, which includes more realistic friction forces and inertia. We find that the latter model with long-range stress transfer exhibits qualitatively different behavior than both the long-ra…
Prediction in complex systems at criticality is believed to be very difficult, if not impossible. Of particular interest is whether earthquakes, whose distribution follows a power law (Gutenberg-Richter) distribution, are in principle unpredictable. We study the predictability of event sizes in the Olmai-Feder-Christensen model at different proximities to criticality using a convolutional neural network. The distribution of event sizes satisfies a power law with a cutoff for large events. We find that prediction decreases as criticality is approached and that prediction is possible only for la…
Recently, slow earthquakes (slow EQ) have received much attention relative to understanding the mechanisms underlying large earthquakes and to detecting their precursors. Low-frequency earthquakes (LFE) are a specific type of slow EQ. In the present paper, we reveal the relevance of LFEs to the 2011 Great Tohoku Earthquake (Tohoku-oki EQ) by means of cluster analysis. We classified LFEs in northern Japan in a data-driven manner, based on inter-time, the time interval between neighboring LFEs occurring within 10 km. We found that there are four classes of LFE that are characterized by median in…
Earthquake Dynamics as a Benchmark for Scale-Invariant Behavior
Université Lyon 1（里昂第一大学）；CNRS, Institut Lumière Matière, UMR5306（法国国家科学研究中心，光与物质研究所）；Instituto de Física, Pontificia Universidad Católica de Valparaiso (PUCV)（天主教辅仁瓦尔帕莱索大学物理研究所）
