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 temporal correlations. When analyzing global seismicity we discovered a universal relation linking the spatial Influence Length of a given earthquake to the time elapsed from the event itself. Following an event, time correlations (i.e. causality effects) exist in a region that shrinks over time, suggesting a long-range dissipating stress transfer. A different process is acting in the short-range where events are randomly set, evidencing a sub-diffusive growth of the seismogenic zone.
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…
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…
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…
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…
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…
Glaciations were attributed to variations of the Earths orbit (Milankovitch cycles). But the best ever dated paleoclimatic record (from a speleothem from Devils Hole, Nevada) demonstrated that the end of the last glacial period (termination II) happened 10 000 years before the one suggested by the orbital variations, i.e. the result appeared before the reason. This fact suggests that there is something wrong in the theory. Glaciations and deglaciations drive changes of the sea level. Changes in the speed of Earths rotation during glacial- interglacial transitions produce fracturing of the Eart…
Dynamics of earthquake nucleation process is studied on the basis of the one-dimensional Burridge-Knopoff (BK) model obeying the rate- and state-dependent friction (RSF) law. We investigate the properties of the model at each stage of the nucleation process, including the quasi-static initial phase, the unstable acceleration phase and the high-speed rupture phase or a mainshock. Two kinds of nucleation lengths L_sc and L_c are identified and investigated. The nucleation length L_sc and the initial phase exist only for a weak frictional instability regime, while the nucleation length L_c and th…
The rapid characterisation of earthquake parameters such as its magnitude is at the heart of Earthquake Early Warning (EEW). In traditional EEW methods the robustness in the estimation of earthquake parameters have been observed to increase with the length of input data. Since time is a crucial factor in EEW applications, in this paper we propose a deep learning based magnitude classifier and, further we investigate the effect of using five different durations of seismic waveform data after first P wave arrival of length 1s, 3s, 10s, 20s and 30s. This is accomplished by testing the performance…
The nature of the high-speed rupture or the main shock of the Burridge-Knopoff spring-block model in two dimensions obeying the rate-and-state dependent friction law is studied by means of extensive computer simulations. It is found that the rupture propagation in larger events is highly anisotropic and irregular in shape on longer length scales, although the model is completely uniform and the rupture-propagation velocity is kept constant everywhere at the rupture front. The manner of the rupture propagation sometimes mimics the successive ruptures of neighboring "asperities" observed in real…
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…
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 …
In this article we implemented simulations of the OFC model for earthquakes for two different topologies: regular and small-world, where in the latter the links are randomly rewired with probability $p$ . In both topologies, we have studied the distribution of time intervals between consecutive earthquakes and the border effects present in each one. In addition, we also have characterized the influence that the probability $p$ produces in certain characteristics of the lattice and in the intensity of border effects. From the two topologies, networks of consecutive epicenters were constructed, …
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…
A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world.
Following N.Kozyrev's idea about the influence of the gravitational fields of the Sun and the Moon on the Earth's crust, we consider a low-frequency resonance of the Earth's crust blocks is happening before the occurrence of the earthquake. The resonance affects several geophysical parameters and is associated with many short-term precursory phenomena; the most notable are the release of underground gases (radon), the air temperature rises, change of thermal radiation in the troposphere, and an increase in the electron density in the ionosphere. During the final stage of the earthquake genesis…
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 …
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 …
We consider two statistical regularities that were used to explain Omori's law of the aftershock rate decay: the Levy and Inverse Gaussian (IGD) distributions. These distributions are thought to describe stress behavior influenced by various random factors: post-earthquake stress time history is described by a Brownian motion. Both distributions decay to zero for time intervals close to zero. But this feature contradicts the high immediate aftershock level according to Omori's law. We propose that these statistical distributions are influenced by the power-law stress distribution near the eart…
We analyze 21 aftershock sequences of California to test for evidence of space-time diffusion. Aftershock diffusion may result from stress diffusion and is also predicted by any mechanism of stress weakening. Here, we test an alternative mechanism to explain aftershock diffusion, based on multiple cascades of triggering. In order to characterize aftershock diffusion, we develop two methods, one based on a suitable time and space windowing, the other using a wavelet transform adapted to the removal of background seismicity. Both methods confirm that diffusion of seismic activity is very weak, m…
The 11/5/2011 Lorca, Spain earthquake (Mw5.2) and related seismicity produced extensive damage in the town of Lorca and vicinity. During these earthquakes, evidence of rotations and permanent deformations in structures were observed. To analyze these aspects and study the source properties from the near field, the displacement time histories were obtained including the static component at Lorca station. Displacement time histories were computed by an appropriate double time integration procedure of accelerograms. Using these data, the foreshock and mainshock slip distributions were calculated …
Ground mass is redistributed during an earthquake causing the local gravitational potential to change. These gravitational fluctuations travel at the speed of light meaning they will arrive at a remote location significantly earlier than the fastest seismic waves. If these gravitational signals are measured by a gravimeter then early warning can be provided for an imminent earthquake. Earlier detection of earthquakes could be used to protect crucial infrastructure and save lives. The Torsion Pendulum Dual Oscillator (TorPeDO) is a gravity gradient sensor that has been constructed at the Austra…
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…
A recently proposed method of constructing seismic networks from 'record breaking events' from the earthquake catalog of California (Phy. Rev. E, 77 6,066104, 2008) was successfull in establishing causal features to seismicity and arrive at estimates for rupture length and its scaling with magnitude. The results of our implementation of this procedure on the earthquake catalog of Japan establishes the robustness of the procedure. Additionally, we find that the temporal distributions are able to detect heterogeneties in the seismicity of the region.
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…
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…
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…
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…
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…
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…
Upon employing a natural time window of fixed length sliding through a time series, an explicit interrelation between the variability $β$ of the variance $κ_1$($=< χ^2 > - < χ>^2$) of natural time $χ$ and events' correlations is obtained. In addition, we investigate the application of the fluctuation theorem, which is a general result for systems far from equilibrium, to the variability $β$. We consider for example, major earthquakes that are nonequilibrium critical phenomena. We find that four (out of five) mainshocks in California during 1979-2003 were preceded by $β$ minima lower than the r…
This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties such as phase transitions and regime shifts. Then, a detailed correspondence between the phenomenology of earthquakes, financial crashes and epileptic seizures is offered. The presented statistical evidence provides the substance of a general phase diagram for understanding the many facets of the spatio-temporal organization of these systems. A key insight is…
Many recent studies have tried to determine the influence of geometry of faults in earthquake mechanics. In this paper, we suggest a new interpretation of the effect of geometry on the stress on a fault. Starting from the representation theorem, which links the displacement in a medium to the slip distribution on its boundary, and assuming homogeneous infinite medium, a regularized boundary-element equation can be obtained. Using this equation, it is possible to separate the influence of geometry, as expressed by the curvatures and torsions of the field line of a dislocation on the fault surfa…
Influence of sedimentary layering on tsunami generation
Université de Savoie, Laboratoire de Mathématiques LAMA - UMR 5127（萨瓦大学，拉马数学实验室）；CMLA, ENS Cachan, CNRS, PRES UniverSud（法国国家科学研究中心，巴黎南大学联盟，巴黎高等师范学院卡尚校区计算与实验力学中心）
