Scaling analysis of seismicity in the space-time-magnitude domain very often starts from the relation N(m,L)=a(L)*10**(-bm)*L**c for the rate of seismic events of magnitude M>m in an area of size L. There are some evidences in favor of multifractal property of seismic process. In this case the choice of the scale exponent 'c' is not unique. It is shown how different 'c''s are related to different types of spatial averaging applied to lambda(m, L) and what are the 'c''s for which the distributions of a(L) best agree for small L. Theoretical analysis is supplemented with an analysis of California data for which the above issues were recently discussed on an empirical level.
Recently, attempts have been made to take into account the fractal properties of seismicity when mapping the long-term rate of earthquakes. The paper touches upon the theoretical aspects of fractality and provides a critical analysis of its applications to the problems of seismic risk
It has been shown [Phys. Rev. E 84, 022101 (2011); Chaos 22, 023123 (2012)] that earthquakes of magnitude $M$ greater or equal to 7 are globally correlated. Such correlations were identified by studying the variance $κ_1$ of natural time which has been proposed as an order parameter for seismicity. Here, we study the fluctuations of this order parameter using the Global Centroid Moment Tensor catalog for a magnitude threshold $M_{thres}=5.0$ and focus on its behavior before major earthquakes. Natural time analysis reveals that distinct minima of the fluctuations of the order parameter of seism…
Scaling analysis of seismicity in the space-time-magnitude domain very often starts from the relation N(m,L)=a(L)*10**(-bm)*L**c for the rate of seismic events of magnitude M>m in an area of size L. There is some evidence in favor of multifractality being present in seismicity. In this case the optimal choice of the scale exponent c is not unique. It is shown how different c's are related to different types of spatial averaging applied to N(m,L) and what are the c's for which the distributions of a(L) best agree for small L. Theoretical analysis is tested using California data.
The analysis of the earthquakes catalog of Greece for the period 1964 to 2010 indicates a continuously increasing no. of seismic events. A detailed determination of the cumulative seismic energy release, for specific earthquake magnitudes, revealed that for magnitudes up to Ms = 5.0R the Greek territory, considered as a unified seismogenic area, is at a state of accelerating deformation for almost the last 10 years. The background seismicity rate, considering constant cumulative seismic energy release for the entire study period, corresponds to a magnitude of Ms = 5.5R, while for earthquakes o…
The magnitude distribution of three seismic sequences occurred in Morocco were investigated by means of the Tsallis-based non-extensive analysis. The non-extensive parameters were estimated by means of the Levenberg-Marquadt nonlinear least square fitting method. It was found that the q value could be a good indicator of the complexity of seismic phenomena. Such findings could contribute in better understanding the dynamics of seismicity and suggesting a unifying view of earthquake occurrence.
Spatial and temporal data for earthquakes with magnitude M greater than or equal to 6.5 can provide crucial information about the seismic history and potential for large earthquakes in a region. We analyzed approximately 313,500 events that occurred in the Sunda-arc region during the last 56 years, from 1964 to 2020, reported by the International Seismological Center. We report a persistent increase in the annual number of the events with mb greater than or equal to 6.5. We tested this increase against the null hypothesis and discarded the possibility of the increase being due to random groupi…
Cross-Sectional and Spatio-Temporal Analysis of Seismicity Parameters in the Zagros Orogenic Belt: Insights into Crustal Stress Distribution and Seismic Hazard
Farhangian University（法尔坎吉安大学）；Ankara University（安卡拉大学）；Arak University（阿拉克大学）；the University of Tokyo（东京大学）；Skolkovo Institute of Science and Technology (Skoltech)（斯科尔科沃科学技术研究所）
We show the capabilities of a downhole Distributed Acoustic Sensing (DAS) array in detecting, locating and characterizing low-magnitude earthquakes occurring in the vicinity of the Frontier Observatory for Research in Geothermal Energy (FORGE) site in Utah. 10.5 days of continuous data were acquired in a monitoring well at the FORGE geothermal site during the initial stimulation of an Enhanced Geothermal System in April-May 2019. Earthquake activity beneath Mineral Mountains, Utah also occurred within 10 km of the FORGE monitoring well. During the experiment, four events from those areas were …
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.
The productivity of a magnitude $m$ event can be characterized in term of triggered events of magnitude above $m-Δ$: it is the number of direct "descendants" $ν_Δ$ and the number of all "descendants" $V_Δ$. There is evidence in favour of the discrete exponential distribution for both $ν_Δ$ and $V_Δ$ with a dominant magnitude $m$ (the case of aftershock cluster). We consider the general Epidemic Type Aftershock Sequence (ETAS) model adapted to any distribution of $ν_Δ$. It turns out that the branching structure of the model excludes the possibility of having exponential distributions for both p…
The aftershock productivity law, first described by Utsu in 1970, is an exponential function of the form K=K0.exp(αM) where K is the number of aftershocks, M the mainshock magnitude, and α the productivity parameter. The Utsu law remains empirical in nature although it has also been retrieved in static stress simulations. Here, we explain this law based on Solid Seismicity, a geometrical theory of seismicity where seismicity patterns are described by mathematical expressions obtained from geometric operations on a permanent static stress field. We recover the exponential form but with a break …
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 …
Prediction of the Kamchatka July 29, 2025, earthquake by the evolution of low-magnitude seismicity recovered using waveform cross-correlation at IMS seismic arrays
Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Bath's law. Our theory shows that Bath's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +- 0.1 for Bath's constant value arou…
Despite the enormous efforts towards searching for precursors, no precursors have exhibited real predictive power with respect to an earthquake thus far. Seismogenic locked segments that can accumulate adequate strain energy to cause major earthquakes are very heterogeneous and less brittle; progressive failures of the locked segments with these properties can produce an interesting seismic phenomenon: a characteristic earthquake and a sequence of smaller subsequent earthquakes (pre-shocks) always arise prior to another characteristic earthquake within a well-defined seismic zone and its curre…
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.…
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 seismicity, which took place at the Methoni seismogenic area, in the time period of 20/2/2008 - 10/4/2008, is analyzed in terms of its location, time of occurrence and magnitude. Furthermore, it is compared to the tidal (T=14 days, T=1 day) lithospheric oscillation and to the epicentral area suggested by the analysis of the Earth_s electric field registered on 21-22/2/2008 by PYR, ATH and HIO monitoring sites. Moreover, a comparison is made between the actual seismic energy released, during the same time period (20/2/2008 - 10/4/2008) in this specific seismogenic region and the suggested o…
We present a model for estimating the probabilities of future earthquakes of magnitudes m > 4.95 in Italy. The model, a slightly modified version of the one proposed for California by Helmstetter et al. (2007) and Werner et al. (2010), approximates seismicity by a spatially heterogeneous, temporally homogeneous Poisson point process. The temporal, spatial and magnitude dimensions are entirely decoupled. Magnitudes are independently and identically distributed according to a tapered Gutenberg-Richter magnitude distribution. We estimated the spatial distribution of future seismicity by smoothing…
Numerical simulation of seismicity has been successfully developed and used for the two last decades. Presently, the general theory of modeling and the progress in computational techniques provide wide options for simulation of seismic and aseismic events with various source mechanisms accounting for blocky structure of rock mass, inclusions, faults, cracks, complicated contact conditions and various mechanical properties of rock. Meanwhile, in practical applications, the input data are limited and uncertain. The data on observed seismicity are also often limited with a few parameters, like co…
We analyze the effect of seismic activity on sealevel variations, by computing the time-dependent vertical crustal movement and geoid change due to coseismic deformations and postseismic relaxation effects. Seismic activity can affect both the absolute sealevel, by changing the Earth gravity field and hence the geoid height, and the relative sealevel, i.e. the radial distance between seafloor and geoid level. By using comprehensive seismic catalogues we assess the net effect of seismicity on tidal relative sealevel measurements as well as on the global oceanic surfaces, and we obtain an estima…
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 report a similarity of fluctuations in equilibrium critical phenomena and non-equilibrium systems, which is based on the concept of natural time. The world-wide seismicity as well as that of San Andreas fault system and Japan are analyzed. An order parameter is chosen and its fluctuations relative to the standard deviation of the distribution are studied. We find that the scaled distributions fall on the same curve, which interestingly exhibits, over four orders of magnitude, features similar to those in several equilibrium critical phenomena (e.g., 2D Ising model) as well as in non-equilib…
The optimal scaling problem for the time t(LxL) between two successive events in a seismogenic cell of size L is considered. The quantity t(LxL) is defined for a random cell of a grid covering a seismic region G. We solve that problem in terms of a multifractal characteristic of epicenters in G known as the tau-function or generalized fractal dimensions; the solution depends on the type of cell randomization. Our theoretical deductions are corroborated by California seismicity with magnitude M>2. In other words, the population of waiting time distributions for L = 10-100 km provides positive i…
It is shown that considering a fixed increment of a given magnitude at a fault is equivalent to factoring the mechanical moment at the fault as done in structural engineering with the applied loads, by the most currently used structural engineering standards (e.g. Eurocodes). A special safety factor is introduced and related to the partial factor acting on the mechanical moment representing the fault. A comparison is then made between the hazard maps obtained for Italy with the Neo Deterministic Seismic Hazard Assessment (NDSHA) technique, using two approaches for the definition of the seismic…
In this work the data of the earthquake catalog of the NOAA, National Geophysical Data Center (NGDC) are processed in terms of global seismic energy release. The determined Global Cumulative Seismic Energy Release (GCSER) graph as a function of time, is analyzed in the magnitude domain (discrete energy windows). Characteristic components of the analyzed graph are: its accelerated deformation character observed for energy windows lower than the background seismicity (M = 7.0 - 7.5), its lock state that started on 1923 and long seismic quiescence periods that preceded recent mega - earthquakes. …
We analyze the ground motion time histories due to the local seismicity near the Itoiz reservoir to estimate the near-source, surface 3D displacement-gradients and dynamic deformations. The seismic data were obtained by a semi-permanent broadband and accelerometric network located on surface and at underground sites. The dynamic deformation field was calculated by two different methodologies. First, by the Seismo-Geodetic method using the data from a three-station micro-array located close to the dam; second, by Single-Station estimates of the displacement gradients. The dynamic deformations o…
Starting in April 2004, unusual seismic activity was observed in the interior of the island of Tenerife (Canary Islands, Spain) with much evidence pointing to a reawakening of volcanic activity. This seismicity is now analyzed with techniques unprecedented in previous studies of this crisis. The 200 earthquakes located onshore during 2004 and 2005 have been classified by cross-correlation, resulting in a small number of significant families. The application of a relative location algorithm (hypoDD) revealed important features about the spatial distribution of the earthquakes. The seismic catal…
Crustal deformation due to the 2016 earthquake sequence in Kumamoto, Japan, that culminated in a preceding earthquake of magnitude M6.5 and a subsequent M7.3 earthquake 28 hours later, caused stress perturbation on and around the causative Futagawa-Hinagu fault zone. Monitoring changes in seismicity pattern along this zone plays a role in understanding the process before and after major earthquakes. For this purpose, stress-dependent laws in statistical seismology can be used: the Gutenberg-Richter frequency-size law and the Omori-Utsu aftershock-decay law. We review the results obtained by us…
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…
The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamental. A general form for the distribution is derived imposing only the self-similarity of the process, which also yields a scaling relation between the Gutenberg-Richter b-value, the exponent characterizing the correlations, and the recurrence-time exponent. This a…
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?
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 Roles of Low-Noise Stations, Arrays and Ocean-Bottom Seismometers in Monitoring UK Offshore Seismicity associated with Subsurface Storage of Carbon Dioxide
School of Geosciences, University of Edinburgh（爱丁堡大学地球科学学院）
Coulomb-stress theory has been used for years in seismology to understand how earthquakes trigger each other. Whenever an earthquake occurs, the stress field changes, and places with positive increases are brought closer to failure. Earthquake models that relate earthquake rates and Coulomb stress after a main event, such as the rate-and-state model, assume that the magnitude distribution of earthquakes is not affected by the change in the Coulomb stress. By using different slip models, we calculate the change in Coulomb stress in the fault plane for every aftershock after the Landers event (C…
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…
We present a multifractal analysis of Mount St. Helens seismic activity during 1980-2002. The seismic time distribution is studied in relation to the eruptive activity, mainly marked by the 1980 major explosive eruptions and by the 1980-1986 dome building eruptions. The spectrum of the generalized fractal dimensions, i.e. Dq vs q, extracted from the data, allows us to identify two main earthquake time-distribution patterns. The first one exhibits a multifractal clustering correlated to the intense seismic swarms of the dome building activity. The second one is characterized by an almost consta…
In this paper, we used the Global Catalog of the National Earthquake Information Center US Geological Survey (NEIC USGS) for analysis of the magnitude-frequency distribution of earthquakes. We selected the unimodal part of the distribution and proposed an empirical formula that approximates this part in a wide range of magnitudes. The formula may be useful in studying the problems seismology, in which the expected effect is manifested in relatively weak earthquakes. The paper will be sent to the journal Geodynamics and Tectonophysics (ISSN 2078-502X). Keywords: planetary seismicity, Gutenberg-…
The recent evolution of induced seismicity in Central United States calls for exhaustive catalogs to improve seismic hazard assessment. Over the last decades, the volume of seismic data has increased exponentially, creating a need for efficient algorithms to reliably detect and locate earthquakes. Today's most elaborate methods scan through the plethora of continuous seismic records, searching for repeating seismic signals. In this work, we leverage the recent advances in artificial intelligence and present ConvNetQuake, a highly scalable convolutional neural network for earthquake detection a…
The 2016 Mw 7.0 Kumamoto Earthquake Sequence, Japan revisited: Insights from Spatio-Temporal Analysis of Seismicity Parameters
Farhangian University（法尔干大学）；Ankara University（安卡拉大学）；University of Beira Interior（贝拉内陆大学）；Atmosphere and Ocean Research Institute (AORI), the University of Tokyo（东京大学大气海洋研究所）
Volcanic seismicity at Mt. Etna is studied. It is found that the associated stochastic process exhibits a subdiffusive phenomenon. The jump probability distribution well obeys an exponential law, whereas the waiting-time distribution follows a power law in a wide range. Although these results would seem to suggest that the phenomenon could be described by temporally-fractional kinetic theory based on the viewpoint of continuous-time random walks, the exponent of the power-law waiting-time distribution actually lies outside of the range allowed in the theory. In addition, there exists the aging…
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
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…
Low-magnitude seismic activity between the Kamchatka July 20 and July 29, 2025, earthquakes. Spatio-temporal evolution recovered using waveform cross-correlation
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 …
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…
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 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…
