Magnitude Distribution Of Earthquakes Research Articles

Chile2015: Lévy Flight and Long-Range Correlation Analysis of Earthquake Magnitudes in Chile

The stochastic Truncated Levy Flight model and detrended fluctuation analysis (DFA) are used to investigate the temporal distribution of earthquake magnitudes in Chile. We show that Levy Flight is appropriated for modeling the time series of the magnitudes of the earthquakes. Furthermore, DFA shows that these events present memory effects, suggesting that the magnitude of impeding earthquakes depends on the magnitude of previous earthquakes. Based on this dependency, we use a non-linear regression to estimate the magnitude of the 2015, M8.3 Illapel earthquake based on the magnitudes of the previous events.

Long-Term Seismicity Behavior of the Zagros Region in Iran

To achieve a comprehensive attitude about seismicity, it is necessary to consider spatial and magnitude distributions of earthquakes. Earthquake distributions in space and magnitude can be quantified by means of spatial fractal dimension D(s) and Gutenberg–Richter b value. In this paper, b value and D(s) are used to evaluate seismicity of the Zagros zone (Iran) in time interval 1964 to 2012. Seismic catalog of the Zagros zone is extracted from unified seismic catalog of the Iranian Plateau. The b value and D(s) are estimated using frequency–magnitude distribution, Kijko-Sellevoll (Bull Seism Soc Am 79(3):645–654, 1989) and correlation integral methods. Correlations between spatial variations in b value and D(s) along individual profiles across the North Zagros and the Central Zagros indicate different stress release regimes for North and Central parts of the Zagros zone. Evaluation of b value with respect to depth along the profiles indicates larger b values at shallower depths. Temporal variations in b value and D(s) are also obtained from background seismicity to evaluate seismicity behavior of the Zagros zone. Our results indicate high b values and moderate D(s) for seismicity of the North Zagros, while seismicity of the Central Zagros has low b values and high D(s) during time interval 1964–2012. Asperities of the Main Zagros Thrust are also located by investigating ratio D(s)/b along the Main Zagros Thrust.

Earthquake rate and magnitude distributions of great earthquakes for use in global forecasts

We have obtained new results in the statistical analysis of global earthquake catalogues with special attention to the largest earthquakes, and we examined the statistical behaviour of earthquake rate variations. These results can serve as an input for updating our recent earthquake forecast, known as the ‘Global Earthquake Activity Rate 1’ model (GEAR1), which is based on past earthquakes and geodetic strain rates. The GEAR1 forecast is expressed as the rate density of all earthquakes above magnitude 5.8 within 70km of sea level everywhere on earth at 0.1 × 0.1 degree resolution, and it is currently being tested by the Collaboratory for Study of Earthquake Predictability. The seismic component of the present model is based on a smoothed version of the Global Centroid Moment Tensor (GCMT) catalogue from 1977 through 2013. The tectonic component is based on the Global Strain Rate Map, a ‘General Earthquake Model’ (GEM) product. The forecast was optimized to fit the GCMT data from 2005 through 2012, but it also fit well the earthquake locations from 1918 to 1976 reported in the International Seismological Centre-Global Earthquake Model (ISC-GEM) global catalogue of instrumental and pre-instrumental magnitude determinations. We have improved the recent forecast by optimizing the treatment of larger magnitudes and including a longer duration (1918–2011) ISC-GEM catalogue of large earthquakes to estimate smoothed seismicity. We revised our estimates of upper magnitude limits, described as corner magnitudes, based on the massive earthquakes since 2004 and the seismic moment conservation principle. The new corner magnitude estimates are somewhat larger than but consistent with our previous estimates. For major subduction zones we find the best estimates of corner magnitude to be in the range 8.9 to 9.6 and consistent with a uniform average of 9.35. Statistical estimates tend to grow with time as larger earthquakes occur. However, by using the moment conservation principle that equates the seismic moment rate with the tectonic moment rate inferred from geodesy and geology, we obtain a consistent estimate of the corner moment largely independent of seismic history. These evaluations confirm the above-mentioned corner magnitude value. The new estimates of corner magnitudes are important both for the forecast part based on seismicity as well as the part based on geodetic strain rates. We examine rate variations as expressed by annual earthquake numbers. Earthquakes larger than magnitude 6.5 obey the Poisson distribution. For smaller events the negative-binomial distribution fits much better because it allows for earthquake clustering.

Implication of Focal Depth, Temporal and Magnitude Distribution of Earthquakes in Oceanic Ridges

Implication of Focal Depth, Temporal and Magnitude Distribution of Earthquakes in Oceanic Ridges

A comparison of long‐term changes in seismicity at The Geysers, Salton Sea, and Coso geothermal fields

AbstractGeothermal energy is an important source of renewable energy, yet its production is known to induce seismicity. Here we analyze seismicity at the three largest geothermal fields in California: The Geysers, Salton Sea, and Coso. We focus on resolving the temporal evolution of seismicity rates, which provides important observational constraints on how geothermal fields respond to natural and anthropogenic loading. We develop an iterative, regularized inversion procedure to partition the observed seismicity rate into two components: (1) the interaction rate due to earthquake‐earthquake triggering and (2) the smoothly varying background rate controlled by other time‐dependent stresses, including anthropogenic forcing. We apply our methodology to compare long‐term changes in seismicity to monthly records of fluid injection and withdrawal. At The Geysers, we find that the background seismicity rate is highly correlated with fluid injection, with the mean rate increasing by approximately 50% and exhibiting strong seasonal fluctuations following construction of the Santa Rosa pipeline in 2003. In contrast, at both Salton Sea and Coso, the background seismicity rate has remained relatively stable since 1990, though both experience short‐term rate fluctuations that are not obviously modulated by geothermal plant operation. We also observe significant temporal variations in Gutenberg‐Richter b value, earthquake magnitude distribution, and earthquake depth distribution, providing further evidence for the dynamic evolution of stresses within these fields. The differing field‐wide responses to fluid injection and withdrawal may reflect differences in in situ reservoir conditions and local tectonics, suggesting that a complex interplay of natural and anthropogenic stressing controls seismicity within California's geothermal fields.

Reply to: “Comment on Pisarenko et al., ‘Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory’” by Mathias Raschke in Pure Appl Geophys (2015)

Reply to: “Comment on Pisarenko et al., ‘Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory’” by Mathias Raschke in Pure Appl Geophys (2015)

The Cardston Earthquake Swarm and Hydraulic Fracturing of the Exshaw Formation (Alberta Bakken Play)

More than 60 small earthquakes ( M L 0.7–3.0) were detected from December 2011 to March 2012 north of Cardston, Alberta, an area with little evidence for previous seismic activity. The timing of these events closely correlates (>99.7% confidence) with hydraulic fracturing completions of the Devonian–Mississippian-age Exshaw Formation at a nearby horizontal well. Unanimous waveform multiplicity within the swarm suggests that the events share a similar origin and source mechanism. This observation is corroborated by the point-like collocation of hypocenters within the crystalline basement during robust, double-difference relocations. Furthermore, the presence of a pre-existing fault is confirmed via formation-top offset mapping and interpreted to be a Late Cretaceous extensional fault. The confirmation of this fault at depth provides a plausible pathway for rapid hydraulic communication from the fracturing interval into the crystalline basement. Consistent with structural interpretations and available stress information, moment tensor inversion of the largest magnitude event ( M w 3.0) indicates reactivation of a basement fault with normal slip. We conclude that the genesis of this earthquake swarm was likely caused by increased pore pressure, within the basement fault, as a result of fracturing stimulation. Online Material: Figure showing frequency–magnitude distribution of earthquakes, and table of the velocity models used in the study.

Building icelandic igneous crust by repeated melt injections

AbstractObservations of microseismicity provide a powerful tool for mapping the movement of melt in the crust. Here we record remarkable sequences of earthquakes 20 km below the surface in the normally ductile crust in the vicinity of Askja Volcano, in northeast Iceland. The earthquakes occur in swarms consisting of identical waveforms repeating as frequently as every 8 s for up to 3 h. We use template waveforms from each swarm to detect and locate earthquakes with an automated cross‐correlation technique. Events are located in the lower crust and are inferred to be the result of melt being injected into the crust. During melt intrusion high strain rates are produced in conjunction with high pore fluid pressures from the melt or exsolved carbon dioxide. These cause brittle failure on high‐angle fault planes located at the tips of sills. Moment tensor solutions show that most of the earthquakes are opening cracks accompanied by volumetric increases. This is consistent with the failure causing the earthquakes by melt injection opening new tensile cracks. Analysis of the magnitude distribution of earthquakes within a swarm reveals a complicated relationship between the imposed strain rates and the fluids that cause brittle failure. The magnitude of the earthquakes is controlled by the distance fluids can migrate along a fault, whereas the frequency of the events is controlled by the strain rate. Faults at the tips of sills act to focus melt transport between sills and so must be an important method of transporting melt through the lower crust.

Testing the Basic Assumption for Probabilistic Seismic‐Hazard Assessment: 11 Failures

In the probabilistic seismic‐hazard assessment (PSHA), one calculates the peak ground acceleration (PGA) (alternatively velocity, displacement, or intensity) at a given location that is expected not to be exceeded by a probability chosen by expert judgment (differing in different cases) and during a selected period. This is usually done by considering the influence of several seismogenic sources in the vicinity of a site. Here we consider the simple case in which one source capable of a large earthquake dominates the PGA calculation, a situation often encountered in practice. The first parameter one needs to know for estimating the PGA is the maximum magnitude of earthquakes M max that is possible in each seismogenic source. When one of the M max events clearly dominates the PGA at the site in question, as in this case, one speaks of the maximum credible earthquake (MCE) affecting the site. Estimating the PGA due to the MCE is specified as one of the requirements for assessing the seismic hazard for large dams as detailed by the International Commission on Large Dams (ICOLD, 2010). Once the MCE is identified, one needs to know the annual probability of the MCE, which is proportional to its recurrence time. The PSHA method assumes the occurrence rate (or probability of occurrence) of the MCE can be estimated by extrapolating the occurrence rate and magnitude distribution of small earthquakes in the volume in question. In cases of large MCEs, the extrapolation is performed over one to five orders of magnitude. This basic assumption of the standard PSHA method that the occurrence probability of MCEs can be derived by extrapolation from the occurrence rate of small earthquakes is not supported by a physical theory. I am showing here that this hypothesis fails 11 out of 11 tests. The tests consist of …

Impact of channel-like erosion patterns on the frequency–magnitude distribution of earthquakes

Reactive flow at depth (either related to underground activities, like enhancement of hydrocarbon recovery and CO2 storage, or to natural flow like in hydrothermal zones) can alter fractures’ topography, which might in turn change their seismic responses. Depending on the flow and reaction rates, instability of the dissolution front can lead to a wormhole-like pronounced erosion pattern. In a fractal structure of rupture process, we question how the perturbation related to well-spaced long channels alters rupture propagation initiated on a weak plane and eventually the statistical feature of rupture appearance in frequency–magnitude distribution (FMD). Contrary to intuition, a spatially uniform dissolution is not the most remarkable case, since it affects all the events proportionally to their sizes leading to a downward translation of FMD: the slope of FMD (b-value) remains unchanged. The parameter–space study shows that the increase of b-value (of 0.08) is statistically significant for optimum characteristics of the erosion pattern with spacing to length ratio of the order of ∼1/40: large-magnitude events are more significantly affected leading to an imbalanced distribution in the magnitude bins of the FMD. The larger the spacing, the lower the channel's influence. Besides, a spatial analysis shows that the local seismicity anomaly concentrates in a limited zone around the channels: this opens perspective for detecting these eroded regions through high-resolution imaging surveys.

Interseismic re-strengthening and stabilization of carbonate faults by “non-Dieterich” healing under hydrothermal conditions

Friction experiments, consisting of a “velocity stepping” stage, a “slide-hold-slide” (SHS) stage and a second “velocity stepping” stage, have been performed to study the frictional healing behavior of carbonate fault gouge, and the effects of healing on the velocity dependence of friction, at 20–140 °C and at 50 MPa effective normal stress. Dry experiments show classical Dieterich healing characterized by a transient peak in friction after each hold period, with no effects of SHS testing on steady-state friction or velocity dependence. By contrast, the wet tests show 1) an increase in apparent steady-state friction upon re-sliding after a hold period, and 2) a pronounced increase in the velocity dependence parameter, (a−b), after the SHS stage. While the first of these “non-Dieterich-type” healing effects has been observed in previous hydrothermal experiments on simulated quartz gouges, it has not been reported previously for carbonate gouges. The observed effect of SHS-testing on (a−b) has never been reported. Our findings suggest that, under in-situ hydrothermal conditions, interseismic fluid-assisted deformation processes, such as pressure solution, can significantly promote fault re-strengthening in carbonates and can cause slip stabilization. If the results are applicable to active faults in carbonate terrains, they have important implications for understanding how the extent of the seismogenic zone, and how earthquake magnitude and aftershock distributions, may evolve with repeated cycles of natural seismicity and interseismic healing.

Spatial variations of earthquake occurrence and coseismic deformation in the Upper Rhine Graben, Central Europe

Seismic activity in the densely populated Upper Rhine Graben (URG) is an aspect in the public, political, and industrial decision making process. The spatial analysis of magnitude–frequency distributions provides valuable information about local seismicity patterns and regional seismic hazard assessment and can be used also as a proxy for coseismic deformation to explore the seismo-tectonic setting of the URG.We combine five instrumental and one historic earthquake bulletins to obtain for the first time a consistent database for events with local magnitudes ML≥2.0 in the whole URG and use it for the determination of magnitude frequencies. The data processing results in a dataset with 274 Poisson distributed instrumentally recorded earthquakes within the URG between 01/1971 and 02/2012 and 34 historic events since the year 1250.Our analysis reveals significant b-value variations along the URG that allow us to differentiate four distinct sections (I–IV) with significant differences in earthquake magnitude distributions: I: Basel region in the Swiss–France–German border region (b=0.83), II: region between Mulhouse and Freiburg in the southern URG (b=1.42), III: central URG (b=0.93), and IV: northern URG (b=1.06). High b-values and thus a relatively low amount of high magnitude events in the Freiburg section are possibly a consequence of strongly segmented, small-scale structures that are not able to accumulate high stresses.We use the obtained magnitude–frequency distributions and representative source mechanisms for each section to determine coseismic displacement rates. A maximum horizontal displacement rate of 41μm/a around Basel is found whereas only 8μm/a are derived for the central and northern URG. A comparison with geodetic and geological constraints implies that the coseismic displacement rates cover less than 10% of the overall displacement rates, suggesting a high amount of aseismic deformation in the URG.

Comment on Pisarenko et al., “Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory”

In this short note, I comment on the research of Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014) regarding the extreme value theory and statistics in the case of earthquake magnitudes. The link between the generalized extreme value distribution (GEVD) as an asymptotic model for the block maxima of a random variable and the generalized Pareto distribution (GPD) as a model for the peaks over threshold (POT) of the same random variable is presented more clearly. Inappropriately, Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014) have neglected to note that the approximations by GEVD and GPD work only asymptotically in most cases. This is particularly the case with truncated exponential distribution (TED), a popular distribution model for earthquake magnitudes. I explain why the classical models and methods of the extreme value theory and statistics do not work well for truncated exponential distributions. Consequently, these classical methods should be used for the estimation of the upper bound magnitude and corresponding parameters. Furthermore, I comment on various issues of statistical inference in Pisarenko et al. and propose alternatives. I argue why GPD and GEVD would work for various types of stochastic earthquake processes in time, and not only for the homogeneous (stationary) Poisson process as assumed by Pisarenko et al. (Pure Appl. Geophys 171:1599–1624, 2014). The crucial point of earthquake magnitudes is the poor convergence of their tail distribution to the GPD, and not the earthquake process over time.

Synthetic earthquake catalogs simulating seismic activity in the Corinth Gulf, Greece, fault system

AbstractThe characteristic earthquake hypothesis is the basis of time‐dependent modeling of earthquake recurrence on major faults. However, the characteristic earthquake hypothesis is not strongly supported by observational data. Few fault segments have long historical or paleoseismic records of individually dated ruptures, and when data and parameter uncertainties are allowed for, the form of the recurrence distribution is difficult to establish. This is the case, for instance, of the Corinth Gulf Fault System (CGFS), for which documents about strong earthquakes exist for at least 2000 years, although they can be considered complete forM ≥ 6.0 only for the latest 300 years, during which only few characteristic earthquakes are reported for individual fault segments. The use of a physics‐based earthquake simulator has allowed the production of catalogs lasting 100,000 years and containing more than 500,000 events of magnitudes ≥ 4.0. The main features of our simulation algorithm are (1) an average slip rate released by earthquakes for every single segment in the investigated fault system, (2) heuristic procedures for rupture growth and stop, leading to a self‐organized earthquake magnitude distribution, (3) the interaction between earthquake sources, and (4) the effect of minor earthquakes in redistributing stress. The application of our simulation algorithm to the CGFS has shown realistic features in time, space, and magnitude behavior of the seismicity. These features include long‐term periodicity of strong earthquakes, short‐term clustering of both strong and smaller events, and a realistic earthquake magnitude distribution departing from the Gutenberg‐Richter distribution in the higher‐magnitude range.

Morlet Wavelet Analysis of ML ≥ 3 Earthquakes in the Taipei Metropolitan Area

M_L ≥ 3 earthquakes (M_L=local magnitude) that occurred in the Taipei Metropolitan Area (TMA) from 1973-2013 are selected to study the dominant seismicity period of this area. The epicentral distribution and temporal sequences of earthquake magnitudes are simply described. These earthquakes can be divided into two groups: one for events shallower than 40 km and one for events deeper than 60 km. Shallow earthquakes are located mainly in the 0-10 km depth range north of 25.1°N, and down to 35 km for those south of 25.1°N. Deep events are located in the subduction zone, with a dip angle of about 70°. The Morlet wavelet technique is applied to analyze the dominant periods of temporal variations in numbers of monthly earthquakes in the shallow and deep ranges for three magnitude ranges, i.e., M_L ≥ 3, 4, and 5. The results show that for shallow earthquakes the dominant periods are 15.4, 30.8, 66.1, and 132.2 months when M_L ≥ 3 and 30.8 months when M_L ≥ 4; while for deep earthquakes, the dominant periods are 16.5 and 141.7 months when M_L ≥ 3 and 141.7 months when M_L ≥ 4. The dominant period cannot be obtained for both shallow and deep M_L ≥ 5 earthquakes.

The magnitude distribution of dynamically triggered earthquakes

Large dynamic strains carried by seismic waves are known to trigger seismicity far from their source region. It is unknown, however, whether surface waves trigger only small earthquakes, or whether they can also trigger large earthquakes. To partially address this question, we evaluate whether current data can distinguish between the magnitude distribution of triggered and untriggered small earthquakes. We use a mixing model approach in which total seismicity is decomposed into two classes: “triggered” events initiated or advanced by far-field dynamic strains and “untriggered” spontaneous events consisting of everything else. The b-value of a mixed data set, bMIX, is decomposed into a weighted sum of b-values of its constituent components, bT and bU. We utilize the previously observed relationship between triggering rate and dynamic strain amplitude to identify the fraction of triggered events in populations of earthquakes and then invert for bT. For Californian seismicity, data are consistent with a single-parameter Gutenberg-Richter hypothesis governing the magnitudes of both triggered and untriggered earthquakes.

Temporal distribution of recorded magnitudes in Serbia earthquake catalog

We focus on earthquakes that were recorded in Serbia between 1970 and 2011 within shallow parts of the Earth’s crust, having local magnitudes from the 1.2–5.8 interval. The main goal of the performed analysis is to examine whether the temporal sequence of these recorded magnitudes exhibits some deterministic pattern or whether it simply represents a series of random events. For this purpose, the temporal distribution of earthquake magnitudes above the magnitude of completeness is analyzed by means of nonlinear time series analysis and surrogate data testing, as well as by means of the autocorrelation function. Piece-wise low cross-prediction errors, with 75% of segment pairs having the error smaller than its average value, indicate stationary properties of the examined sequence. Results of surrogate data testing indicate high zeroth-order prediction error that is independent of prediction time for the original dataset and 20 different surrogates, implying that the observed magnitude sequence is a series of independent random events drawn from some fixed but unknown distribution. These findings are supported further by a low value of the determinism factor for an earthquake treated as a system with four degrees of freedom (epicentral latitude and longitude, hypocentral depth and magnitude). The randomness in observed data is indicated further by the properties of the autocorrelation function, whose values for different time lags fall within the 95% confidence limit without an apparent pattern.

Characterization of the Tail of the Distribution of Earthquake Magnitudes by Combining the GEV and GPD Descriptions of Extreme Value Theory

The present work is a continuation and improvement of the method suggested in Pisarenkoet al. (Pure Appl Geophys 165:1–42, 2008) for the statistical estimation of the tail of the distribution of earthquake sizes. The chief innovation is to combine the two main limit theorems of Extreme Value Theory (EVT) that allow us to derive the distribution of T-maxima (maximum magnitude occurring in sequential time intervals of duration T) for arbitrary T. This distribution enables one to derive any desired statistical characteristic of the future T-maximum. We propose a method for the estimation of the unknown parameters involved in the two limit theorems corresponding to the Generalized Extreme Value distribution (GEV) and to the Generalized Pareto Distribution (GPD). We establish the direct relations between the parameters of these distributions, which permit to evaluate the distribution of the T-maxima for arbitrary T. The duality between the GEV and GPD provides a new way to check the consistency of the estimation of the tail characteristics of the distribution of earthquake magnitudes for earthquake occurring over an arbitrary time interval. We develop several procedures and check points to decrease the scatter of the estimates and to verify their consistency. We test our full procedure on the global Harvard catalog (1977–2006) and on the Fennoscandia catalog (1900–2005). For the global catalog, we obtain the following estimates: \( \hat{M}_{{\rm max} } \) = 9.53 ± 0.52 and \( \hat{Q}_{10} (0.97) \) = 9.21 ± 0.20. For Fennoscandia, we obtain \( \hat{M}_{{\rm max} } \) = 5.76 ± 0.165 and \( \hat{Q}_{10} (0.97) \) = 5.44 ± 0.073. The estimates of all related parameters for the GEV and GPD, including the most important form parameter, are also provided. We demonstrate again the absence of robustness of the generally accepted parameter characterizing the tail of the magnitude-frequency law, the maximum possible magnitude Mmax, and study the more stable parameter QT(q), defined as the q-quantile of the distribution of T-maxima on a future interval of duration T.

A Nonextensive Statistical Physics Analysis of the 1995 Kobe, Japan Earthquake

This paper presents an analysis of the distribution of earthquake magnitudes for the period 1990–1998 in a broad area surrounding the epicenter of the 1995 Kobe earthquake. The frequency–magnitude distribution analysis is performed in a nonextensive statistical physics context. The nonextensive parameter q M , which is related to the frequency-magnitude distribution, reflects the existence of long-range correlations and is used as an index of the physical state of the studied area. Examination of the possible variations of q M values is performed during the period 1990–1998. A significant increase of q M occurs some months before the strong earthquake on April 9, 1994 indicating the start of a preparation phase prior to the Kobe earthquake. It should be noted that this increase coincides with the occurrence of six seismic events. Each of these events had a magnitude M = 4.1. The evolution of seismicity along with the increase of q M indicate the system’s transition away from equilibrium and its preparation for energy release. It seems that the variations of q M values reflect rather well the physical evolution towards the 1995 Kobe earthquake.

Large earthquakes in the Baikal region as response to bifurcations in nonlinear resonance hysteresis

The hypothesis that large earthquakes in the Baikal region are a response to bifurcations in nonlinear resonance hysteresis in a system consisting of three oscillators, attractor structures of riftogenesis, is substantiated. The hypothesis is confirmed by the spatial-temporal and magnitude distribution of large earthquakes: all the pairs of earthquakes with magnitude MLH > 5.5 that took place in the region within a small time period but were remote from one another show fair agreement with the main theoretical conclusions.