Gutenberg-Richter Law Research Articles

Fault Prediction of CNC Machine Tools Based on Gutenberg-Richter Law and Fuzzy Neural Networks

Fault Prediction of CNC Machine Tools Based on Gutenberg-Richter Law and Fuzzy Neural Networks

Multifractal structure and Gutenberg–Richter parameter associated with volcanic emissions of high energy in Colima, Mexico (years 2013–2015)

Abstract. The evolution of multifractal structures in various physical processes, such as climatology, seismology, or volcanology, serves as a crucial tool for detecting changes in corresponding phenomena. In this study, we explore the evolution of the multifractal structure of volcanic emissions with varying energy levels (observed at Colima, Mexico, during the years 2013–2015) to identify clear indicators of imminent high-energy emissions nearing 8.0×108 J. These indicators manifest through the evolution of six multifractal parameters: the central Hölder exponent (α0); the maximum and minimum Hölder exponents (αmax, αmin); the multifractal amplitude (W=αmax-αmin); the multifractal asymmetry (γ=[αmax-α0]/[α0-αmin]); and the complexity index (CI), calculated as the sum of the normalized values of α0, W, and γ. Additionally, the results obtained from adapting the Gutenberg–Richter seismic law to volcanic energy emissions, along with the corresponding skewness and standard deviation of the volcanic emission data, further support the findings obtained through multifractal analysis. These results, derived from multifractal structure analysis, adaptation of the Gutenberg–Richter law to volcanic emissions, and basic statistical parameters, hold significant relevance in anticipating potential volcanic episodes of high energy. Such anticipation can be further quantified using an appropriate forecasting algorithm.

Inhomogeneity effects on earthquake fault events.

We present a detailed analysis of the dynamical behavior of an inhomogeneous Burridge-Knopoff model, a simplified mechanical model of an earthquake. Regardless of the size of seismic faults, a soil element rarely has a continuous appearance. Instead, their surfaces have complex structures. Thus, the model we suggest keeps the full Newtonian dynamics with inertial effects of the original model, while incorporating the inhomogeneities of seismic fault surfaces in stick-slip friction force that depends on the local structure of the contact surfaces as shown in recent experiments. The numerical results of the proposed model show that the cluster size and the moment distributions of earthquake events are in agreement with the Gutenberg-Richter law without introducing any relaxation mechanism. The exponent of the power-law size distribution we obtain falls within a realistic range of value without fine tuning any parameter. On the other hand, we show that the size distribution of both localized and delocalized events obeys a power law in contrast to the homogeneous case. Thus, no crossover behavior between small and large events occurs.

The return period and probabilities of earthquakes occurrence in North-East, India (Eastern-Himalayas) and its vicinity inferred from Gutenberg–Richter relation

The return period and probabilities of earthquakes occurrence in North-East, India (Eastern-Himalayas) and its vicinity inferred from Gutenberg–Richter relation

Probability and recurrence interval of large earthquakes (Mw ≥ 6) in the Himalayan seismicity zone

The Himalayan Mountains are one of the world’s most seismically active regions. Due to the active seismic status of the Himalayan belt and ongoing development activities in the region, it is important to keep the seismic hazard estimates updated by incorporating historical and new data. This study uses the Gutenberg-Richter relations for four seismogenic source zones (SSZ) to estimate the probability of earthquakes of a specified magnitude in a given time interval. We used exponential, Weibull, Rayleigh, and log-normal statistical models to assess the probability of earthquakes (Mw ≥ 6). The probable recurrence time of the large earthquake (Mw ≥ 6) can be estimated by maximizing the conditional probability estimates. This recurrence interval is calculated after the elapsed time since the most recent large earthquake in the region. We also apply an autoregressive (AR) forecasting technique to predict earthquake recurrence intervals. The results indicate that the approximate recurrence interval of the large earthquakes (Mw ≥ 6) may be 22.052 ± 5.65 years within the seismicity zones, as per our statistical estimates based on limited and available datasets. The results of this study may be useful for the agencies involved in assessing seismic hazards and developing mitigation and preparedness strategies in the region.

Source parameters and aftershock pattern of the October 7, 2021, M5.9 Harnai earthquake, Pakistan

On October 7, 2021, a magnitude 5.9 earthquake struck the Harnai (Baluchistan) region of Pakistan, causing several fatalities and injuries within the epicentral area. First-order tectonic deformation in this region is caused by the convergence of the Indian Plate with respect to the Eurasian Plate. The Katwaz Block hinders the motion of the Indian Plate, resulting in the formation of strike-slip faults. In this study, the P-wave first-motion polarity technique was used to determine the mainshock faulting style. Cyclic scanning of the polarity solutions was applied to determine the most suitable focal mechanism solution among the available solutions generated by the FOCMEC (focal mechanism) software. The nodal planes correspond to different faulting styles (i.e., thrust and strike-slip faulting). A nodal plane oriented in the NW-SE direction corresponded to a strike-slip mechanism, which was considered to be the fault plane. Tectonically, this earthquake was associated with the Harnai-Karahi strike-slip fault zone owing to the fault strike and direction of slip. The apparent stress drop, fault length, and moment magnitude of the Harnai earthquake were 35.4 bar, 6.1 km, and 5.9, respectively. A lower b-value for the Gutenberg-Richter law was observed prior to the earthquake. Higher α- than b-values (α >b) indicate that this earthquake was governed by large events as opposed to small-magnitude events. The Harnai sequence had a decay exponent close to unity, lasted for 145 days, and produced few aftershocks. The study will help the future hazard mitigation in the region.

Number of Aftershocks in Epidemic-type Seismicity Models

Summary The Epidemic Type Aftershock Sequence (ETAS) model describes how an earthquake generates its own aftershocks. The regular ETAS model assumes that distribution F of the number of direct aftershocks is Poissonian, however there is evidence suggesting that a geometric distribution might be more adequate. Let ${V}_M({m}_ \bullet )$ be the number of $m > M$ aftershocks generated by ${m}_ \bullet $event. In this study we consider the ${V}_M({m}_ \bullet )$ distribution within Epidemic-type Seismicity models, ETAS(F). These models include the Gutenberg-Richter law for magnitude and Utsu law for average ${m}_ \bullet $- productivity, but differ in the type of F distribution for the number $v({m}_ \bullet )$ of direct aftershocks. The class of F is quite broad and includes both the Poisson distribution, which is the basis for the regular ETAS model, and its possible alternative, the Geometric distribution. We replace the traditional $M = {m}_ \bullet - \Delta $ threshold in $\Delta $-analysis with $M = {m}_a - \Delta $ where ${m}_a$ is the distribution mode of the strongest aftershocks. Under these conditions we find the limit ${V}_M({m}_ \bullet )$ distribution at ${m}_ \bullet > > 1$. In the subcritical case, the limit distribution is extremely simple and identical to the $v({m}_\Delta )$ distribution with a suitable magnitude ${m}_\Delta $. This result allows us to validate both the priority of the geometric distribution of F for direct aftershocks and the very concept of epidemic-type clustering on global seismicity data.

Stable estimation of the Gutenberg–Richter b-values by the b-positive method: a case study of aftershock zones for magnitude-7 class earthquakes

The traditional approach for estimating the b-value of the Gutenberg–Richter law, which is posited to inversely correlate with differential stress, has historically relied on the maximum likelihood technique, utilizing data from earthquakes exceeding a magnitude cutoff, Mc. This traditional approach is significantly influenced by the value of Mc, leading to extensive research focused on methods for determining Mc with greater accuracy. However, a recent study introduced a novel method based on the frequency distribution of magnitude difference, termed the b-positive method. This innovative method could enable more robust b-value estimations, even in scenarios where Mc may vary spatially and temporally. Our study concentrated on analyzing aftershocks, related to 25 magnitude-7 class earthquakes surrounding the Japanese archipelago. We estimated the b-values using both the goodness-of-fit test for Mc, a traditional approach, and the b-positive method. The aftershock data were examined over two distinct time frames: the initial 10 days following each mainshock and an extended period of 1000 days. Our findings indicated that the estimates produced by the b-positive method showed negligible variation between the 10-day and 1000-day aftershock periods (correlation coefficient of 0.95), whereas the traditional approach tended to yield lower b-values for the 10-day aftershocks compared to those from the 1000-day period. Variations in b-values, when analyzed using the traditional approach, could be inaccurately ascribed to temporal fluctuations in differential stress that may not actually be present. The b-positive method offers a vital solution to prevent these erroneous interpretations, serving as an essential alternative.Graphical abstract

A Bayesian Merging of Earthquake Magnitudes Determined by Multiple Seismic Networks

Abstract We introduce a Bayesian algorithm designed to integrate earthquake magnitudes of the same type reported by various seismic networks, aiming to create unified and standardized catalogs suitable for widespread use. The fundamental concept underpinning this algorithm is the utilization of the inherent consistency within each individual network’s magnitude determination process. Assuming that the magnitudes for an earthquake measured by all networks conform to a Gaussian distribution, with a linear function of the unknown true magnitude serving as its mean, we derive the posterior probability distribution of the true magnitude under four different assumptions for the prior distribution: the uninformative uniform distribution, the unbounded Gutenberg–Richter (GR) magnitude–frequency law, the GR magnitude–frequency relationship restricted by the detection rate, and the truncated GR law as priors. We assess the robustness of the method by a test on several synthetic catalogs and then use it to merge the catalogs compiled by five seismic networks in Italy. The results demonstrate that our proposed magnitude-merging algorithm effectively combines the catalogs, resulting in robust and unified data sets that are suitable for seismic hazard assessment and seismicity analysis.

Seismotectonics-Driven Estimation of b-Value: Implications for Seismic Hazard Assessment

Abstract Taking full advantage of good-quality historical earthquake and seismogenic source data available for Italy (Catalogo Parametrico dei Terremoti Italiani [CPTI15] and Database of Individual Seismogenic Sources [DISS] databases), we tested the regional variability of the b-value of the Gutenberg–Richter law, focusing on the dominantly extensional, nearly 1200-km-long seismogenic corridor straddling the Apennines chain; an 18,200 km2 area generating about 45% of the seismic moment released countrywide. We carefully chose and tested the most appropriate completeness interval and completeness magnitude (Mc), and used the Lilliefors method, the Utsu test, and a bootstrap technique to verify the quality of our results and inferences. The 0.65 b-value we obtained is substantially lower than b-values used in Italian seismic hazard models, often close to 1.0; yet it predicts more accurately the observed Apennines earthquake record, suggesting that most currently adopted magnitude-frequency distributions underpredict events in the Mw range 6.0–7.1 and overpredict those in the range 5.2–5.5. We also highlight that the time, space, and magnitude distribution of the largest Italian earthquakes hardly follows the Gutenberg–Richter law: it rather favors a characteristic behavior. We contend that the b-value is too critical of a parameter for being calculated using statistically weak data sets, such as those resulting from overly detailed area-source models: one may end up characterizing low-hazard areas more accurately than high-hazard areas. Conversely, we advocate the use of fewer, larger area sources that fully exploit the current understanding of regional seismotectonics, as a way of obtaining more realistic regional hazard models.

Adaptive estimation of the Gutenberg–Richter b value using a state space model and particle filtering

Earthquakes follow an exponential distribution referred to as the Gutenberg–Richter law, which is characterized by the b value that represents a ratio of the number of large earthquakes to that of small earthquakes. Spatial and temporal variation in the b value is important for assessing the probability of a larger earthquake. Conventionally, the b value is obtained by a maximum-likelihood estimation based on past earthquakes with a certain sample size. To properly assess the occurrence of earthquakes and understand their dynamics, determining this parameter with a statistically optimal method is important. Here, we discuss a method that uses a state space model and a particle filter, as a framework for time-series data, to estimate temporal variation in the b value. We then compared our output with that of a conventional method using data of earthquakes that occurred in Tohoku and Kumamoto regions in Japan. Our results indicate that the proposed method has the advantage of estimating temporal variation of the b value and forecasting magnitude. Moreover, our research suggests no heightened probability of a large earthquake in the Tohoku region, in contrast to previous studies. Simultaneously, there is the potential of a large earthquake in the Kumamoto region, emphasizing the need for enhanced monitoring.

High Resolution Seismicity Smoothing Method for Seismic Hazard Assessment

A high resolution smoothing method is proposed for performing local estimates of the parameters of the Gutenberg-Richter law (GR). Using this method, the smoothing radius can be chosen large enough to ensure that the condition of applicability of GR law is met, while the distinguished areas of high activity align well with the distribution of epicenters and there is no “smearing” of narrow areas of really high seismic activity into wider zones, which are not actually active at the edges.

Relation between earthquake swarm activity and tides in the Noto region, Japan

The Noto region in Japan has been experiencing earthquake swarm activity since mid-2018, with repeated rises and falls in activity. Crustal deformation (expansion and uplift) observed there since the end of 2020 has been connected to crustal fluids. Studies in other regions have suggested that tides are related to earthquake swarm activities associated with crustal fluids. Therefore, we investigated whether tides are also involved in the Noto earthquake swarm activity. Our results suggest a tidal correlation only at greater depths in the southern part of the analyzed area (‘region Sd’). There, we inferred that an increase in pore fluid pressure caused by the inflow of deep fluids may have led to a decrease in fault fracture strength, making the local seismicity relatively susceptible to the effects of tidal forces. The significantly high value in region Sd of the scaling parameter b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b$$\\end{document} of the Gutenberg–Richter law (describing the earthquake magnitude–frequency distribution) and observed crustal deformation are consistent with this interpretation.Graphical

Evaluating the incompleteness magnitude using an unbiased estimate of the b value

SUMMARY The evaluation of the b value of the Gutenberg–Richter (GR) law, for a sample composed of n earthquakes, presents a systematic positive bias δb which is proportional to 1/n . In this study, we show how to incorporate in δb the bias introduced by deviations from the GR law. More precisely we show that δb is proportional to the square of the variability coefficient CV, defined as the ratio between the standard deviation of the magnitude distribution and its mean value. When the magnitude distribution follows the GR law CV = 1 and this allows us to introduce a new graphical procedure, based on the dependence of b on n, which allows us to identify the incompleteness magnitude mc as the threshold magnitude leading to CV = 1. The method is tested on synthetic catalogues and it is applied to estimate mc in Southern California, Japan and New Zealand.

Spatiotemporal variations in seismic activity in and around the focal region of the 2021 [formula omitted]7.3 and 2022 [formula omitted]7.4 Fukushima-Oki earthquakes, Japan

The spatiotemporal evolution of seismic activity is presented for a broad region surrounding the focal areas of the 2021 M7.3 and 2022 M7.4 Fukushima-Oki earthquakes, which occurred within the subducting slab off the Pacific coast of Fukushima Prefecture, northeastern Japan. This study investigates the spatiotemporal variations in seismic activity during the periods before the 2021 M7.3 earthquake, between the 2021 M7.3 and 2022 M7.4 earthquakes, and after the 2022 M7.4 earthquake using the b-value of the Gutenberg–Richter relation, the aftershock decay rate (p-value), and changes in the seismicity rate (Z-value). The study area is also divided into two depth sections to investigate the depth variations in these seismicity parameters relative to the plate interface. The b-values in the deeper section (intraslab) are generally lower than those in the shallower section (around the plate interface) throughout the entire analysis period, including the hypocentral areas of the M7.3 and M7.4 earthquakes. The aftershock decay rates for the M7.3 and M7.4 earthquakes also show depth-dependent characteristics, with a slower decay rate (p < 1.0) at many grid nodes in the deeper section than in the shallower section. Furthermore, seismic quiescence was noted in the hypocentral area of the M7.3 earthquake about two years before the occurrence of this mainshock. The locations of the M7.3 and M7.4 earthquakes around the down-dip edge of the slip area of the 2011 M9.0 Tohoku earthquake suggests that the variations in seismic activity detected in this study mainly reflect stress increases due to the coseismic slip and postseismic deformation of this great earthquake. The present study suggests that the effect of viscoelastic relaxation is a dominant factor in the deeper section. Furthermore, the variations in seismicity may also reflect heterogeneous structures within the slab.

Time-Independent Grid-Based Forecast Model for M ≥6.0 Earthquakes in Southeastern Tibetan Plateau Using GNSS Strain Rates and Seismicity

ABSTRACT Earthquake forecasting models play a vital role in earthquake occurrence assessment. Despite improved availability of seismic and geodetic data and processing techniques to produce high-resolution catalogs and deformation history, the implementation of earthquake forecasting models with seismic and geodetic data remains a challenge. In this study, we utilize seismicity and Global Navigation Satellite Systems (GNSS) data to propose time-independent grid-based regional earthquake likelihood models for southeastern Tibetan plateau (RELM-TibetSE). First, we solve the GNSS velocity field and strain rates from 1999 to 2017, deriving geodetic moment rates and introducing empirical correction coefficients to balance them with historical seismic moment rate. Subsequently, we employ a truncated Gutenberg–Richter law and Poisson process to calculate time-independent probabilities for M ≥ 6 earthquakes in 0.2° × 0.2° cells. The grid-based forecasting models indicate that the 30-year probability for M ≥ 6 earthquakes exceeds 1% in more than one-third of the entire study area, highlighting prominently higher earthquake occurrence in these regions. Probability distribution exhibits significant spatial variations. Finally, the predictive performance of the forecasting models is validated based on historical seismicity. The validation indicates that all RELM-TibetSE exhibit good predictive capability relative to a spatially uniform model. The RELM-TibetSE incorporating principal strain rates outperforms those involving maximum shear strain rate in forecasting seismicity. And the differences in forecasting performance between the RELM-TibetSE accounting for spatially varied seismogenic thickness and rigidity and those with uniform thickness and rigidity are not significant. The forecasting models also exhibit better predictive performance for seismic source areas than for epicenters. Moreover, the optimal model highlights zones with higher earthquake occurrence, including the zones about 50 km wide across the Ninglang fault, the zones across the southwestern segment of the Lijiang–Xiaojinhe fault, the China–Myanmar borderland north of the Nantinghe fault, and so on. Therefore, it is justified to conduct multidisciplinary rigorous observations to capture the potential nucleation process of future large earthquakes in these zones.

Comparison of earthquake catalogs for the Korean Peninsula declustered using three different methods

Earthquake catalogs include dependent earthquakes, which are spatiotemporally related, and independent or background earthquakes. In order to predict long-term seismicity or conduct a seismic hazard assessment, the dependent earthquakes must be removed to generate a declustered earthquake catalog. Several declustering methods have been proposed to date; however, the result of seismic hazard assessment may vary depending on which declustering methods are selected. In the present study, the catalog of earthquakes that were observed between 2016 and 2021 in and around the Korean Peninsula is declustered using the methods proposed by Gardner and Knopoff [1974], Reasenberg [1985], and Zhuang et al. [2002], and the resultant catalogs are compared. The seismicity parameters (a- and b-values) in the Gutenberg-Richter relationship are found to vary among the three declustered catalogs, thus affecting long-term earthquake predictions and seismic hazard assessment. The raw (original) and three declustered catalogs are also tested to see whether they follow the Poisson process. The minimum magnitude ( ) above which the null hypothesis of the Poisson process cannot be rejected in the earthquake catalogs ranges from 1.6 to 2.2, depending on the declustered catalog. Further, the obtained herein shows a large value compared to the completeness magnitude estimated in the present study. Comparing the curves representing the cumulative number of background earthquakes against the elapsed time for the declustered catalogs shows that the method by Zhuang et al. [2002] produces the result in the closest agreement with the real background seismicity curve.

Predicting the Future Performance of the Planned Seismic Network in Chinese Mainland

Abstract The China Earthquake Administration has currently launched an ambitious nationwide seismicity monitoring network project that will increase the number of stations from ∼950 to 2000 for the broadband seismic stations used to compile the earthquake catalog. The new network is planned to go online by the end of 2023. For more than half of Chinese mainland, the interstation distance of the broadband seismic network will soon be smaller than 100 km, for 27% smaller than 50 km, and for 6% smaller than 25 km. Of all possible ways to characterize the higher-resolution monitoring of the frequent smaller earthquakes expected inside Chinese mainland, the completeness magnitude (Mc) remains one of the most commonly used. Using the prior model of the Bayesian magnitude of completeness method calibrated on the Chinese earthquake catalog from 1 January 2009 to 26 June 2022, we predict the spatial distribution of Mc for the new network based on the planned network configuration. If almost the entire Chinese mainland is at present covered down to Mc=3.3, this threshold will fall to Mc=2.9 in the near future. This means approximately two times more earthquakes will be recorded in the complete catalog available for statistical analysis per year (for a = 6.77 and b = 0.80 in the Gutenberg–Richter law log10N=a−b·M, in which N represents the number of events of magnitude larger than or equal to M and M≥Mc). Based on the observation that abnormal seismicity as precursors are most likely to be observed at least at three units below the mainshock magnitude, and assuming earthquakes to be potentially damaging at M ≥ 5, the new seismic network shall achieve the goal of 76% coverage for optimal seismic-based earthquake prediction research.

One decade of b-value variations from volcano-tectonic seismicity as an early indicator of episodes of crisis in a volcano: the case of Copahue, Southern Andes

Volcanoes can enter in episodes of unrest, which might end later in an eruption, with little warning. They are normally produced due to the inner dynamics of the volcano, but can also be triggered by external earthquakes. To detect these periods early, it becomes crucial to understand the dynamics of the different structures (such as fault systems) of the volcano, as they can act as magma pathways and can also generate instabilities on it. In this article we study the seismicity of Copahue (central-south Chile), which sits atop a complex system of faults, and was importantly affected by the 2010 Mw 8.8 Maule earthquake. We focused ourselves in the temporal variations of the b-value of the Gutenberg-Richter law during the 2012–2022 period. During this timeframe the volcano had a series of crises, which led to seven eruptive phases. Our results show that the system does exhibit signs of a future unrest phase weeks to months before there is a change on its alert level, and they are mostly linked to the activity of a N-S fault zone, located not beneath the main crater of Copahue, but around 10 km to the East. Most of the crises start after drops in the b-value of this structure, with sudden variations in b-value being also noticeable as a response to the 2015 Mw 8.3 Illapel earthquake. Our results show a correlation between instances of fluid injection and release in the relevant structures of an active volcano with the variations of the b-value. This allow us to use the temporal variations of the b-value as a tool to anticipate the inner dynamics of the system, particularly when there is a strong structural control on it, such as in the case of Copahue. We also found out that the influence of the 2010 Mw 8.8 Maule earthquake was long-lived, affecting mostly the structures that later destabilized the volcano for the most part of a decade, therefore enhancing magma injection into the whole system. This seems to have changed since 2021, which might indicate a waning in the influence of the megathrust earthquake in Copahue volcano.

Impact of printing orientation on inter and intra-layer bonds in 3D printed thermoplastic elastomers: A study using acoustic emission and tensile tests

The use of the Material Extrusion technique with Thermoplastic Elastomers is currently growing because of the large number of benefits of this family of materials. They are processable materials with high flexibility, which makes them very useful, for example, in biomedical applications that require flexible objects with complex geometries. This study aims to characterize a specific polymer, namely polyether-block-amide-based polymer (PEBA), by analyzing its anisotropic behavior in printed samples and investigating the mechanical properties based on different printing orientations. Three orientations (X, Y, and Z) were used to relate the printing orientation to the type of bonds formed in the samples: intra-layer bonds, inter-layer bonds, and the deposited filament. Tensile tests following ASTM D638 were conducted to measure sample rigidity, while Acoustic Emission, an advanced Non-Destructive Technique, was employed to examine the trend of the failure process. The presence of voids was also observed to assess printing quality, which is influenced by the printing orientation and alters the quality of bonds. The results revealed that samples printed horizontally exhibited higher Young’s Modulus values and fewer voids in the inner parts. Vertically printed samples displayed inferior mechanical properties and a greater number of voids. Consequently, the intra-layer yielded better bond formation and minimized voids. Acoustic Emission analysis corroborated these findings by demonstrating distinct energy distribution patterns among the different printing orientations. Hits were concentrated at maximum stresses, primarily observed in the vertically printed samples, which experienced macroscopic failure. Furthermore, this particular specimen exhibited a vertical asymptote near the maximum stress level. The analysis of the energy of Acoustic Emission hits demonstrated a reasonably good fit with the Gutenberg-Richter (GBR) law based on the printing direction.