Comparison of seismicity declustering methods using a probabilistic measure of clustering

We present a new measure of earthquake clustering and explore its use for comparing the performance of three different declustering methods. The advantage of this new clustering measure over existing techniques is that it can be used for non-Poissonian background seismicity and, in particular, to compare the results of declustering algorithms where different background models are used. We use our approach to study inter-event times between successive earthquakes using earthquake catalog data from Japan and southern California. A measure of the extent of clustering is introduced by comparing the inter-event time distributions of the background seismicity to that of the whole observed seismicity. Theoretical aspects of the clustering measure are then discussed with respect to the Poissonian and Weibull models for the background inter-event time distribution. In the case of a Poissonian background, the obtained clustering measure shows a decrease followed by an increase, defining a V-shaped trend, which can be explained by the presence of short- and long-range correlation in the inter-event time series. Three previously proposed declustering methods (i.e., the methods of Gardner and Knopoff, Reasenberg, and Zhuang et al.) are used to obtain an approximation of the residual “background” inter-event time distribution in order to apply our clustering measure to real seismicity. The clustering measure is then estimated for different values of magnitude cutoffs and time periods, taking into account the completeness of each catalog. Plots of the clustering measure are presented as clustering attenuation curves (CACs), showing how the correlation decreases when inter-event times increase. The CACs demonstrate strong clustering at short inter-event time ranges and weak clustering at long time ranges. When the algorithm of Gardner and Knopoff is used, the CACs show strong correlation with a weak background at the short inter-event time ranges. The fit of the CACs using the Poissonian background model is successful at short and intermediate inter-event time ranges, but deviates at long ranges. The observed deviation shows that the residual catalog obtained after declustering remains non-Poissonian at long time ranges. The apparent background fraction can be estimated directly from the CAC fit. The CACs using the algorithms of Reasenberg and Zhuang et al. show a relatively similar behavior, with a time correlation decreasing more rapidly than the CACs of Gardner and Knopoff for shorter time ranges. This study offers a novel approach for the study of different types of clustering produced as a result of various hypotheses used to account for different backgrounds.     

Sensitivity analysis of the parameters of earthquake recurrence time power law scaling

The stability of the power law scaling of earthquake recurrence time distribution in a given space–time window is investigated, taking into account the magnitude of completeness and the effective starting time of aftershock sequences in earthquake catalogs from Southern California and Japan. A new method is introduced for sampling at different distances from a network of target events. This method allows the recurrence times to be sampled many times on the same area. Two power laws with unknown exponents are assumed to govern short- and long-recurrence-time ranges. This assumption is developed analytically and shown to imply simple correlation between these power laws. In practice, the results show that this correlation structure is not satisfied for short magnitude cutoffs (m _c = 2.5, 3.5, 4.5), and hence the recurrence time distribution departs from the power law scaling. The scaling parameters obtained from the stack of the distributions corresponding to different magnitude thresholds are quite different for different regions of study. It is also found that significantly different scaling parameters adjust the distribution for different magnitude thresholds. In particular, the power law exponents decrease when the magnitude cutoff increases, resulting in a slower decrease of the recurrence time distribution, especially for short time ranges. For example, in the case of Japan, the exponent p₂ of the power law scaling at large recurrence times follows roughly the relation: , where m _c is the magnitude cutoff. In case of Southern California, it is shown that Weibull distribution provides a better alternative fit to the data for moderate and large time scales.     

Testing a scaling law for the earthquake recurrence time distributions

The earthquake recurrence time distribution in a given space-time window is being studied, using earthquake catalogues from different seismic regions (Southern California, Canada, and Central Asia). The quality of the available catalogues, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogues, it was determined that the probability densities of the earthquake recurrence times can be described by a universal gamma distribution, in which the time is normalized with the mean rate of occurrence. The results show a deviation from the gamma distribution at the short interevent times, suggesting the existence of clustering. This holds from worldwide to local scales and for quite different tectonic environments.     

Analysis of the Temporal Occurrence of Seismicity at Deception Island (Antarctica). A Nonlinear Approach

—Deception Island is characterized by small magnitude local events with constant energy flux and very low stress drop. To obtain information about its origin, an interevent time series of 546 events, corresponding to an observational period of two month, has been analyzed. From a statistical point of view, data satisfies a Weibull distribution and presents clustering. A rescaled range analysis reveals that data are not independent, i.e. have memory, and the correlation dimension saturates at 2.2; as a consequence, the system can be modeled as a nonlinear iterative equation with three degrees of freedom that presents chaotic behavior. Taking into account that the average interevent time is of the order of 130 minutes, too short to be only due to tectonic activity, the above results indicate that some other mechanism may coexist with the regional tectonic one. According to several geological and geophysical observations, we suggest that most of the local events may be originated by pressure waves generated by a sudden change of phase, of sea and fresh water infiltrated into the main fractures and faults and also from shallow and confined water-saturated layers.     

Joint interpretation of the size and time distributions of seismic activity around the Hengill triple junction (SW Iceland) between 1993 and 1999

A newly developed clustering algorithm is described which uses the Unified Scaling Law for earthquakes to identify correlations between events that lead to clustering. This algorithm is applied to a dataset from the Hengill triple junction in south west Iceland to separate spatially and temporally overlapping earthquake sequences. We show that the algorithm successfully identifies spatio-temporally clustered events.A search for certain patterns in the identified clusters is performed. These patterns emerged in numerical simulations of seismicity performed by Hainzl (2003) when viscous coupling was introduced in order to reproduce features of swarm earthquakes. Namely we look for a combination of increased Gutenberg-Richter b-value and decreased exponent of the waiting-time distribution α. This pattern, indicating the strongest influence of viscous coupling on the characteristics of the seismicity, could be localized beneath an extinct volcano approximately 5 km north of an area of recent crustal uplift.     

基于时-空ETAS模型给出的川滇地区背景地震活动和强震潜在危险区

利用基于时-空传染型余震序列（Epidemic Type Aftershock Sequence, 简称ETAS）模型的随机除丛法,重新审视了2008年5月12日汶川M_S8.0地震前可能存在的长期地震活动异常,研究了川滇地区背景地震活动特征,并评估了当前的强震危险状态.对川滇地区1970年以来的M_L3.0以上的背景地震和丛集地震活动的研究结果表明,该地区地震丛集特征明显、时空分布很不均匀、地震序列常有前震事件.直接将概率值作为地震计数的权重,对地震丛集率空间分布图像分析表明,汶川M_S8.0地震前,龙门山断裂带中南段存在着长期、大范围的地震丛集率低值区,震前该段处于应力闭锁状态.对川滇地区地震丛集率低值区内背景地震与全部地震的累积次数、b值和新定义的Δb等统计参量的分析表明,龙日坝与龙门山断裂带具有地震活动的关联性,川滇地区当前的强震潜在危险区可能是巧家地区和汶川M_S8.0地震破裂尚未穿越的龙门山断裂带南段.此外,还发现b值倾向于反映局部应力场变化,而Δb能较为敏感地给出更大范围应力场的相对变化.     

Spatial distribution of aftershocks and background seismicity in central California

We examine the spatial distribution of earthquake hypocenters in four central California areas: the aftershock zones of the (1) 1984 Morgan Hill (2) 1979 Coyote Lake, and (3) 1983 Coalinga earthquakes, as well as (4) the aseismically creeping area around Hollister. The basic tool we use to analyze these data are frequency distributions of interevent distances between earthquakes. These distributions are evaluated on the basis of their deviation from what would be expected if earthquakes occurred randomly in the study areas. We find that both background seismic activity and aftershocks in the study areas exhibit nonrandom spatial distribution. Two major spatial patterns, clustering at small distances and anomalies at larger distances, are observed depending on tectonic setting. While both patterns are seen in the strike-slip environments along the Calaveras fault (Morgan Hill, Coyote Lake, and Hollister), aftershocks of the Coalinga event (a thrust earthquake) seem to be characterized by clustering only. The spatial distribution of earthquakes in areas gradually decreasing in size does not seem to support the hypothesis of a self-similar distribution over the range of scales studied here, regardless of tectonic setting. Spatial distributions are independent of magnitude for the Coalinga aftershocks, but events in strike-slip environments show increasing clustering with increasing magnitude. Finally, earthquake spatial distributions vary in time showing different patterns before, during, and following the end of aftershock sequences.     

Seismicity acceleration model and its application to several earthquake regions in China

With the theory of subcritical crack growth, we can deduce the fundamental equation of regional seismicity acceleration model. Applying this model to intraplate earthquake regions, we select three earthquake subplates: North China Subplate, Chuan-Dian Block and Xinjiang Subplate, and divide the three subplates into seven researched regions by the difference of seismicity and tectonic conditions. With the modified equation given by Sornette and Sammis (1995), we analysis the seismicity of each region. To those strong earthquakes already occurred in these region, the model can give close fitting of magnitude and occurrence time, and the result in this article indicates that the seismicity acceleration model can also be used for describing the seismicity of intraplate. In the article, we give the magnitude and occurrence time of possible strong earthquakes in Shanxi, Ordos, Bole-Tuokexun, Ayinke-Wuqia earthquake regions. In the same subplate or block, the earthquake periods for each earthquake region are similar in time interval. The constant αin model can be used to describe the intensity of regional seismicity, and for the Chinese Mainland, α is 0.4 generally. To the seismicity in Taiwan and other regions with complex tectonic conditions, the model does not fit well at present.     

Regional seismicity triggered by the Hyogo-Ken Nanbu, Japan, M =7.2 earthquake on January 17, 1995

The time and spatial feature of the regional seismicity triggered by the Hyogo-Ken Nanbu, Japan, M=7.2 earthquake on January 17,1995, was studied. The concerned region is about several hundred kilometers in length and breadth surrounding the epicenter (33°～37°N, 133°～138°E). It is divided into 16 subregions. The seismicity of these subregions from January of 1976 to June of 1996 has been analyzed. It is showed that,① there were significant seismicity changes in 10 subregions triggered by the Hyogo-Ken Nanbu, Japan, M=7.2 earthquake on January 17, 1995. These changes passed a Z statistic test exceeding 0.95 confidence level and the greatest epicenter distance of these subregions was 280 km;②seismicity changes were triggered within 1～5 days in three subregions near the main shock while in other subregions the seismicity changes were triggered within several ten days after the main shock;③ the greatest triggered event is 5.4, which is about the same size as the greatest aftershock;④the regional stress change resulted from the main shock may be the triggered mechanism of the regional seismicity.     

Numerical calculations of tectonic stress field of Chinese mainland and its neighboring regions and their applications to explanation of seismic activity

IntroductionChinesemainlandliesinthesoutheastofEurasianPlateandisclampedbyindian,PacificandPhilippineSeaPlates.Besides,itislocatedatbetweenthetwobigseismicactivebeltsintheworldatthesametime.Differingfromtheshowoftwobigseismicbeltswhichhaveseismiczonaldistributionalongplateboundary,Chinesemainlandanditsperipheralareahaveapeculiarcharacter,expressingseismicallylargestrength,highfrequency,widedistribution,shallowfocus,seriousdamage,multiplestyles,extremelynonuniformspace-timedistributionandsoo…     

A comprehensive analysis of Kamchatka seismicity for the period 2005–2007 using the regional catalog

We characterize the Kamchatka seismicity for the period 2005–2007. Regional catalogs of Kamchatka earthquakes were used to develop 2D distributions of parameters of background seismicity. The characteristics we consider include the activity A ₁₀, the slope of the recurrence curve γ, the parameters involved in the methods RTL, ΔS, and the “Z-function”, as well as the control of earthquake clustering. We have detected the space-time agreement between the anomalies exhibited by several parameters.     

日本海区地震活动的初步研究

利用日本海区丰富的震史资料，研究了该区强震活动时一空变化的某些特征。并以此为据，将１９００年以来的地震活动划分了三个地震轮回。文中讨论了各幕的持续时间及其强震的频度分布，同时还分析了各轮回的强震地区分布，探讨了每个强震高潮主体活动区形成特点，这些结果可作为研究日本海区强震高潮到来和结束的标志以及为判断未来主体活动区等强震预测问题提供线索。此外，本文还分析了我国大陆强震高潮与日本海沟地震的相关关系。     

Magma intrusion as a driving mechanism for the seismic clustering following the 9 May 1989 earthquake swarms at the Canary Islands

On 9 May 1989 a M _L = 5.2 earthquake struck a region between the islands of Tenerife and Gran Canaria. We investigated the time-spatial evolution of seismic patterns affecting the Canary Islands region during 1989–1995, using a quantitative spatial fractal analysis method. This method allows quantitative investigation of subtle trends in seismicity distribution through time. The fractal analysis indicates that epicenters clustered around a large zone during the May 1989 sequence affected narrow zones during 1991–1993, but then larger zones during 1993–1995 with an overall trend to shallower focal depths. The spatial localisation of seismic data and its time evolution appear to be related to magmatic rather than tectonic activity. Spatial clustering properties of seismicity are consistent with a major intrusive episode in 1989, followed by a period of quiescence and renewed deep intrusive activity from 1993 onwards. This interpretation suggests an increasing probability of future volcanic hazard in the region investigated.     

On Mechanistic Explanation of the Shape of the Universal Curve of Earthquake Recurrence Time Distributions

This paper outlines an idea for an explanation of a mechanism underlying the shape of the universal curve of the Earthquake Recurrence Time Distributions. The proposed simple stochastic cellular automaton model is reproducing the gamma distribution fit with the proper value of parameter γ characterizing the Earth’s seismicity and also imitates a deviation from the fit at short interevent times, as observed in real data.Thus the model suggests an explanation of the universal pattern of rescaled Earthquake Recurrence Time Distributions in terms of combinatorial rules for accumulation and abrupt release of seismic energy.     

2022年泸定M6.8地震前地震活动参数变化研究

2022年9月5日四川泸定发生M6.8地震,为研究泸定地震孕震区的应力变化,选取b值、小震调制比和丛集率这3个参数,对泸定地震前的区域地震活动状态进行计算研究。结果显示:泸定及周边区域几次强震发生前,区域地震活动均存在持续时间较长的低b值时段,且在低b值状态下震前短期内出现小震高丛集、高调制比的现象;鲜水河断裂带的地震活动状态分析显示,此次泸定地震前该断裂带存在持续时间近10个月的低b值状态,且短期内出现丛集率升高、调制比高值现象。通过对比分析,认为泸定地震是鲜水河断裂带构造运动的结果。综合分析认为,结合应力场背景和构造条件研究地震活动b值、固体潮调制比和丛集率的时空变化有助于理解大地震的孕育演化过程。     

Evidence of non extensivity in the evolution of seismicity along the San Andreas Fault,California, USA: An approach based on Tsallis statistical physics

We examine the nature of the seismogenetic system along the San Andreas Fault (SAF), California, USA, by searching for evidence of complexity and non-extensivity in the earthquake record. We use accurate, complete and homogeneous earthquake catalogues in which aftershocks are included (raw catalogues), or have been removed by a stochastic declustering procedure (declustered catalogues). On the basis of Non-Extensive Statistical Physics (NESP), which generalizes the Boltzmann–Gibbs formalism to non-equilibrating (complex) systems, we investigate whether earthquakes are generated by an extensive self-excited Poisson process or by a non-extensive complex process. We examine bivariate cumulative frequency distributions of earthquake magnitudes and interevent times and determine the size and time dependence of the respective magnitude and temporal entropic indices, which indicate the level on non-equilibrium (correlation). It is shown that the magnitude entropic index is very stable and corresponds to proxy b-values that are remarkably consistent with the b-values computed by conventional means. The temporal entropic index computed from the raw catalogues indicate moderately to highly correlated states during the aftershock sequences of large earthquakes, progressing to quasi-uncorrelated states as these die out and before the next large event. Conversely, the analysis of the declustered catalogues shows that background seismicity exhibits moderate to high correlation that varies significantly albeit smoothly with time. This indicates a persistent sub-extensive seismogenetic system. The degree of correlation is generally higher in the southern SAF segment, which is consistent with the observation of shorter return periods for large earthquakes. A plausible explanation is that because aftershock sequences are localized in space and time, their efficient removal unveils long-range background interactions which are obscured by their presence! Our results indicate complexity in the expression of background seismicity along the San Andreas Fault, with criticality being a very likely mechanism as a consequence of the persistent non-equilibrium inferred from the temporal entropic index. However, definite conclusions cannot be drawn until the earthquake record is exhaustively studied in all its forms.     

Interevent Time Distribution in Seismicity: A Theoretical Approach

This paper presents an analysis of the distribution of the time τ between two consecutive events in a stationary point process. The study is motivated by the discovery of unified scaling laws for τ for the case of seismic events. We demonstrate that these laws cannot exist simultaneously in a seismogenic area. Under very natural assumptions we show that if, after rescaling to ensure Eτ =1, the interevent time has a universal distribution F, then F must be exponential. In other words, Corral’s unified scaling law cannot exist in the whole range of time. In the framework of a general cluster model we discuss the parameterization of an empirical unified law and the physical meaning of the parameters involved. An erratum to this article is available at .     

Primary component analysis method and reduction of seismicity parameters

Introduction Data mining (SHAO and YU, 2003) is a new kind of technique developed with database and artificial intelligence in recent years, which processes the data in the database to abstract the im- plied and pre-unknown, but potentially useful information and knowledge from large amounts of incomplete, noisy, blurring and stochastic data. For data mining, data purging is an important link beforehand that includes eliminating noise, making up lost domain, and deleting ineffective data, as…     

Spatio-temporal epidemic type aftershock sequence model for Tangshan aftershock sequence

Shallow earthquakes usually show obvious spatio-temporal clustering patterns. In this study, several spatio-temporal point process models are applied to investigate the clustering characteristics of the well-known Tangshan sequence based on classical empirical laws and a few assumptions. The relative fit of competing models is compared by Akaike Information Criterion. The spatial clustering pattern is well characterized by the model which gives the best fit to the data. A simulated aftershock sequence is generated by thinning algorithm and compared with the real seismicity.