河北省及邻区地震活动时间间隔的一些特征

介绍了地震活动时间间隔的研究历史和定义，对河北省及邻近地区地震活动时间间隔分布的统计点图、间隔一频次统计图进行了分析，分析时结合不同的震级层次、不同的统计时段（长段不同）、不同的活动水平以及地震活动的丛集与孤立。统计结果显示地震活动时间间隔对数一频次统计结果与G－L关系式的统计结果类似，地震活动时间间对数一频镒也呈指数分布。最后对预测中存在的不足进行了一些简单说明。     

泊松与更新复合模型及其在地震危险性分析中的应用

利用更新模型描述大地震的记忆特性,用泊松模型描述小地震的无记忆性,同时考虑了由于采用时间记忆模型而引起的震级分布随时间的变化,克服了目前研究中时间、震级分布模型相互独立的缺陷.文中利用实例计算了震级分布随时间变化对地震危险性分析结果的影响,所得结果对目前研究大地震时间记忆模型具有一定的意义.      

基于特征地震模型含时间的概率地震危险性分析方法及其应用研究

本文介绍了特征地震的对数正态分布模型、 正态分布模型和布朗过程时间模型, 提出了使用地震破裂面源模型的特征地震含时间的概率地震危险性分析理论和方法. 通过具体算例对不同的特征地震模型进行了比较, 并对特征地震危险性分析方法进行了系统探索. 研究结果表明, 特征地震含时间模型在复发周期早期的地震危险性低于不含时间模型, 而在后期其地震危险性则高于不含时间模型. 特征地震复发周期的对数正态分布模型与布朗过程时间模型计算得出的地震危险性差别不大. 在未到期望复发时间时, 正态分布模型与前两种模型计算的地震危险性差别不大; 而接近期望复发时间及之后时段, 正态分布模型计算的地震危险性则迅速增大.      

滇西地震序列类型的统计特征分析

统计分析了滇西地区1966－2001年36个Ms≥5．0地震序列。结果表明，滇西地震类型的分布有一定的地域性，和震级的大小也有明显的关系，并得出最大地震（Mmax)与次大地震（M2）的经验统计公式，以及最大余震的时间分布特征，最后得出滇西地震序列类型判定方法。     

混杂地震复发模型及其对地震危险性分析结果的影响

为了考虑某一给定断层特征地震的影响，提出了地震危险性分析混杂地震复发模型并进行了深入的研究。该模型综合考虑了大地震的更新时间、特征震级模型和中小地震的传统指数－时间及指数－震级模型。     

地震震级和地震间隔时间的统计分布研究

依据最大熵原理求解出地震震级和地震间隔时间的最可几分布和威布尔（Weibull)分布。以甘肃天祝为例，应用极值分布模型、对数正态分布模型和威尔分布模型以及K－S检验和直方图检验2种方法，分别对该地区实际地震数据进行检验。所得结果与理论求解结果一致。     

基于三参量威布尔分布的潜在震源区强震危险性估计

本文提出了一种基于三参量威布尔分布模型估计潜在震源区强震危险性的方法。选择日本东海-南海地震带为潜在震源区,分别基于强震发震时间间隔服从二参量和三参量的威布尔分布,估计该区强震危险性,结果表明三参量威布尔分布的拟合效果优于二参量威布尔分布。选择马尼拉海沟俯冲带为潜在震源区,基于三参量威布尔分布估计该区强震危险性,结果显示未来10、30和50年该区强震（M≧7.5）复发概率分别为62%、82%和89%,最短发震时间间隔估计为1.70年。     

中国大陆强震序列次大地震及第三大地震的时间分布特征

从地震现场早期地震趋势判断工作需要出发，本文对中国大陆地区１９６６年以来的４８个Ｍｓ≥６．０级地震序列的次大地震及第三大地震与主震（或最大地震）的时间间隔进行了统计分析。结果表明，强震序列的次大及第三大地震与主震（或最大地震）的时间间隔分布，总体上呈随机分布，其与主震（或最大地震）震级无关，而与序列类型有关。     

地震丛集的统计模型和随机除丛法

本文总结了地震丛集的统计模型化方法以及相应的除丛方法.地震在时间和空间上的分布很不均匀.地震成丛现象使得地震活动难以分析.这是因为地震丛集与地震丛集、地震丛集与背景活动往往重叠在一起.在进行长期预报和地震危险性评估时,需要删除地震在时间上的成丛效应以便估计地震背景活动强度.而在进行短期或实时预报时,需要充分理解地震丛集的特征.地震丛集可以用传染型余震序列(epidemic-type aftershocks sequcrice,简称ETAS)模型来进行描述.     

环太平洋会聚带的长期地震预报

对大陆274个孕震区地震活动性的时间相关研究表明，每个地区的浅源强地震显示出遵循幂定律时间分布的短期和中期的震群特征（时间长达几年）。然而，主震显示出准周期特征，遵循“区域时间和震级可预报地震活动模式”。该模式由下列公式表示：logTt=0.19Mmin 0.33Mp-0.39logm0 q Mf=0.73Mmin-0.28Mp 0.40logm0 m 该公式将孕震区的后续主震面波震级Mf地震之间的时间Tt与认为是最小的主震震级Mmin，前至的主震震级MP和地震矩速率相联系。不同地区的q和m值是不同的。本文描述了该模式的基本特征并且讨论了与其物理意义相关的问题。这些关系中的第一关系式已被用于计算1993－2002年期间141个孕震区的下一次大震的重复概率。在这些孕震区中，环太平洋会聚带已被分离，并引入一个假设，即T／Tt比率遵循对数正态分布，其中T为观测到的地震之间的时间，第二个关系已被用于估计各地区的主震震级。     

Probabilistic assessment of earthquake recurrence in the January 26, 2001 earthquake region of Gujrat, India

Kutch region of Gujrat is one of the most seismic prone regions of India. Recently, it has been rocked by a large earthquake (M _w = 7.7) on January 26, 2001. The probabilities of occurrence of large earthquake (M≥6.0 and M≥5.0) in a specified interval of time for different elapsed times have been estimated on the basis of observed time-intervals between the large earthquakes (M≥6.0 and M≥5.0) using three probabilistic models, namely, Weibull, Gamma and Lognormal. The earthquakes of magnitude ≥5.0 covering about 180 years have been used for this analysis. However, the method of maximum likelihood estimation (MLE) has been applied for computation of earthquake hazard parameters. The mean interval of occurrence of earthquakes and standard deviation are estimated as 20.18 and 8.40 years for M≥5.0 and 36.32 and 12.49 years, for M≥6.0, respectively, for this region. For the earthquakes M≥5.0, the estimated cumulative probability reaches 0.8 after about 27 years for Lognormal and Gamma models and about 28 years for Weibull model while it reaches 0.9 after about 32 years for all the models. However, for the earthquakes M≥6.0, the estimated cumulative probability reaches 0.8 after about 47 years for all the models while it reaches 0.9 after about 53, 54 and 55 years for Weibull, Gamma and Lognormal model, respectively. The conditional probability also reaches about 0.8 to 0.9 for the time period of 28 to 40 years and 50 to 60 years for M≥5.0 and M≥6.0, respectively, for all the models. The probability of occurrence of an earthquake is very high between 28 to 42 years for the magnitudes ≥5.0 and between 47 to 55 years for the magnitudes ≥6.0, respectively, past from the last earthquake (2001).     

Probabilistic Assessment of Earthquake Recurrence in Northeast India and Adjoining Regions

Northeast India and adjoining regions (20°–32° N and 87°–100° E) are highly vulnerable to earthquake hazard in the Indian sub-continent, which fall under seismic zones V, IV and III in the seismic zoning map of India with magnitudes M exceeding 8, 7 and 6, respectively. It has experienced two devastating earthquakes, namely, the Shillong Plateau earthquake of June 12, 1897 (M _w 8.1) and the Assam earthquake of August 15, 1950 (M _w 8.5) that caused huge loss of lives and property in the Indian sub-continent. In the present study, the probabilities of the occurrences of earthquakes with magnitude M ≥ 7.0 during a specified interval of time has been estimated on the basis of three probabilistic models, namely, Weibull, Gamma and Lognormal, with the help of the earthquake catalogue spanning the period 1846 to 1995. The method of maximum likelihood has been used to estimate the earthquake hazard parameters. The logarithmic probability of likelihood function (ln L) is estimated and used to compare the suitability of models and it was found that the Gamma model fits best with the actual data. The sample mean interval of occurrence of such earthquakes is estimated as 7.82 years in the northeast India region and the expected mean values for Weibull, Gamma and Lognormal distributions are estimated as 7.837, 7.820 and 8.269 years, respectively. The estimated cumulative probability for an earthquake M ≥ 7.0 reaches 0.8 after about 15–16 (2010–2011) years and 0.9 after about 18–20 (2013–2015) years from the occurrence of the last earthquake (1995) in the region. The estimated conditional probability also reaches 0.8 to 0.9 after about 13–17 (2008–2012) years in the considered region for an earthquake M ≥ 7.0 when the elapsed time is zero years. However, the conditional probability reaches 0.8 to 0.9 after about 9–13 (2018–2022) years for earthquake M ≥ 7.0 when the elapsed time is 14 years (i.e. 2009).     

Temporal distribution of earthquakes using renewal process in the Dasht-e-Bayaz region

Temporal distribution of earthquakes with M _w > 6 in the Dasht-e-Bayaz region, eastern Iran has been investigated using time-dependent models. Based on these types of models, it is assumed that the times between consecutive large earthquakes follow a certain statistical distribution. For this purpose, four time-dependent inter-event distributions including the Weibull, Gamma, Lognormal, and the Brownian Passage Time (BPT) are used in this study and the associated parameters are estimated using the method of maximum likelihood estimation. The suitable distribution is selected based on logarithm likelihood function and Bayesian Information Criterion. The probability of the occurrence of the next large earthquake during a specified interval of time was calculated for each model. Then, the concept of conditional probability has been applied to forecast the next major (M _w > 6) earthquake in the site of our interest. The emphasis is on statistical methods which attempt to quantify the probability of an earthquake occurring within a specified time, space, and magnitude windows. According to obtained results, the probability of occurrence of an earthquake with M _w > 6 in the near future is significantly high.     

Study on Integrated Recurrence Behaviors of Strong Earthquakes Along Entire Active Fault Zones in the Sichuan-Yunnan Region, China

Based on historical earthquake data, we use statistical methods to study integrated recurrence behaviors of strong earthquakes along 7 selected active fault zones in the Sichuan-Yunnan region. The results show that recurrences of strong earthquakes in the 7 fault zones display near-random, random and clustering behaviors. The recurrence processes are never quasiperiodic, and are neither strength-time nor time-strength dependent. The more independent segments for strong earthquake rupturing a fault zone has, the more complicated the corresponding recurrence process is. And relatively active periods and quiescent periods for earthquake activity occur alternatively. Within the active periods, the distribution of recurrence time intervals between earthquakes has relatively large discretion, and can be modelled well by a Weibull distribution. The time distribution of the quiescent periods has relatively small discretion, and can be approximately described by some distributions as the normal. Both the durations of the active periods and the numbers of strong earthquakes within the active periods vary obviously cycle by cycle, leading to the relatively active periods having never repeated quasi-periodically. Therefore, the probabilistic assessment for middle- and longterm seismic hazard for entireties of active fault zones based on data of historical strong earthquakes on the fault zones still faces difficulty.     

Statistical properties of aftershock rate decay: Implications for the assessment of continuing activity

Aftershock rates seem to follow a power law decay, but the assessment of the aftershock frequency immediately after an earthquake, as well as during the evolution of a seismic excitation remains a demand for the imminent seismic hazard. The purpose of this work is to study the temporal distribution of triggered earthquakes in short time scales following a strong event, and thus a multiple seismic sequence was chosen for this purpose. Statistical models are applied to the 1981 Corinth Gulf sequence, comprising three strong (M = 6.7, M = 6.5, and M = 6.3) events between 24 February and 4 March. The non-homogeneous Poisson process outperforms the simple Poisson process in order to model the aftershock sequence, whereas the Weibull process is more appropriate to capture the features of the short-term behavior, but not the most proper for describing the seismicity in long term. The aftershock data defines a smooth curve of the declining rate and a long-tail theoretical model is more appropriate to fit the data than a rapidly declining exponential function, as supported by the quantitative results derived from the survival function. An autoregressive model is also applied to the seismic sequence, shedding more light on the stationarity of the time series.     

Rupture model of the 2013 M_W 6.6 Lushan (China) earthquake constrained by a new GPS data set and its effects on potential seismic hazard

Vertical records are critically important when determining the rupture model of an earthquake, especially a thrust earthquake. Due to the relatively low fitness level of near-field vertical displacements, the precision of previous rupture models is relatively low, and the seismic hazard evaluated thereafter should be further updated. In this study, we applied three-component displacement records from GPS stations in and around the source region of the 2013 MW6.6 Lushan earthquake to re-investigate the rupture model.To improve the resolution of the rupture model, records from both continuous and campaign GPS stations were gathered, and secular deformations of the GPS movements were removed from the records of the campaign stations to ensure their reliability. The rupture model was derived by the steepest descent method(SDM), which is based on a layered velocity structure. The peak slip value was about 0.75 m, with a seismic moment release of 9.89 × 10~(18) N·m, which was equivalent to an M_W6.6 event. The inferred fault geometry coincided well with the aftershock distribution of the Lushan earthquake. Unlike previous rupture models, a secondary slip asperity existed at a shallow depth and even touched the ground surface. Based on the distribution of the co-seismic ruptures of the Lushan and Wenchuan earthquakes, post-seismic relaxation of the Wenchuan earthquake, and tectonic loading process, we proposed that the seismic hazard is quite high and still needs special attention in the seismic gap between the two earthquakes.     

Seismic characteristics near the epicenter of the 1303 Hongtong M=8 earthquake, Shanxi Province and its implication

In this paper, we calculated the seismic pattern of instrumental recorded small and moderate earthquakes near the epicenter of the 1303 Hongtong M=8 earthquake, Shanxi Province. According to the spatial distribution of small and moderate earthquakes, 6 seismic dense zones are delineated. Temporal distribution of ML≥2 earthquakes since 1970 in each seismic dense zone has been analyzed. Based on temporal distribution characteristics and historical earthquake activity, three types of seismicities are proposed. The relationship between seismic types and crustal medium is analyzed. The mechanism of three types is discussed. Finity of strong earthquake recurrence is proposed. Seismic hazard in mid-long term and diversity of earthquake disaster in Shanxi seismic belt are discussed.     

Statistical prediction of the next great earthquake around Tehran,Iran

The analysis of seismic activity variations with space and time is a complex problem. Several statistical methods have been adopted to study these variations. One of the tasks that has attracted the attention of the seismological and statistical community is to explain seismicity patterns by statistical models and apply the results for earthquake prediction. Here the probability distribution of recurrence times as described by Exponential, Gamma, Lognormal, Pareto, Rayleigh and Weibull probability distributions and the idea of conditional probability has been applied to predict the next great (Ms ≥ 6.0 and Ms ≥ 6.5) earthquake around Tehran (r ≤ 200 km). Conditional probability specifies the likelihood that a given earthquake will happen within a specified time. This likelihood is based on the information about past earthquake occurrences in the given region and the basic assumption that future seismic activity will follow the pattern of past activity. The rapid growth of Tehran to approximately 12 million inhabitants has resulted in a much more rapid increase in its vulnerability to natural disasters, especially earthquakes. Several earthquakes affected this region in the past, mostly on the Mosha, Taleqan, Eyvankey and Garmsar faults. The estimated recurrence times for Exponential, Gamma, Lognormal, Pareto, Rayleigh and Weibull distributions has been computed to be 66.64, 14.79, 26.88, 2.37, 67.58 and 80.47, respectively. Accordingly, one may expect that a large damaging earthquake may occur around Tehran approximately every 10 years.     

川滇地区若干活动断裂带整体的强地震复发特征研究

我们根据历史地震资料，采用统计学方法研究了川滇地区7条活动断裂带整体的强地震复发特征。结果表明，这7条断裂带的强地震复发表现出趋于随机的、随机的、以及丛集的行为，复发过程不具有良好的准周期性，也不存在强度－时间或者时间－强度的相依性。组成断裂带的强震破裂段落的数量越多，复发过程就越复杂。相对的地震活跃期与平静期交替出现。其中，活跃期内地震复发间隔分布的离散性较大，可用Weibull分布近似描述；而平静期的持续时间分布的离散性较小，可用正态等分布近似描述。不同相对活跃期的持续时间及强震的数量差别很大，导致相对活跃期并非准周期重视。因此，基于断裂带整体强震复发间隔分布的中长期危险性概率评估仍然面临一定的困难。