板内大震原地准周期复发间隔的概率分布

以中国大陆大震原地复发资料为基础,采用比较合理的方法确定了板内大震在其活跃期内原地准确周期复发的概率密度函数,所得结果表明,板内大震在重复行为上具有板间特征地震相类似的分布特征,两者的差异在于,板内大震复发间隔的变分系数ＣＯＶ为０．２６,而板间特征地震的该值为０．２１５,即板内大震的重复间隔相对稍显离散。     

中国大陆强地震时间间隔的概率

以东经１０８°线为界，把中国大陆分为东、西两部，东部取震级Ｍ≥６的地震、西部取Ｍ≥７的地震为强地震．利用有史以来全部地震资料，针对不同情况和不同时期，系统地研究了相继两次强地震之间的时间间隔，目的在于讨论一次强地震发生之后，下一次强地震何时发生．在所有情况下地震间隔数目都随时间间隔值的增大呈明显的趋势性减小．给出了８种情况下的间隔数目统计和相应的模拟函数，以及间隔值的经验概率和相应的函数模拟概率．由此可估计时间间隔为某个值的概率，也可估计时间间隔处于某个区间的概率．反之，对于给定的概率，可估计时间间隔的值或它所处的区间．     

Earthquakes: Recurrence and Interoccurrence Times

The purpose of this paper is to discuss the statistical distributions of recurrence times of earthquakes. Recurrence times are the time intervals between successive earthquakes at a specified location on a specified fault. Although a number of statistical distributions have been proposed for recurrence times, we argue in favor of the Weibull distribution. The Weibull distribution is the only distribution that has a scale-invariant hazard function. We consider three sets of characteristic earthquakes on the San Andreas fault: (1) The Parkfield earthquakes, (2) the sequence of earthquakes identified by paleoseismic studies at the Wrightwood site, and (3) an example of a sequence of micro-repeating earthquakes at a site near San Juan Bautista. In each case we make a comparison with the applicable Weibull distribution. The number of earthquakes in each of these sequences is too small to make definitive conclusions. To overcome this difficulty we consider a sequence of earthquakes obtained from a one million year “Virtual California” simulation of San Andreas earthquakes. Very good agreement with a Weibull distribution is found. We also obtain recurrence statistics for two other model studies. The first is a modified forest-fire model and the second is a slider-block model. In both cases good agreements with Weibull distributions are obtained. Our conclusion is that the Weibull distribution is the preferred distribution for estimating the risk of future earthquakes on the San Andreas fault and elsewhere.     

基于概率密度演化的基础隔震结构随机响应分析

针对抗震结构和基础隔震结构,应用概率密度演化方法对其进行多遇地震作用下的线性随机响应分析。通过引入工程地震动物理随机函数模型,采用数论选点法对多维外荷载随机变量进行离散代表点的生成并求得其赋得概率,利用离散代表点合成地震动加速度时程样本作为输入结构的随机激励,对于每条地震波,相当于对结构进行确定性动力反应分析。在求得结构响应及其相关导数后,应用TVD差分格式求解广义概率密度演化方程即可得到所求响应的时变概率密度及其演化。结果表明：基础隔震结构在随机地震作用下相比抗震结构具有良好的减震性能,隔震层的设置能够减小结构位移响应的标准差,减少了结构响应的离散型;概率密度演化方法不仅能够给出结构响应的二阶统计矩,还能全面地反映结构响应的时变概率信息,位移响应的概率密度函数分布不服从正态分布或其他常用分布,且随着时间演化。     

海原活断层上的史前大地震

地质证据和微地貌证据表明,全新世以来海原断层共发生过五次8.5级左右的大地震,1920年海原大地震是它们中最晚的一次。其它大地震的~(14)C年代分别为距今3680±60年;距今6300±70年;距今7830±>103年(内插);距今9360±75年。可以看出全新世以来,大地震的重现间隔是明显增加的     

中国海域及邻区地震时间分布特征研究

地震时间分布特征研究是进行地震预测和地震危险性分析的重要基础.以中国海域统一地震目录为基础资料,以指数分布模型、伽马分布模型、威布尔分布模型、对数正态分布模型以及布朗过程时间分布(BPT)模型为目标模型,采用极大似然法估算模型参数.根据赤池信息准则(AIC)、贝叶斯信息准则(BIC)以及K-S检验结果确定能够描述海域地...     

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.     

Hastening of occurrences of earthquakes due to dynamic triggering: The observation at Matsushiro, central Japan

Dynamic stress/strain changes associated with the passage of seismic waves perturb the state of stress of a fault.We hypothesize that this perturbation increases the instability of the fault and that it hastens the occurrence of an earthquake that would otherwise occur somewhat later.To test this hypothesis, we investigate a time interval defined as a time difference between the occurrence of a dynamic strain change and the origin time of the first subsequent earthquake.If the occurrence of an earthquake is hastened by the strain change, the time interval would be shortened, compared with a case of a random occurrence.Here we used two datasets: 1) origin times of earthquakes at Matsushiro, Nagano Prefecture, central Japan, with magnitudes of 1.6 or greater, between November 1984 and December 1994; and 2) strainmeter records of remote earthquakes at the Matsushiro Seismological Observatory over the same period.We applied a statistical test to the distribution of the observed time intervals between dynamic strain changes due to remote earthquakes and the first earthquakes at Matsushiro subsequent to the strain changes, in order to compare it to the distribution of expected time intervals generated by a random (Monte Carlo) simulation.Because of limitations of the statistical test, we could not establish the quantitative relationship between the degree of hastening and the amplitude of the strain changes, but we found a statistically significant decrease of the observed time intervals.We also investigated the number of the earthquakes before and after the strain changes, and found that dynamic triggering has little significant impact on the occurrences of earthquakes at Matsushiro.Therefore, we conclude that dynamic triggering at Matsushiro is weaker than those reported in previous studies and that the time interval might be an important parameter for a statistical study of weak dynamic triggering.     

A Probabilistic Estimation of Strong Earthquakes'''' Occurrence in Aeghion Area, Central Greece

INTRODUCTIONTheexaminedareaislocatedintheGulfofCorinthandhasbeenrecognizedasoneofthemostactiveriftsinthewholeAegeanSea .Itsquaternarynormalfaulting (Sebriere ,1 977)anditshighseismicity (PapazachosandPapazachou ,1 997;AmbraseysandJackson ,1 990 )makeitaphysicallaboratorywithintheMediterraneanarea ,wherethephysicalprocessrelatedtotheseismiccyclecouldbestudied .ThecityofAeghionexperiencedastrong (MW =6 4 )earthquakeinJune 1 995,whichcausedseveredamage (Tselentis ,etal.,1 996 ) .Twent…     

Analysis of Shallow and Deep Earthquake Doublets in the Fiji-Tonga-Kermadec Region

For the Fiji-Tonga-Kermadec area and for the period from January 1977 to July 2003, the Harvard CMT catalogue lists 1022 shallow, 410 intermediate and 633 deep earthquakes of moment magnitude from 4.9 to 8.0. The magnitude threshold, above which the catalogue is complete, is 5.3–5.4, and the number of earthquakes of magnitude above this value is 691 for shallow, 329 for intermediate and 476 for deep events, respectively. The proportion of earthquakes associated with doublets and multiplets against the total number of earthquakes is approximately the same in both data sets and therefore all earthquake pairs were considered regardless of their magnitude. We investigated all the pairs of earthquakes that occurred at a centroid distance of less than 40, 60 or 90 km from each other and within a time interval of 200, 300 or 450 days, depending on their magnitude. We found 208 pairs of shallow, 31 of intermediate and 92 of deep events. To ascertain whether these earthquakes in pairs are not connected by chance, the possibility of their occurrence in an uncorrelated Poissonian catalogue was considered. It was assumed that in such a catalogue the inter-event time is exponentially distributed, the earthquake magnitude follows the Gutenberg-Richter relation, and the distribution of centroid distances between the events in pairs is controlled by its non-parametric kernel estimate. The probability of the appearance of the observed proportion of doublets of shallow earthquakes in the Poissonian catalogue was found to be very low. The low probability of occurrence in a semi-random catalogue, created by randomising centroid locations in the actual data set, also indicates major importance of the distance criterion used for a doublet specification. In general, shallow earthquakes tend to form pairs at shorter distances and within shorter time intervals than deep earthquakes. Both the distance and the time intervals do not depend on the magnitude of involved events. The largest number of pairs of deep earthquakes is observed at a depth of about 600 km, and the proportion of deep events associated with doublets against the number of all events increases with depth. From comparison of the focal mechanism of earthquakes in pairs, measured by the 3-D rotation angle, it follows that deep earthquakes forming pairs have a more diverse focal mechanism than shallow events; the rotation angle for three quarters of shallow pairs and only for about one third of deep pairs is reasonably small. The azimuth between two events forming a doublet is in about 60–65% of cases close to the strike of one of nodal planes of the first or the second event.     

Post-eruptive seismic activity of Mount Cameroon (Cameroon), West Africa: a statistical analysis

Recent seismological studies of the Cameroon Volcanic Line show that Mt. Cameroon is the most active centre, so a permanent seismic network of six seismographs was set up in its region between 1984 and 1986. The network was reinforced with temporary stations up till 1987, and the local seismicity was studied. Here we emphasise a statistical analysis of seismic events recorded by the permanent seismic stations. Four swarms lasting 9 to 14 months are identified at intervals of 2–3 years. Most earthquakes are felt (intensity and magnitude, respectively, less than VI MM and 5) during the first three swarms and a few during repose periods. The main focal regions are the northwest and southeast flanks, the Bimbia and Bioko regions in the South of the volcano. Hypocentres are distributed from the surface to 60 km depth indicating crustal and subcrustal activities. The subcrustal events are observed only in the southeast flank, they are the most regular earthquakes with a monthly frequency of 9 to 15 events. They are characteristic earthquakes with magnitude 2.8 ± 0.1. Between 1984 and 1992, their yearly mean time interval between successive events range from 50 to 86 hours. For that period their occurrence can be modelled as a stationary renewal process with a 3-day period. But the analysis of variance shows possible significant differences among yearly means. A Weibull's distribution confirms that the time intervals between successive deep events are not independent, and in 1993 a swarm of deep earthquakes is recorded, hence a non-loglinear magnitude/frequency relation. The deep seismicity is thought to be associated with a zone of weakness (perhaps a magmatic conduit) and may have some close relationship with the magmatic activity.     

Rupture segmentation and assessment of probabilities of seismic potential on the Xiaojiang fault zone

Spatial distribution of sources of strong and large earthquakes on the Xiaojiang fault zone in eastern Yunnan is studied according to historical earthquake data. 7 segments of relatively independent sources or basic units of rupture along the fault zone have been identified preliminarily. On every segment, time intervals between main historical earthquakes are generally characterized by “time-predictable” recurrence behavior with indetermination. A statistic model for the time intervals between earthquakes of the fault zone has been preliminarily established. And a mathematical method has been introduced into this paper to reckon average recurrence interval between earthquakes under the condition of having known the size of the last event at a specific segment. Based on these, ranges of the average recurrence intervals given confidence have been estimated for events of various sizes on the fault zone. Further, the author puts forward a real-time probabilistic model that is suitable to analyze seismic potential for individual segments along a fault zone on which earthquake recurrence intervals have been characterized by quasi-time-predictable behavior, and applies this model to calculate conditional probabilities and probability gains of earthquake recurring on the individual segments of the Xiaojiang fault zone during the period from 1991 to 2005. As a consequence, it has shown that two parts of this fault zone, from south of Dongchuan to Songming and from Chengjiang to Huaning, have relatively high likelihoods for strong or large earthquake recurring in the future. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 322–330, 1993.     

The bayesian probabilistic prediction of the next earthquake in the ometepec segment of the mexican subduction zone

A predictive equation to estimate the next interoccurrence time () for the next earthquake (M6) in the Ometepec segment is presented, based on Bayes' theorem and the Gaussian process.Bayes' theorem is used to relate the Gaussian process to both a log-normal distribution of recurrence times () and a log-normal distribution of magnitudes (M) (Nishenko andBuland, 1987;Lomnitz, 1964). We constructed two new random variablesX=InM andY=In with normal marginal densities, and based on the Gaussian process model we assume that their joint density is normal. Using this information, we determine the Bayesian conditional probability. Finally, a predictive equation is derived, based on the criterion of maximization of the Bayesian conditional probability. The model forecasts the next interoccurrence time, conditional on the magnitude of the last event.Realistic estimates of future damaging earthquakes are based on relocated historical earthquakes. However, at the present time there is a controversy between Nishenko-Singh and Gonzalez-Ruiz-Mc-Nally concerning the rupturing process of the 1907 earthquake. We use our Bayesian analysis to examine and discuss this very important controversy. To clarify to the full significance of the analysis, we put forward the results using two catalogues: (1) The Ometepec catalogue without the 1907 earthquake (González-Ruíz-McNally), and (2) the Ometepec catalogue including the 1907 earthquake (Nishenko-Singh).The comparison of the prediction error reveals that in the Nishenko-Singh catalogue, the errors are considerably smaller than the average error for the González-Ruíz-McNally catalogue of relocated events.Finally, using the Nishenko-Singh catalogue which locates the 1907 event inside the Ometepec segment, we conclude that the next expected damaging earthquake (M6.0) will occur approximately within the next time interval =11.82 years from the last event (which occurred on July 2, 1984), or equivalently will probably occur in April, 1996.     

川滇地震的时空对应特征

研究了记录较全的1920年以来的川滇 M6级地震资料,发现两区地震之间有较好的对应关系,其对应概率为78%.分析了时空对应特征后得到:两区对应地震的发震时序概率几近相等,平均发震时差大致相同,对应优势方向为北东向.统计结果表明,川滇对应地震的对应时差（）普遍较短,平均约为9个月.经 X2检验近似服从泊松分布.在讨论分区对应特点的基础上,给出了高概率对应区.当一区发生地震后,可对另一区地震的时间、地点和发震概率进行估计,为中期预报提供某些线索.文中还对对应机制的某些问题进行了讨论.      

Forecasting aftershock activity: 1. Adaptive estimates based on the Omori and Gutenberg–Richter laws

The method for forecasting the intensity of the aftershock processes after strong earthquakes in different magnitude intervals is considered. The method is based on the joint use of the time model of the aftershock process and the Gutenberg–Richter law. The time model serves for estimating the intensity of the aftershock flow with a magnitude larger than or equal to the magnitude of completeness. The Gutenberg–Richter law is used for magnitude scaling. The suggested approach implements successive refinement of the parameters of both components of the method, which is the main novelty distinguishing it from the previous ones. This approach, to a significant extent, takes into account the variations in the parameters of the frequency–magnitude distribution, which often show themselves by the decreasing fraction of stronger aftershocks with time. Testing the method on eight aftershock sequences in the regions with different patterns of seismicity demonstrates the high probability of successful forecasts. The suggested technique can be employed in seismological monitoring centers for forecasting the aftershock activity of a strong earthquake based on the results of operational processing.     

优化减震距离

本文对中国大陆内部不同时段发生的七级地震和六级地震分别进行统计分析,求得不同震级的优势地震间距,减震距离以及地震间距随时间变化的关系式。提出地震间距的数值分布可用正态概率分布函数描述,并得到含有时间参量的地震间距概率密度函数。此外,根据弹性位错理论,求得一次地震后在减震距离处所产生的位移,进而求出平均位移速率。     

云南及邻区中强震连发和平静与强震关系研究

系统研究了1925年以来云南及邻区5级以上地震的时间分布特征, 分别给出了云南及邻区5级以上地震连发和平静的定义。 分析了中强震连发、 平静的一些基本特征, 研究了5级以上地震连发、 平静事件与该区强震活跃、 平静过程的关系。 这些分析结果对云南及邻区的地震趋势预测有一定实际意义。     

南北地震带强震迁移特征及其与南亚地震带的联系

南北地震带1500年以来7级以上强震迁移显示出3种方式:由北往南大致等时距的迁移、由南往北多样式的迁移和一个时段内全带范围内的成组强震群发活动。从以往100年的强震活动分析,南北地震带的活动还与从缅甸至印尼苏门答腊的南亚地震带强震活动相关联,前者的强震往往滞后于后者几月至数年发生。因此,2004年12月26日苏门答腊岛西面海里发生8·7级大地震后南北地震带发生强震的可能性不能忽视。南北地震带上述多种强震迁移活动特征既与印度板块向NNE的碰撞、俯冲过程有关,也与青藏高原与其东北缘稳定、坚硬的鄂尔多斯和阿拉善块体的相互作用有关     

印度尼西亚巨震对华东地震形势的影响

根据印度板块和缅甸次板块运动GPS观测资料, 分析了印度尼西亚巨震的发震构造背景, 震后印、 缅板块的正应力减小, 剪应力相对增大, 剪应力是对华东地震形势产生影响的主要动力源。 简单统计印缅板块地震后3年内华东地区发生中强震的对应组数为21组, 利用概率增益公式得出印、 缅板块地震和华东地区中强震的对应关系是有物理基础的对应, 而不是随机的对应。 通过β分布函数预测华东地区未来3年发生5级以上地震的概率为0.67, 风险经验概率为0.65。     

地震活动性正常与异常的群体概率特征及其在地震预测中的应用以汶川地震为例

地震事件一般具有离散性, 即它们的发生和转移具有一定的时间和空间间隔。 当孕震系统处于平衡(或正常)状态时, 系统状态变量X(这里以地震活动性为例)的时间序列概率分布表现为单峰型(如泊松分布); 其时间间隔(或等候时间)Δt分布可用负指数分布来描述。 当系统处于非平衡(或异常)状态时, X的概率分布表现为双峰型或多峰型, 其时间间隔Δt(或空间间隔ΔS)可采用幂函数关系来描述。 可以计算X的1~4阶矩统计参数识别X的概率分布性质, 进一步判断系统所处的状态。 根据这个思路, 本文尝试针对地震活动性的群体概率特征, 探索研究地震活动系统时间和空间结构的演变以及正常和异常状态的辨别, 并将这些方法应用于2008年汶川8.0级地震及其余震趋势和强余震预测实践。