Relative Seismic Quiescence Before Large Aftershocks

--In terms of the modified Omori's formula and Akaike's Information Criterion, thirteen aftershock sequences have been analysed quantitatively, to check if any anomalous change of seismic activity took place before the occurrence of the largest aftershock. The analysis follows the method proposed by . The epicentre distribution of the main shocks covers the Aegean Sea (Greece) area and the surrounding regions. The earthquakes occurred from 1988 to 1998.¶Although difficulties existed for a quantitative treatment of seismic quiescence, the results of the temporal analysis of the aftershock activities seem to be promising. In eight of thirteen cases the observed temporal pattern is similar. The aftershock activity decreases significantly before the occurrence of the largest aftershock, with respect to the level expected according to the modified Omori's formula. Thereafter, the activity recovers to its previous level just before or immediately after the occurrence of the main aftershock. Moreover, an estimation of the reliability of the method is made, based on the results of this study as well as of previous similar investigations. From a total of 41 aftershock sequences which have been analysed following Matsu'ura's method, 29 of them (71%) show a remarkable relative quiescence before the occurrence of the main shock.¶Although it is difficult to construct a model which explains the precursory pattern, the real time monitoring and check for seismic quiescence could at least contribute to a 'qualitative' prediction of the largest aftershock which could at times be as large and disastrous as the main shock.     

序列衰减与余震激发研究进展及应用成果

着重于序列衰减与余震激发,系统介绍了修改的大森公式、ETAS模型及BASS模型的最新理论研究进展及应用成果。修改的大森公式是迄今为止对序列衰减的最好描述,据此可对序列衰减特征进行定量表述。大森公式本质上是一种典型的现象统计模型,但由于其参数少、计算简单,并且确实能够反映序列衰减的总体特征,因而在实际中应用广泛。ETAS模型考虑了具有统计自相似特征的次级余震激发问题,次级余震激发强度与父地震强度有关,这在物理过程方面对大森公式进行了大大的拓展。由于考虑了次级余震的激发问题,ETAS模型不但在余震序列研究方面比修改的大森公式有了明显的进展,而且在诸如平静检测、余震群集剔除、背景地震活动评估、外因触发地震活动检测等方面也有诸多应用。BASS模型遵循修改的Bath定律,而ETAS模型遵循的是与父地震震级有关的相似率,这是BASS模型与ETAS模型的最大区别,因而相对ETAS模型而言,BASS模型是一种完全自相似的理想化模型,但目前基于BASS模型的应用研究尚不多见     

Characteristics of the May 12,2008 Wenchuan M_S8.0 Earthquake Sequence and Discussion on Relevant Problems

The aftershock activity of the May 12, 2008 Wenchuan Ms8.0 Earthquake Sequence shows an obvious segmented feature. Most of the large aftershocks were distributed in the north and south parts of the aftershock zone. Thrusting was dominant with a small amount of strike-slip component in the south part. The aftershock activity decayed gradually, presenting the sequence features of a mainshock-aftershock pattern. The north part was the ending area of the maiushock fracture where strike-slipping was dominant, showing an obvious swarm feature. Therefore it became the major area for large aftershocks. The modulation of the earth tide on aftershock activity is remarkable; most large aftershocks occur during the period of flood and neap tide. The time period around 16:00 was the dominant occurring time for large aftershocks. The p-value, a parameter of modified Omori formula, increases gradually with time, and reaches about 1 at the end. Based on previous study, the sequence patterns, magnitude of maximum aftershock, as well as the duration of aftershock activity has been discussed. The primary results also show that the magnitude difference between the maiushockand the maximum aftershock is proportional to the rupture size of the maiushock for huge earthquakes of about Ms8.0. This means that when the magnitudes of the earthquakes are nearly the same, large rupture size corresponds to sufficient energy release.     

汶川8.0级地震序列及相关问题讨论

汶川8.0级地震序列具有明显的分段特性,较强余震分布于茂县、绵竹以南及平武以北。主破裂过程在中南段以逆冲为主,序列逐渐衰减,呈主余型的序列衰减特征;北段是汶川地震破裂过程的终止区域,主破裂过程在该区域以走滑为主,形成多震型的序列特征,也成为汶川序列较大余震的主体活动区域。序列较强余震活动明显受引潮力调制,大多数较强余震发生在固体潮大、小潮时段,并且16时前后是较强余震的优势发震时段。序列衰减系数p值随时间增加而逐渐增大,最终基本稳定在1附近变化。结合以往的研究,对序列类型及最大强余震震级、强余震活动持续时间等进行了初步讨论。初步的统计结果还显示,8级左右强震序列中主震与最大余震之间的震级差正比于主震破裂尺度,这意味着当震级大体接近时,较大的破裂尺度与较为充分的能量释放相对应     

中国大陆中强地震余震序列的部分统计特征

依据1970年以来记录相对完整的294次50级以上地震序列资料,研究中国大陆中强地震余震序列统计特征,探讨序列类型、最大余震震级、强余震活动持续时间等与主震震级及主震断层性质之间的关系.中国大陆孤立型、主余型及多震型地震余震序列分别约占23%、59%及18%.其中走滑型、具有倾滑分量的走滑型、具有走滑分量的倾滑型及逆冲型分别占48%、24%、17%及11%. 余震序列1年内最大余震震级与主震震级正相关,但主震震级较低时相对离散,孤立型序列离散程度较高,主余型及多震型序列线性相关性较好.绝大多数序列最大余震均发生在震后200天内,少数具有晚期强余震的序列主要属主余型序列,孤立型及多震型序列通常没有晚期强余震发生.68%的序列1年内最大余震发生在震后10天内,77%发生在震后30天之内,95%发生在震后120天之内.序列最大余震发生时间及5、6级强余震活动持续时间与序列类型及主震震级大小有关,多震型序列最大余震发生最快,孤立型次之、主余型最长.若仅就主余型序列而言,当主震震级较高时最大余震与主震间时间间隔相对较短,主震震级较低时最大余震与主震间时间间隔相对较长.     

Statistical evaluation and probabilistic modeling of aftershock sequences of Iranian plateau

The present research focuses on the statistical evaluation of Iranian plateau aftershocks from an engineering perspective and presents probabilistic models applicable for generating random earthquake scenarios. Accordingly, a comprehensive earthquake data catalog including the period from 1964 to 2016 is prepared. Data are declustered into 37 separate mainshock-aftershock sequences by considering the completeness moment magnitude of the database. The well-known modified Omori occurrence rate formula is adopted to determine the recurrence time of the events, considering the effect of secondary aftershocks. In addition to computing the probability density functions of the parameters of the Omori formula, the joint probability distribution of the aftershock occurrence versus magnitude and occurrence time is obtained for modeling their magnitude sequences. The obtained results are applicable for producing randomly generated mainshock-aftershock scenarios.     

1990年4月17日新疆乌恰6.4级地震序列特征

1990年4月17日乌恰6.4级地震序列有以下特征:(1)主震型序列;(2)强余震前小地震震中向强余震的震中附近迁移;(3)余震频度衰减快;(4)余震在主震和最大余震之间活动;(5)较大余震存在“密集-平静-发震”的规律;(6)存在晚期较强余震。     

Application of array-based waveform cross-correlation techniques to aftershock sequences: the 2003 Lefkada Island,Greece, case

Cross-correlation analysis was applied to events in the 2003 Lefkada Island, Greece, sequence in order to identify clusters of seismicity within the extensive aftershock sequence along a fault zone of approximately 100 km length. Data from the small-aperture TRISAR array, covering the first 2 days of aftershock activity, were used. Array-based waveform correlation has a great advantage over single channel correlation analysis in that the validity of waveform matches with relatively low correlation coefficients can be examined by checking the alignment of correlation traces on the different channels. The length of the fault zone leads inevitably to a great diversity in the waveforms, although a small number of clusters of very similar events emerge from the TRISAR data. Events which the correlation analysis had placed within the same cluster were listed in the ISC Bulletin with separations of up to tens of kilometres. This made it necessary to check the validity of the TRISAR clusters by applying the same procedure independently to the three-component stations of the National Seismographic Network of the National Observatory of Athens, located at local to regional distances from the aftershock area. Results suggest that array-based waveform correlation provides a robust tool both for identifying event clusters within large aftershock areas and for identifying situations in which bulletin event location estimates need re-evaluation.     

Aftershocks of the San Marcos earthquake of April 25, 1989 (M S =6.9) and some implications for the Acapulco-San Marcos,Mexico, seismic potential

Aftershock activity following the April 25, 1989 (M _S =6.9) earthquake near San Marcos, Guerrero, Mexico, was monitored by a temporary network installed twelve hours after the mainshock and remaining in operation for one week. Of the 350 events recorded by this temporary array, 103 were selected for further analysis in order to determine spatial characteristics of the aftershock activity. An aftershock area of approximately 780 km² is delimited by the best quality locations. The area of highest aftershock density lies inside an area delimited by the aftershocks of the latest large event in the region in 1957 (M _S =7.5) and it partially overlaps the zone of maximum intensity of the earlier 1907 (M _S =7.7) shock. Aftershocks also appear to cluster close to the mainshock hypocenter. This clustering agrees with the zone of maximum slip during the mainshock, as previously determined from strong motion records. A low angle Benioff zone is defined by the aftershock hypocenters with a slight tendency for the slab to follow a subhorizontal trajectory after a 110 km distance from the trench axis, a feature which has been observed in the neighboring Guerrero Gap. A composite focal mechanism for events close to the mainshock which also coincides with the zone of largest aftershock density, indicates a thrust fault similar to the mainshock fault plane solution.The San Marcos event took place in an area which could be considered as a mature seismic gap. Due to the manner in which strain release has been observed to previously occur, the occurrence of a major event, overlapping both the neighboring Guerrero Gap and the San Marcos Gap segments of the Mexican thrust, cannot be overlooked.     

Aftershock Statistics

The statistical properties of aftershock sequences are associated with three empirical scaling relations: (1) Gutenberg-Richter frequency-magnitude scaling, (2) Båths law for the magnitude of the largest aftershock, and (3) the modified Omoris law for the temporal decay of aftershocks. In this paper these three laws are combined to give a relation for the aftershock decay rate that depends on only a few parameters. This result is used to study the temporal properties of aftershock sequences of several large California earthquakes. A review of different mechanisms and models of aftershocks are also given. The scale invariance of the process of stress transfer caused by a main shock and the heterogeneous medium in which aftershocks occur are responsible for the occurrence of scaling laws. We suggest that the observed partitioning of energy could play a crucial role in explaining the physical origin of Båths law. We also study the stress relaxation process in a simple model of damage mechanics and find that the rate of energy release in this model is identical to the rate of aftershock occurrence described by the modified Omoris law.     

A catalog of aftershock sequences in Greece (1971–1997): Their spatial and temporal characteristics

A complete catalog of aftershock sequences is provided for main earthquakes with M_L 5.0, which occurred in the area of Greece and surrounding regions the last twenty-seven years. The Monthly Bulletins of the Institute of Geodynamics (National Observatory of Athens) have been used as data source. In order to get a homogeneous catalog, several selection criteria have been applied and hence a catalog of 44 aftershock sequences is compiled. The relations between the duration of the sequence, the number of aftershocks, the magnitude of the largest aftershock and its delay time from the main shock as well as the subsurface rupture length versus the magnitude of the main shock are calculated. The results show that linearity exists between the subsurface rupture length and the magnitude of the main shock independent of the slip type, as well as between the magnitude of the main shock (M) and its largest aftershock (Ma). The mean difference M–Ma is almost one unit. In the 40% of the analyzed sequences, the largest aftershock occurred within one day after the main shock.The fact that the aftershock sequences show the same behavior for earthquakes that occur in the same region supports the theory that the spatial and temporal characteristics are strongly related to the stress distribution of the fault area.     

余震序列的时空特征ht

研究我国东部9次余震序列的总体特征得到:余震频度符合 n=n1t-h关系;频度和强度随时间衰减较慢;最大地震后3、4天内发生的余震所勾划的余震区常常比最终余震区小;多数余震分布在地壳中5至10公里的深度上.一些强余震前的中小余震时空分布有下述特征:（1）强余震前几天至十几天,余震序列的频度偏离正常衰减值;（2）强余震前有中小余震震中向下一次强余震的震中附近扩展或形成空区的现象;（3）强余震前震级序列出现缺震现象;（4）余震序列有准周期性.上述特性预示其后将发生强余震,同时表明强余震有类似于大地震的孕震过程.种种现象还表明余震序列在时间和空间上可能是由主震的直接余震和强余震的次级余震相互叠加所组成的.最后将某些特性和岩石试验结果进行了比较和讨论.      

A Recent Application of the ETAS Model and a Proposed Method for Prediction of Strong Aftershocks

In this paper, 28 aftershock sequences are selected, which are distributed in different areas including north China, southwest of China, northwest of China, Taiwan area, Turkey and Greece. In order to investigate the characteristics of these sequences along with different temporal and spatial coordinates, each sequence has been divided into dozens of segments called ``sub-sequences''. The ETAS (Epidemic Type Aftershock Sequences) model is applied to each ``sub-sequence'', and therefore the vectors of parameters of ETAS could be evaluated. Another model named LR (Logistic Regression) model is used to seek the correlate relation between the parameters of ETAS applied to every earthquake ``sub-sequence'' and seismicity. All the analyses and estimations imply that the characteristic of decay of aftershock sequences in different temporal and spatial domains seems to be characterized by the parameters of the ETAS model applied to some aftershock sequences or ``sub-sequences'', and there are some proportional correlate relations between the evaluation of LR model and the occurrence probability of the succeeding strong seismic energy release.     

Bayesian estimation of the Modified Omori Law parameters for the Iranian Plateau

The forecasting of large aftershocks is a preliminary and critical step in seismic hazard analysis and seismic risk management. From a statistical point of view, it relies entirely on the estimation of the properties of aftershock sequences using a set of laws with well-defined parameters. Since the frequentist and Bayesian approaches are common tools to assess these parameter values, we compare the two approaches for the Modified Omori Law and a selection of mainshock–aftershock sequences in the Iranian Plateau. There is a general agreement between the two methods, but the Bayesian appears to be more efficient as the number of recorded aftershocks decreases. Taking into account temporal variations of the b-value, the slope of the frequency-size distribution, the probability for the occurrence of strong aftershock, or larger main shock has been calculated in a finite time window using the parameters of the Modified Omori Law observed in the Iranian Plateau.     

Evolution of the vigorous 2006 swarm in Zakynthos (Greece) and probabilities for strong aftershocks occurrence

A multiplet of moderate-magnitude earthquakes (5.1?≤?M?≤?5.6) took place in Zakynthos Island and offshore area (central Ionian Islands, Greece) in April 2006. The activity in the first month occupied an area of almost 35 km long, striking roughly NNW–SSE, whereas aftershocks continued for several months, decaying with time but persisting at the same place. The properties of the activated structure were investigated with accurate relocated data and the available fault plane solutions of some of the stronger events. Both the distribution of seismicity and fault plane solutions show that thrusting with strike-slip motions are both present in high-angle fault segments. The segmentation of the activated structure could be attributed to the faulting complexity inherited from the regional compressive tectonics. Investigation of the spatial and temporal behavior of seismicity revealed possible triggering of adjacent fault segments that may fail individually, thus preventing coalescence in a large main rupture. In an attempt to forecast occurrence probabilities of six of the strong events (M _w?≥?5.0), estimations were performed following the restricted epidemic-type aftershock sequence model, applied to data samples before each one of these strong events. Stochastic modeling was also used to identify “quiescence” periods before the examined aftershocks. In two out of the six cases, real aftershock rate did decrease before the next strong shock compared to the modeled one. The latter results reveal that rate decrease is not a clear precursor of strong shocks in the swarm and no quantitative information, suitable to supply probability gain, could be extracted from the data.     

基于ETAS模型对青海地区余震预测效能评估的研究

为系统评估青海地区余震短期发生率的预测效能,以及构建适合地震活动特点的余震早期预测策略和预测指标体系,利用国际上当前较为前沿的时间序列ETAS模型和"瘦化算法"对青海地区2009年以来的8个地震的早期余震序列参数进行拟合,并利用N-test检验方法对预测结果进行回溯性的效能评估。研究表明:ETAS模型和"瘦化算法"对青海地区的余震发生率具有很好的预测能力,建议采用3天的预测时间窗,且对序列早期阶段进行应用,或可取得"最佳"的预测效果。     

p values of continental aftershock activity in China

The temporal attenuation characteristics of the frequency of aftershock activity for 32 earthquakes (M being more than or equal to 5) were quantitatively analyzed by using the maximum likelihood estimation for point process. The results indicated that the average value of the attenuation coefficient of aftershock activity (p-value in the modified Omori’s formula) of the East China and the North—South Seismic Belt of China (NSB) was 0.91, being less than thep value of the western China. Comparing thep values of aftershock activities in the continental part of China with those in the Japanese islands, it was found that thep value in the continental part of China was less than that in the Japanese islands. Wherewith thep value is not related to the magnitude of main shock.     

A Review of Earthquake Statistics: Fault and Seismicity-Based Models, ETAS and BASS

There are two fundamentally different approaches to assessing the probabilistic risk of earthquake occurrence. The first is fault based. The statistical occurrence of earthquakes is determined for mapped faults. The applicable models are renewal models in that a tectonic loading of faults is included. The second approach is seismicity based. The risk of future earthquakes is based on the past seismicity in the region. These are also known as cluster models. An example of a cluster model is the epidemic type aftershock sequence (ETAS) model. In this paper we discuss an alternative branching aftershock sequence (BASS) model. In the BASS model an initial, or seed, earthquake is specified. The subsequent earthquakes are obtained from statistical distributions of magnitude, time, and location. The magnitude scaling is based on a combination of the Gutenberg-Richter scaling relation and the modified Båth’s law for the scaling relation of aftershock magnitudes relative to the magnitude of the main earthquake. Omori’s law specifies the distribution of earthquake times, and a modified form of Omori’s law specifies the distribution of earthquake locations. Unlike the ETAS model, the BASS model is fully self-similar, and is not sensitive to the low magnitude cutoff.     

Development of an aftershock occurrence model calibrated for Turkey and the resulting likelihoods

This paper presents the calibration of Omori's aftershock occurrence rate model for Turkey and the resulting likelihoods. Aftershock occurrence rate models are used for estimating the probability of an aftershock that exceeds a specific magnitude threshold within a time interval after the mainshock. Critical decisions on the post-earthquake safety of structures directly depend on the aftershock hazard estimated using the occurrence model. It is customary to calibrate models in a region-specific manner. These models depend on rate parameters(a, b, c and p) related to the seismicity characteristics of the investigated region. In this study, the available well-recorded aftershock sequences for a set of Mw ≥ 5.9 mainshock events that were observed in Turkey until 2012 are considered to develop the aftershock occurrence model. Mean estimates of the model parameters identified for Turkey are a =-1.90, b = 1.11, c = 0.05 and p = 1.20. Based on the developed model, aftershock likelihoods are computed for a range of different time intervals and mainshock magnitudes. Also, the sensitivity of aftershock probabilities to the model parameters is investigated. Aftershock occurrence probabilities estimated using the model are expected to be useful for post-earthquake safety evaluations in Turkey.     

东南沿海大震一例探讨

本文利用最近的海上石油物探资料,从地质构造等方面论证1918年南沃大震的震中位置,并用历史水位及宏观资料推断了本次地震的震源机制解,讨论了震级问题,余震序列特征,估算了强余震震级的方法和预测强余震发生的时间问题,由于震级参数的重新论证,对泉州—汕头地震带地震活动性应作重新估计。上述问题的讨论对指导今后该区的地震监视预报均有一定的参考价值。