基于经验模型和物理模型研究2013 M_S7.0芦山地震余震序列

基于中国地震台网中心2013 MS7.0芦山地震余震数据我们首先确定了余震空间分布范围并根据G-R关系计算了主震后半小时内的完备震级Mc=3.5,并且得到了ML≥3.5和ML≥3.0的地震在2001年至芦山地震前的背景场地震发生率.通过Omori-Ustu经验定律和两种Dieterich模型对芦山地震余震发生率的拟合,我们发现阶梯型Dieterich模型只能模拟p=1的情况,从而造成了模拟曲线与观测数据的差别;前人研究表明震后滑移同样是产生余震的原因,如果假设余震序列由主震静态剪应力Δτ和震后滑移共同作用所产生,我们数值模拟得到的对数型Dieterich模型能够较好地推断余震发生率R随时间t增加而衰减的趋势,能够从物理机制上解释MS7.0芦山地震余震序列衰减指数大于1这一现象.通过对数型Dieterich模型的拟合并结合Andrews的方法,我们还得到MS7.0芦山地震Aσ约为0.155 MPa,ta约为8.4年,这一值与前人研究结果十分接近.     

Aftershock Statistics of the 1999 Chi–Chi, Taiwan Earthquake and the Concept of Omori Times

In this paper we consider the statistics of the aftershock sequence of the m = 7.65 20 September 1999 Chi–Chi, Taiwan earthquake. We first consider the frequency-magnitude statistics. We find good agreement with Gutenberg–Richter scaling but find that the aftershock level is anomalously high. This level is quantified using the difference in magnitude between the main shock and the largest inferred aftershock $ {{\Updelta}}m^{ *}. $ Typically, $ {{\Updelta}}m^{ *} $ is in the range 0.8–1.5, but for the Chi–Chi earthquake the value is $ {{\Updelta}}m^{ *} $  = 0.03. We suggest that this may be due to an aseismic slow-earthquake component of rupture. We next consider the decay rate of aftershock activity following the earthquake. The rates are well approximated by the modified Omori’s law. We show that the distribution of interoccurrence times between aftershocks follow a nonhomogeneous Poisson process. We introduce the concept of Omori times to study the merging of the aftershock activity with the background seismicity. The Omori time is defined to be the mean interoccurrence time over a fixed number of aftershocks.     

Preliminary study on aftershock decay rate of the 2013 M s7.0 Lushan earthquake

We obtained a catalog of early aftershocks of the 2013 Lushan earthquake by examining waveform from a nearby station MDS which is 30.2 km far away from the epicenter, and then we analyzed the relation between aftershock rate and time. We used time-window ratio method to identify aftershocks from continuous waveform data and compare the result with the catalog provided by China Earthquake Networks Center (CENC). As expected, a significant amount of earthquakes is missing in CENC catalog in the 24 h after the main shock. Moreover, we observed a steady seismicity rate of aftershocks nearly in the first 10,000 s before an obvious power-law decay of aftershock activity. We consider this distinct early stage which does not fit the Omori law with a constant p (p ~ 1) value as early aftershock deficiency (EAD), as proposed by previous studies. Our study suggests that the main shock rupture process is different from aftershocks’ processes, and EAD can vary in different cases as compared to earthquakes of strike-slip mechanism in California.     

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     

基于指数函数的川滇地区余震序列衰减规律研究

较大的余震可能造成额外损失并有二次触发建筑物受灾的风险。为研究余震序列衰减规律,文章尝试采用指数衰减模型拟合分析5个不同地区余震序列,并借助修正赤池信息准则、贝叶斯信息准则与调整后R²,分析其与传统余震衰减模型的性能。结果表明,指数模型描述余震序列衰减规律的能力与修正的大森余震模型、修正的拉伸指数模型接近。尤其对于四川长宁M_S6.0余震序列和云南彝良M_S5.7余震序列,指数模型表现优于其他两种模型。指数模型参数具有明确的物理意义：参数A与r之和能够准确代表强震后的实际初始余震数,5个余震序列初始余震数偏差均小于1.70%;参数k可作为反映余震序列衰减快慢的特征值,k值越大则余震序列衰减越慢,其值与主震震级呈反比例关系。     

Aftershock sequence simulations using synthetic earthquakes and rate-state seismicity formulation

We use an efficient earthquake simulator that incorporates rate-state constitutive properties and uses boundary element method to discretize the fault surfaces, to generate the synthetic earthquakes in the fault system. Rate-and-state seismicity equation is subsequently employed to calculate the seismicity rate in a region of interest using the Coulomb stress transfer from the main shocks in the fault system. The Coulomb stress transfer is obtained by resolving the induced stresses due to the fault patch slips onto the optimal-oriented fault planes. The example results show that immediately after a main shock the aftershocks are concentrated in the vicinity of the rupture area due to positive stress transfers and then disperse away into the surrounding region toward the background rate distribution. The number of aftershocks near the rupture region is found to decay with time as Omori aftershock decay law predicts. The example results demonstrate that the rate-and-state fault system earthquake simulator and the seismicity equations based on the rate-state friction nucleation of earthquake are well posited to characterize the aftershock distribution in regional assessments of earthquake probabilities.     

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 Stochastic Two-node Stress Transfer Model Reproducing Omori's Law

— We present an alternative to the epidemic type aftershock sequence (ETAS) model of Ogata (1988). The continuous time two-node network stress release/transfer Markov model is able to reproduce the (modified) Omori law for aftershock frequencies. One node (denoted by A) is loaded by external tectonic forces at a constant rate, with `events' (main shocks) occurring at random instances with risk given by a function of the `stress level' at the node. Each event is a random (negative) jump of the stress level, and adds (or removes) a random amount of stress to the second node (B), which experiences `events' in a similar way, but with another risk function (of the stress level at that node only). When that risk function satisfies certain simple conditions (it may, in particular, be exponential), the frequency of jumps (aftershocks) at node B, in the absence of any new events at node A, follows Omori's law \((\prpto (c + t)^{-1})\) for aftershock squences. When node B is allowed tectonic input, which may be negative, i.e., aseismic slip, the frequency of events takes on a decay form that parallels the constitutive law derived by Dieterich (1994), which fits very well to the modified Omori law. We illustrate the model by fitting it to aftershock data from California post-1973, and from the Valparaiso earthquake of March 3 1985.     

Aftershock sequences of the strongest earthquakes of the world: Stages of development

Analysis of aftershock sequences of the strongest earthquakes of the world showed that previously discovered empirical relations are not universal. Båth’s law is found to be invalid in the majority of cases, while Omori’s law is valid only in a short initial interval of aftershock activity. It is supposed that aftershocks of the strongest earthquakes of normal depths are related initially to fracture of zones that preserved their integrity after the rupture in the source of the main shock and at a later stage to relaxation of stresses in the medium adjacent to the rupture.     

Can Damage Mechanics Explain Temporal Scaling Laws in Brittle Fracture and Seismicity?

Time delays associated with processes leading to a failure or stress relaxation in materials and earthquakes are studied in terms of continuum damage mechanics. Damage mechanics is a quasi-empirical approach that describes inelastic irreversible phenomena in the deformation of solids. When a rock sample is loaded, there is generally a time delay before the rock fails. This period is characterized by the occurrence and coalescence of microcracks which radiate acoustic signals of broad amplitudes. These acoustic emission events have been shown to exhibit power-law scaling as they increase in intensity prior to a rupture. In case of seismogenic processes in the Earth's brittle crust, all earthquakes are followed by an aftershock sequence. A universal feature of aftershocks is that their rate decays in time according to the modified Omori's law, a power-law decay. In this paper a model of continuum damage mechanics in which damage (microcracking) starts to develop when the applied stress exceeds a prescribed yield stress (a material parameter) is introduced to explain both laboratory experiments and systematic temporal variations in seismicity.     

余震活动机理研究综述

从介质和应力的不均匀性、力学加载、流体侵入及应力腐蚀、速率-状态依从等几方面对余震活动机理研究进行综述.已有的研究表明,介质和应力的不均匀性是余震产生的基本前提.瞬时蠕变和余滑观点能够从力学的角度解释震后极短时间内余震的快速衰减,而应力松弛过程更有利于解释长时期的余震活动特征.流体侵入及应力腐蚀在一定条件下控制着余震的演化过程.受主震应力扰动影响的断层间的相互作用,始终存在于余震的活动过程之中.各类模型和理论解释都在努力寻求与G-R关系和修改的大森公式这两个统计地震学基本关系的一致性.     

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.     

自维持断层蠕滑过程和余震发生率的衰减特征—以汶川MW7.9地震序列为例

基于Dieterich地震活动性理论,本文推导出计算余震发生率和余震累积次数的一般表达式,其中主震后发震断层内部的剪切应力随时间的演化过程遵从Jeffreys-Lomnitz蠕变模型,且与修正Omori定律直接相关。修正Omori定律中的p值与震后断层的短时应力加卸载过程正相关。采用Rubin和Ampuero 给出的震后断层自维持蠕滑模型本文得出计算余震发生率的近似表达式,并对2008年汶川地震序列进行拟合。结果表明,p值的大小直接对应了速率-状态摩擦定律中摩擦参量b/a,而修正Omori定律中的c值则与速率-状态摩擦定律中的临界滑移D_c相关。对于汶川余震序列而言,拟合结果显示b/a约为1.13,D_c约为2—3 cm。Rubin-Ampuero震后自维持蠕滑描述了震后孕震层内部短暂的速率变化特征,是孕震断层演化过程不可缺少的环节。      

大森-宇津定律的一种可能机制以唐山大地震为例

为了探讨大森-宇津定律的物理机制, 本文在余震区等效黏度远低于其外部, 且构造应力场在整个余震活动时间间隔内基本保持不变的假设条件下, 提出了一个开尔文黏弹性地震震源体概念模型． 该模型可用于模拟主震后断层蠕变和震源区应力调整触发的余震序列以及蠕变停止后余震终结、 介质恢复到弹性状态、 断层重新闭锁和积累下一次地震的整个过程． 有限元方法可用来计算非均匀黏弹性地震震源体模型中主震和每次余震所引起的应力场及其随时间的演化过程． 在此基础上, 采用开尔文黏弹性地震震源体概念模型和有限元方法模拟了1976年唐山M_S7.8地震余震序列． 结果表明: 经验的大森-宇津定律可以用开尔文黏弹性震源体模型来解释, 这意味着余震衰减的频度取决于蠕变的速率; 余震序列持续时间受控于震源体的黏度, 即黏度越大, 蠕变时间越长, 余震持续的时间也就越长．      

Statistical Variability and Tokunaga Branching of Aftershock Sequences Utilizing BASS Model Simulations

Aftershock statistics provide a wealth of data that can be used to better understand earthquake physics. Aftershocks satisfy scale-invariant Gutenberg–Richter (GR) frequency–magnitude statistics. They also satisfy Omori’s law for power-law seismicity rate decay and Båth’s law for maximum-magnitude scaling. The branching aftershock sequence (BASS) model, which is the scale-invariant limit of the epidemic-type aftershock sequence model (ETAS), uses these scaling laws to generate synthetic aftershock sequences. One objective of this paper is to show that the branching process in these models satisfies Tokunaga branching statistics. Tokunaga branching statistics were originally developed for drainage networks and have been subsequently shown to be valid in many other applications associated with complex phenomena. Specifically, these are characteristic of a universality class in statistical physics associated with diffusion-limited aggregation. We first present a deterministic version of the BASS model and show that it satisfies the Tokunaga side-branching statistics. We then show that a fully stochastic BASS simulation gives similar results. We also study foreshock statistics using our BASS simulations. We show that the frequency–magnitude statistics in BASS simulations scale as the exponential of the magnitude difference between the mainshock and the foreshock, inverse GR scaling. We also show that the rate of foreshock occurrence in BASS simulations decays inversely with the time difference between foreshock and mainshock, an inverse Omori scaling. Both inverse scaling laws have been previously introduced empirically to explain observed foreshock statistics. Observations have demonstrated both of these scaling relations to be valid, consistent with our simulations. ETAS simulations, in general, do not generate Båth’s law and do not generate inverse GR scaling.     

Spatio-temporal characteristics of aftershocks and seismogenic structure of the 2011 MW9.0 Tohoku earthquake,Japan

The Tohoku megathrust earthquake, which occurred on March 11, 2011 and had an epicenter that was 70 km east of Tohoku, Japan, resulted in an estimated ten's of billions of dollars in damage and a death toll of more than 15 thousand lives, yet few studies have documented key spatio-temporal seismogenic characteristics. Specifically, the temporal decay of aftershock activity, the number of strong aftershocks (with magnitudes greater than or equal to 7.0), the magnitude of the greatest aftershock, and area of possible aftershocks. Forecasted results from this study are based on Gutenberg-Richter's relation, Bath's law, Omori's law, and Well's relation of rupture scale utilizing the magnitude and statistical parameters of earthquakes in USA and China (Landers, Northridge, Hector Mine, San Simeon and Wenchuan earthquakes). The number of strong aftershocks, the parameters of Gutenberg-Richter's relation, and the modified form of Omori's law are confirmed based on the aftershock sequence data from the M_W9.0 Tohoku earthquake. Moreover, for a large earthquake, the seismogenic structure could be a fault, a fault system, or an intersection of several faults. The seismogenic structure of the earthquake suggests that the event occurred on a thrust fault near the Japan trench within the overriding plate that subsequently triggered three or more active faults producing large aftershocks.     

Rapid estimation of the hazard posed by strong aftershocks for Kamchatka and the Kuril Islands

This paper deals with the rapid estimation of the hazard posed by strong aftershocks for Kamchatka and the Kuril Islands based on the 12-hour aftershocks, namely, their rate, time of expectation, and maximum magnitude. The data set consists of main shocks and aftershocks as reported in the Catalog of the Kamchatka Branch of the Geophysical Survey, Russian Academy of Sciences (GS RAS) for 1968–2016. We used both the Gutenberg–Richter relation and the Omori–Utsu law to find that the aftershock rates in two time intervals are connected by a relationship of proportionality, with the constant of proportionality being independent of the lowest magnitude of these earthquakes. With this property in mind, we calculated the constants of proportionality for estimating the rate of aftershocks with a magnitude above threshold values based on the data for the first 12 hours after the main shock. We have derived easily remembered rules for estimating the aftershock rates that can be expected for 5 days and for 1 month with magnitudes above a fixed value based on the 12-hour aftershock observations. We also derived empirical regression relations to estimate the magnitude of the largest aftershock that can be expected to occur during 1 year after the main shock and the time of the last aftershock to occur whose magnitude is 5.2 or greater.     

Analysis of the 1997 Zirkuh (Ghean-Birjand) aftershock sequence in east-central Iran

IntroductionThesouthernpartofKhorasanProvinceineast-centralIranisoneoftheseismicallyactiveregionsintheMiddleeast.Historicalreportsindicatedseveralearthquakeshavecausedseveredestructionsandhumanlossinthisregionduringthepastcenturies(Ambraseys,Melville,1982).Theinstrumentallyrecordedearthquakesaswellastheexistenceofseveralactivefaultsalsosug-gestedthattheregionhadahighpotentialofseismicactivities.OnMay10,1997at07:57:29.6GMT,12:27:29.6localtime,ashallowdestructiveearthquakewithoutanyfeltfores…     

1997年伊朗中东部加恩-比尔兼德(GheanBirjiand)Zirkuh余震序列分析

分析了由当地地震台网记录的1997年伊朗加恩-比尔兼德(Ghean-Birjiand)Zirkuh余震序列. 基于余震的分布，可以判断出一垂直的北西南东走向的断层，其长度90 km. 加恩比尔兼德Zirkun地震的断层破裂明显地表现为起始于震中区，单方向地向东南方向传播. 沿断层的余震分布剖面显示，余震分布的深度范围可达20 km. 表明地震活动发生在上地壳，这一地区地震发生层的厚度20 km. 余震的分布表明，在主震的震源过程中块体西部是断层的上盘. 余震的时空分布表现出两个显著的空区，与地表断裂中所见到的间断一致. 可以得出这样的结论: 在主震和余震过程中第一个空区起着障碍体的作用，而第二个空区较深的部位在主震或余震的过程中发生了破裂. 地震后的前10天, 其余震的时间频次衰减图象遵循修正的大森关系，而此后的余震序列非常好地遵循大森模型.      

1976年唐山MS7.8地震余震序列持续时间及对地震危险性分析的意义

1976年7月28日唐山MS7.8大地震对唐山及其周边地区造成了重大的人员伤亡和财产损失. 主震之后约15小时滦县又发生了MS7.1地震; 同年11月15日宁河也发生了MS6.9地震. 唐山MS7.8主震后的余震一直持续至今,使该区域至今保持了与主震前相比具有较高的地震活动性．如何估计余震的持续时间,并进一步将余震从主震目录中去除,一直是地震学中所关注的问题．该文通过对数线性回归和理论计算,从不同角度求取并讨论了1976年唐山MS7.8大地震的余震持续时间．结果表明,由对数线性回归计算得到的余震持续时间约为80 a．而基于Dieterich的余震触发理论所得到的余震持续时间则与区域剪应力变化率有关．区域剪应力变化率可有几种不同方法求得: ① 根据剪应力变化率和静态应力降Delta;tau;e及地震回复周期tr之间的关系求取应力变化率,该方法所得到的余震持续时间约为70——100 a;② Ziv和Rubin对Dieterich的方法进行了修正,给出了通过远场加载速率和断层宽度求取应力变化率, 该方法得到的余震持续时间约为80 a;③ 由背景场地震活动性求取远场剪应力速率, 可以得到该地区二维分布式的余震持续时间,此方法得到的研究区域内余震持续时间为130——160 a．综上,唐山地区余震持续时间约为70——140 a,据此, 该地区现今所发生的地震仍为MS7.8唐山地震所触发的余震．