On the applicability of the RETAS model for forecasting aftershock probability in underground mines (Kiirunavaara Mine,Sweden)

Aftershock series of even comparatively small seismic events can pose a risk to the mining operation or the personnel in deep underground mines as the main shocks and some of the aftershocks can cause damage in the rock mass. Stochastic modeling was applied in this study for the analysis of the temporal evolution of aftershock occurrence probability during a M1.85 aftershock sequence in Kiirunavaara Mine, Sweden. The Restricted Epidemic-Type Aftershock Sequence (RETAS) model was chosen for estimation of the aftershock occurrence probability. This model considers all events with magnitude above the magnitude of completeness M₀ and has the advantage of including the Modified Omori Formula (MOF) model and Epidemic-Type Aftershock Sequence (ETAS) model as its end versions, considering also all intermediate models. The model was applied sequentially to data samples covering cumulative periods of time, starting from the first 2 h after the main event and increasing them by 2 h until the period covered the entire 72-h sequence. For each sample, the best-fit RETAS version was identified and the probability of a M?≥?0.5 aftershock for every next 2 h was determined through Monte Carlo simulation. The feasibility of the resulting probability evolution for suspension and re-starting of the mining operations was discussed together with possible prospects for future development of the methodology.

     

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.     

Properties of the Aftershock Sequences of the 2003 Bingöl, M D = 6.4, (Turkey) Earthquake

Aftershock sequences of the magnitude M _{W =}6.4 Bingöl earthquake of 1 May, 2003 (Turkey) are studied to analyze the spatial and temporal variability of seismicity parameters of the b value of the frequency-magnitude distribution and the p value describing the temporal decay rate of aftershocks. The catalog taken from the KOERI contains 516 events and one month’s time interval. The b value is found as 1.49 ± 0.07 with Mc =3.2. Considering the error limits, b value is very close to the maximum b value stated in the literature. This larger value may be caused by the paucity of the larger aftershocks with magnitude M _D ≥ 5.0. Also, the aftershock area is divided into four parts in order to detect the differences in b value and the changes illustrate the heterogeneity of the aftershock region. The p value is calculated as 0.86 ± 0.11, relatively small. This small p value may be a result of the slow decay rate of the aftershock activity and the small number of aftershocks. For the fitting of a suitable model and estimation of correct values of decay parameters, the sequence is also modeled as a background seismicty rate model. Constant background activity does not appear to be important during the first month of the Bingöl aftershock sequences and this result is coherent with an average estimation of pre-existing seismicity. The results show that usage of simple modified Omori law is reasonable for the analysis. The spatial variability in b value is between 1.2 and 1.8 and p value varies from 0.6 to 1.2. Although the physical interpretation of the spatial variability of these seismicity parameters is not straightforward, the variation of b and p values can be related to the stress and slip distribution after the mainshock, respectively. The lower b values are observed in the high stress regions and to a certain extent, the largest b values are related to Holocene alluvium. The larger p values are found in some part of the aftershock area although no slip occurred after the main shock and it is interpreted that this situation may be caused by the alluvium structure of the region. These results indicate that the spatial distribution in b and p values are generally related to the rupture mechanism and material properties of an aftershock area.     

A probabilistic framework for quantification of aftershock ground‐motion hazard in California: Methodology and parametric study

This paper presents a proposed method of aftershock probabilistic seismic hazard analysis (APSHA) similar to conventional ‘mainshock’ PSHA in that it estimates the likelihoods of ground motion intensity (in terms of peak ground accelerations, spectral accelerations or other ground motion intensity measures) due to aftershocks following a mainshock occurrence. This proposed methodology differs from the conventional mainshock PSHA in that mainshock occurrence rates remain constant for a conventional (homogeneous Poisson) earthquake occurrence model, whereas aftershock occurrence rates decrease with increased elapsed time from the initial occurrence of the mainshock. In addition, the aftershock ground motion hazard at a site depends on the magnitude and location of the causative mainshock, and the location of aftershocks is limited to an aftershock zone, which is also dependent on the location and magnitude of the initial mainshock. APSHA is useful for post‐earthquake safety evaluation where there is a need to quantify the rates of occurrence of ground motions caused by aftershocks following the initial rupture. This knowledge will permit, for example, more informed decisions to be made for building tagging and entry of damaged buildings for rescue, repair or normal occupancy. Copyright © 2008 John Wiley & Sons, Ltd.     

地震的"序列归属"问题与ETAS模型——以唐山序列为例

历史上发生过强震地区的余震活动可能持续较长时间,而余震序列在何时可被看作正常的"背景地震活动",即"序列归属"问题在地球动力学和地震物理中有重要意义.时-空"传染型余震序列"(ETAS)模型可分离"背景"地震和"丛集"地震,并用概率形式表示作为相应事件的可能性,为考察此问题提供了可能.本文以1976年唐山M_S7.8地震序列为例,对唐山地区1970年以来的M_L4.0以上地震进行了时-空ETAS模型拟合,并以2010年以来发生的3次M_S4.0以上地震为例讨论了它们的"序列归属"问题.研究结果显示,3次M_S4.0以上地震的背景地震概率分别为0.72、0.88和0.76,表明它们作为1976年唐山M_S7.8的余震的可能性较低,更可能为背景地震.     

Preliminary report of the September 5, 2022 MS 6.8 Luding earthquake,Sichuan, China

The 2022 M_S 6.8 Luding earthquake is the strongest earthquake in Sichuan Province, Western China, since the 2017 M_S 7.0 Jiuzhaigou earthquake. It occurred on the Moxi fault in the southeastern segment of the Xianshuihe fault, a tectonically active and mountainous region with severe secondary earthquake disasters. To better understand the seismogenic mechanism and provide scientific support for future hazard mitigation, we summarize the preliminary results of the Luding earthquake, including seismotectonic background, seismicity and mainshock source characteristics and aftershock properties, and direct and secondary damage associated with the mainshock. The peak ground displacements in the NS and EW directions observed by the nearest GNSS station SCCM are ～35 mm and ～55 mm, respectively, resulting in the maximum coseismic dislocation of 20 mm along the NWW direction, which is consistent with the sinistral slip on the Xianshuihe fault. Back-projection of teleseismic P waves suggest that the mainshock rupture propagated toward south-southeast. The seismic intensity of the mainshock estimated from the back-projection results indicates a Mercalli scale of VIII or above near the ruptured area, consistent with the results from instrumental measurements and field surveys. Numerous aftershocks were reported, with the largest being M_S 4.5. Aftershock locations (up to September 18, 2022) exhibit 3 clusters spanning an area of 100 km long and 30 km wide. The magnitude and rate of aftershocks decreased as expected, and the depths became shallower with time. The mainshock and two aftershocks show left-lateral strike-slip focal mechanisms. For the aftershock sequence, the b-value from the Gutenberg-Richter frequency-magnitude relationship, h-value, and p-value for Omori’s law for aftershock decay are 0.81, 1.4, and 1.21, respectively, indicating that this is a typical mainshock-aftershock sequence. The low b-value implies high background stress in the hypocenter region. Analysis from remote sensing satellite images and UAV data shows that the distribution of earthquake-triggered landslides was consistent with the aftershock area. Numerous small-size landslides with limited volumes were revealed, which damaged or buried the roads and severely hindered the rescue process.     

Aftershocks hazard in Italy Part I: Estimation of time-magnitude distribution model parameters and computation of probabilities of occurrence

We analyzed the available instrumental data on Italian earthquakes from1960 to 1996 to compute the parameters of the time-magnitudedistribution model proposed by Reasenberg and Jones (1989) andcurrently used to make aftershock forecasting in California. From 1981 to1996 we used the recently released Catalogo Strumentale deiTerremoti `Italiani' (CSTI) (Instrumental Catalog Working Group, 2001)joining the data of the Istituto Nazionale di Geofisica e Vulcanologia(INGV) and of the Italian major local seismic network, with magnituderevalued according to Gasperini (2001). From 1960 to 1980 we usedinstead the Progetto Finalizzato Geodinamica (PFG) catalog(Postpischl, 1985) with magnitude corrected to be homogeneous with thefollowing period. About 40 sequences are detected using two differentalgorithms and the results of the modeling for the corresponding ones arecompared. The average values of distribution parameters (p= 0.93±0.21, Log₁₀(c) = –1.53±0.54, b = 0.96±0.18 and a = –1.66±0.72) are in fair agreementwith similar computations performed in other regions of the World. We alsoanalyzed the spatial variation of model parameters that can be used topredict the sequence behavior in the first days of future Italian seismic crisis,before a reliable modeling of the ongoing sequence is available. Moreoversome nomograms to expeditiously estimate probabilities and rates ofaftershock in Italy are also computed.     

基于速率-状态依从摩擦定律的前郭震群余震活动率及模型参数相关性研究

基于速率-状态依从摩擦定律的地震活动率时空预测模型,以同震库伦应力变化作为模型初始应力扰动,模拟了2013年吉林前郭MS5.8震群的余震活动率变化。考虑模型参数相关性,在模拟中采用2种不同的拟合方案,一是余震持续时间t_a不固定条件下的拟合,二是余震持续时间t_a固定条件下的拟合。结果显示,t_a不固定条件下的拟合方式可获得较好的AIC评价,适用于震后早期的趋势判定; t_a固定条件下的拟合计算耗时更短,拟合误差更小,理论模拟结果与前郭震群实际地震时序特征更为吻合。采用该方案对截至2016年10月24日的余震活动率变化进行了回溯性预测检验,结果显示模型预期的余震日频次与实际记录呈较好的正相关关系。研究还发现,主震破裂面附近的同震应力影区导致震后早期模型预测值相对于实际偏低,说明前郭序列余震活动可能还存在其他触发机制。     

基于Gutenberg-Richter定律快速估算最大余震震级:以2017年九寨沟MS7.0地震为例

针对九寨沟M_S7.0地震之后不同时间段的余震序列目录,利用推定最大余震震级,给出了实际最大余震震级的估计值。结果表明,推定最大余震震级随主震后时间尺度的延长而趋于稳定,且该值与实际发生的最大余震的震级一致。需要强调的是,就九寨沟地震序列而言,当余震数据较为完备时,采用主震后较短时间段内（1～2天）的余震目录就可以较准确地估算出主震区域内可能发生的最大余震震级。实际上,主震后12h（0.5天）的余震数据已完全可以给出最大余震震级的有效下限。此外,计算中我们采用了里氏震级M_L和面波震级M_S的余震目录,结果显示,2种震级类型目录的估算结果完全一致,表明利用推定最大余震震级估算实际最大余震震级的方法不受震级类型的影响。据此,该最大余震震级快速评估方法可进一步推广应用于我国大陆地区中强震后强余震灾害分析评估中。目前的拟合技术也显示出随着测震技术的不断进步以及余震识别能力的提高,快速评估方法可以在主震后短时间（<1天）内准确地预测可能发生的最大余震震级。     

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.     

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.     

Analysis of aftershock sequences in South and Southeastern Spain

A probabilistic modeling is used to analyze the spatio-temporal behavior of eleven aftershock sequences occurred in South and Southeastern Spain. This study focuses on the analysis of two seismicity parameters: the b-value of the frequency-magnitude distribution, and the p-value, explaining the temporal decay rate of aftershocks. The estimated b values range between 0.77 ± 0.05 and 1.18 ± 0.10 close to the typical b-values of the aftershock frequency-magnitude relationship b ≈ 1.0. The estimated p-values range between 0.75 ± 0.03 and 1.43 ± 0.10 showing broad regimes of the temporal decay of aftershocks. The modified Bath’s law used to analyze the energy partitioning, suggests that a large fraction of the accumulated energy is released in the mainshock and relatively small fraction of energy is released during aftershock sequence, for example 80% of the total energy is released during the Mula 1999 mainshock, 88% during Bullas 2002 mainshock and 87% during La Paca 2005 mainshock. The fractal dimension D₂ is estimated using the correlation integral, and then used to derive the slip ratio, as the ratio of the slip occurred on primary fault segment to the total slip. For example, we obtained a slip ratio equal to 71% for the Mula 1999 aftershock sequence, 61% for the Bullas 2002 event, 58% for the La Paca 2005 aftershock, 50% for the Lorca 2011 sequence and 63% for the sequence triggered by the Gador 2002 mainshock.Finally, the correlations between the fractal dimension, the b-value and the p-value is analyzed, and the Aki’s relation D = 3b/c is discussed as well.     

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.     

传染型余震序列模型震后早期参数特征及其地震学意义

研究中国大陆地区中强地震序列震后早期阶段（震后15天）ETAS模型参数的平均统计特征，据此讨论不同统计条件下的序列衰减及余震激发问题.宏观而言，模型参数b、p、α数值分布较为离散，不同统计条件下模型参数平均值的差异显著性不十分突出.详细对比不同统计条件下模型参数平均值的微小差异，b值随主震震级增大而增大，但b值随不同区域、不同主震断层类型或不同序列类型的变化不明显.p、α具有一定的区域特征，西南、西北p值略低于新疆及华北，表明西南、西北序列衰减相对较慢而新疆、华北序列衰减相对较快，华北α较低而西北α相对最高，意味着尽管华北序列衰减相对较快，但其激发高阶余震的能力却相对强，西北尽管序列衰减较慢，但序列结构单一，激发高阶余震的能力弱.p与主震断层类型关系不明显，即主震破裂性质不是决定序列衰减快慢的主要因素；α与主震断层类型有一定关系，走滑-近走滑型破裂所导致序列的α值最小、斜滑型次之、倾滑-近倾滑型最大，表明走滑-近走滑型序列激发高阶余震的能力最强、逆冲型最弱、斜滑型居中.p、α随主震震级增大而减小，意味着主震震级越高则序列衰减越慢、激发高阶余震的能力越强.不同类型序列p、α有一定差异，主余型序列p最小、孤立型p最大，表明相对而言主余型序列衰减最慢、孤立型序列衰减最快、多震型序列衰减速率居中.孤立型序列与主余型序列α大体一致、大于多震型序列的α值，即多震型序列激发高阶余震的能力相对最强，孤立型及主余型序列则相对较弱.     

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.     

The partitioning of radiated energy and the largest aftershock of seismic sequences occurred in the northeastern Italy and western Slovenia

We analyzed the most relevant seismic sequences that occurred from 1977 to 2007 in the Friuli-Venezia Giulia region (northeastern Italy) and western Slovenia. The eight aftershock sequences were triggered by low- to moderate-magnitude earthquakes with mainshock duration magnitude ranging from 3.7 to 5.6. The b-value of the Gutenberg–Richter law varies from 0.8 to 1.1. The modified Omori’s modeling of the sequences evidences values of the p exponent ranging from 0.8 to 1.0. Using the Reasenberg and Jones (Science 243:1173–1176, 1989; Science 265:1251–1252, 1994) approach, we computed the probabilistic estimate of the aftershock rates and the largest aftershock in given time intervals. The difference in magnitude between the mainshock and the largest aftershock is calculated according to the modified Båth law and using an approach that considers the partitioning of the radiated seismic energy between mainshock and aftershocks. The partitioning of the radiated seismic energy appears to play a significant role in the evolution of the sequences. We define the parameter R _ES as the ratio between the radiated seismic energy of the mainshock and the summation of the seismic energy radiated by the aftershocks. The difference in magnitude between the mainshock and the largest aftershock, calculated with the parameter R _ES, agrees well with the observed difference. In most sequences, the parameter R _ES decreases very quickly until the occurrence of the largest aftershock and then becomes constant. By analyzing the values of R _ES during the early hours following the mainshock, we found that the R _ES values after 24 h are well related to the final ones, calculated on the whole sequence, and to the differences in magnitude between the mainshock and the largest aftershock.     

Seismic anomalies in the aftershock sequence of November 16, 2000, in Papua New Guinea

The study of seismic anomalies, related both to the temporal trend of aftershock sequences and to the temporal series of mainshocks, is important for an understanding of the physical processes relating to the existence and the characteristics of seismic precursors. The purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay of an aftershock sequence. It is realized by means of several parameters. We focused our work on an analysis of the Papua New Guinea seismic sequence that occurred on November 16, 2000. The magnitude of the mainshock is M = 8.2. The observed temporal series of shocks per day can be considered as a sum of a deterministic contribution and a stochastic contribution. If the decay can be modeled as a nonstationary Poisson process where the intensity function is equal to n(t) = K(t + c)^−p + K ₁, the number of aftershocks in a small time interval Δt is the mean value n(t)Δt, with a standard deviation σ = √n(t)Δt. We observe that there are some variations in seismicity that can be considered as seismic anomalies before the occurrence of a large aftershock. The data, checked according to completeness criteria, come from the website of the USGS NEIC data bank (). The text was submitted by the authors in English.     

Normalized residual displacement spectra for post-mainshock assessment of structures subjected to aftershocks

Residual displacement, as a significant measure of structural inelasticity, is effectively used in post-earthquake seismic assessment of structures. This demand can be considered for seismic evaluation of structures under multiple earthquakes. This study introduces a simple and novel index to predict the residual displacement of mainshock-damaged structures against subsequent aftershock. The proposed index is defined as a ratio between residual displacement of damaged structures against aftershock and peak inelastic displacement of intact structures under mainshock. In this study, constantstrength spectra based on the index are developed considering the effects of important structural characteristics and also significant seismic parameters. Moreover, analytical equations are presented to predict the proposed index for bi-linear single-degree-of-freedom(SDOF) systems considering both the effects of positive and negative polarities of aftershock. Furthermore, an equation is suggested to estimate the peak inelastic displacement of intact systems under mainshock, which is required to compute the index.     

2014年于田MS7.3地震对后续余震和远场小震活动的动态应力触发

本文采用离散波数法,计算了2014年于田M_S7.3地震的断层破裂在近场和远场产生的库仑破裂应力变化,并结合地震活动特征,讨论了M_S7.3地震对后续余震活动和远场区域小震活动的动态应力触发作用.结果表明, ① M_S7.3地震产生的库仑破裂应力变化对其西南侧主体余震区的地震活动起到了抑制作用,这可能是本次M_S7.3地震序列余震活动水平不高的主要原因;距主震约30 km的北东方向余震区后续地震活动受到了主震产生的动态和静态应力变化的共同触发作用,动态应力变化峰值为2.78 MPa,静态应力变化为0.80 MPa,这与该区余震较为活跃相一致;距主震约45 km的北部余震区受到动态应力触发作用,应力变化峰值为0.72 MPa. ② M_S7.3地震产生的动态库仑应力变化空间分布呈非对称性,其中北东方向、北部余震分布与动态应力变化正值区存在相关性,从应力变化的角度解释了M_S7.3地震的后续余震空间活动特征. ③ M_S7.3地震在沙雅、伽师地区的远场接收点产生的动态应力变化峰值分别为0.09 MPa、0.1 MPa,对两个区域的小震活动具有动态触发作用.