最大熵原理在地震时间间隔和震级分布中的应用

基于最大熵原理,得到地震时间间隔和地震震级的概率分布函数。根据时间间隔分布,得到地震发震概率,当概率上升达到警界值时,可对云南5级以上中强地震做出预测。6个月以内中短期预测对应率为91％;3个月以内,短临期预测对应率为73％。根据震级分布,得到用最大熵原理求出的地震理论发生次数,理论发震次数与实际较为接近。用最大熵原理求出了云南不同地区不同震级档次5级以上中强地震的复发周期。分析认为,云南7级以上大震危险性在逐步逼近,西部危险性高于东部。     

The use of the Akaike Information Criterion in the identification of an optimum flood frequency model

Abstract

For a long time now, the hydrologist has been faced with the problem of finding which of the many possible probability distribution functions can be used most effectively in flood frequency analyses. This problem has been mainly due to the insufficiency of the conventional goodness-of-fit procedures when used with the typically skewed flood probability distributions. In this study, the Akaike Information Criterion (AIC) goodness-of-fit test is used to identify more objectively the optimum model for flood frequency analysis in Kenya from a class of competing models. The class is comprised of (a) seven three-parameter density functions, namely, log-normal, Pearson, log-Pearson, Fisher-Tippet, log-Fisher-Tippet, Walter Boughton and log-Walter Boughton; and (b) two five-parameter density functions, namely, Wakeby and log-Wakeby. The AIC is also used in this study as a method of testing for the existence of outlier peak-flow values in the peak annual data used. A modified version of the chi-square goodness-of-fit test is also used, but only for the sake of comparison with the AIC.     

Probabilities of occurrence of large earthquakes in the Aegean and surrounding area during the period 1986–2006

Repeat times of large shocks are obtained for 17 seismic fracture zones of the Aegean and surrounding area, from times of historic and present century earthquakes. The mean standard deviation of the repeat times is approximately 50% of any one observation.A probabilistic approach is then used to forecast the likelihood of large future earthquakes in each fracture zone, using as input the time of the last large shock, the average repeat time and its standard deviation. Shallow and intermediate depth earthquakes are examined separately. The calculated probabilities are high for the entire Hellenic arc, both for shallow and intermediate depth seismicity, for the area of Leucas island (Ionian), of Lesbos island (Aegean), for Patraikos-west Corinthiakos Gulfs, for Evoikos Gulf as well as for southern Bulgaria.The probability estimates based on the most recent large earthquakes, involve a number of basic physical assumptions and we would think that they provide a semi-stochastic approach to the problem of earthquake prediction in Greece.     

Deformation and stress regimes in the Hellenic subduction zone from focal Mechanisms

Fault plane solutions for earthquakes in the central Hellenic arc are analysed to determine the deformation and stress regimes in the Hellenic subduction zone in the vicinity of Crete. Fault mechanisms for earthquakes recorded by various networks or contained in global catalogues are collected. In addition, 34 fault plane solutions are determined for events recorded by our own local temporary network on central Crete in 2000–2001. The entire data set of 264 source mechanisms is examined for types of faulting and spatial clustering of mechanisms. Eight regions with significantly varying characteristic types of faulting are identified of which the upper (Aegean) plate includes four. Three regions contain interplate seismicity along the Hellenic arc from west to east and all events below are identified to occur within the subducting African lithosphere. We perform stress tensor inversion to each of the subsets in order to determine the stress field. Results indicate a uniform N-NNE direction of relative plate motion between the Ionian Sea and Rhodes resulting in orthogonal convergence in the western forearc and oblique (40–50^∘) subduction in the eastern forearc. There, the plate boundary migrates towards the SE resulting in left-lateral strike-slip faulting that extends to onshore Eastern Crete. N110^∘E trending normal faulting in the Aegean plate at this part is in accordance with this model. Along-arc extension is observed on Western Crete. Fault plane solutions for earthquakes within the dipping African lithosphere indicate that slab pull is the dominant force within the subduction process and responsible for the roll-back of the Hellenic subduction zone.     

Mixed model for interoccurrence times of earthquakes based on the expectation-maximization algorithm

In this paper, the goodness-of-fit test based on a convex combination of Akaike and Bayesian information criteria is used to explain the features of interoccurrence times of earthquakes. By analyzing the seismic catalog of Iran for different tectonic settings, we have found that the probability distributions of time intervals between successive earthquakes can be described by the generalized normal distribution. This indicates that the sequence of successive earthquakes is not a Poisson process. It is found that by decreasing the threshold magnitude, the interoccurrence time distribution changes from the generalized normal distribution to the gamma distribution in some seismotectonic regions. As a new insight, the probability distribution of time intervals between earthquakes is described as a mixture distribution via the expectation-maximization algorithm.     

Mediterranean island arcs and origin of high potash volcanoes

Active volcanoes of the Mediterranean Sea are distributed along two arc structures: the Hellenic arc in the Aegean Sea and the Calabrian arc in the Tyrrhenian Sea. The active volcanoes in both arcs lie above earthquakes with focal depth greater than 100 km. The depth of these earthquakes increases generally northward reaching a maximum depth of about 200 km in the Aegean Sea and more than 300 km in the Tyrrhenian Sea.     

Seismic hazard of the Eastern Mediterranean

Earthquake hazard parameters such as maximum magnitude, annual mean seismic activity rate, and the Gutenberg-Richter parameter, have been evaluated for the Hellenic and Cyprean Arc regions of the Eastern Mediterranean. The applied maximum likelihood procedure permits the combination of both historical and instrumental data. The collected data from different sources cover earthquakes with magnitude ≥ 3.5 throughout the last two centuries. The historical part of the catalogue only contains the strongest events, whereas the complete part can be divided into several subcatalogues, each assumed complete above a specific threshold of magnitude. The hazard parameters assessment is performed for the two study regions. The Hellenic Arc region was found to be of higher seismicity level than the Cyprean Arc region. The number of annually expected earthquakes with magnitude ≥ 3.5 is much larger in the Hellenic Arc (56±2) than in the Cyprean Arc (35±2). The maximum magnitude calculated in the Hellenic Arc zone is 7.8±0.4 for the time period equal to the length of the catalogue, i.e., 210 years. For the Cyprean Arc zone, the maximum possible magnitude is 6.8±0.4 for the time span of 330 years.     

Determination of probability distributions for Strahler stream lengths based on Poisson process and DEM

Abstract

One of the basic tasks in geomorphologic analysis is to know the probability distributions of the stream lengths of different orders. In practical applications, this information is useful for basin rainfall-runoff modelling. The objective of this study is to determine the length distributions of the Strahler streams. A Poisson process was used to derive the theoretical distributions. The result showed that the length distribution of the first-order stream is an exponential distribution and the second-order or higher order stream length is a gamma distribution. In order to verify the theoretical distributions, a digital elevation model (DEM) was adopted to calculate the stream lengths of four basins in Taiwan. Kolmogorov-Smirnov and chi-square tests were used to test the goodness-of-fit of the data. Results showed that the length distributions of the first- and second-order streams analysed by using DEM correspond with those from the derived distribution method.     

中国大陆地震空间分布模型检验

本文以中国大陆地震目录为基础资料,以泊松模型为零假设模型,并将Neyman-Scott空间丛集过程的各子模型设为检验模型,采用K-function点过程分析法和最大似然估计法计算各模型参数,并以AIC准侧判定模型的拟合优度,来检验中国大陆地震空间分布模型.检验结果表明:泊松模型的拟合优度最差,说明地震在空间的分布不是完全随机的;广义Thomas模型的拟合优度最好,说明地震的空间分布是丛集的,可用由两个高斯核组成的广义Thomas模型较好地描述.研究结果还表明,同一研究区内,采用不同时段具有不同最小完整起始震级的地震目录计算得到的地震空间分布的丛集尺度几乎不变,这意味着地震空间丛集尺度不受小地震的控制,且可能与研究区的断层规模有关.     

Regional focal mechanisms for earthquakes in the Aegean area

The distribution of the focal mechanisms of the shallow and intermediate depth (h>40 km) earthquakes of the Aegean and the surrounding area is discussed. The data consist of all events of the period 1963–1986 for the shallow, and 1961–1985 for the intermediate depth earthquakes, withM _s 5.5. For this purpose, all published fault plane solutions for each event have been collected, reproduced, carefully checked and if possible improved accordingly. The distribution of the focal mechanisms of the earthquakes in the Aegean declares the existence of thrust faulting following the coastline of southern Yugoslavia, Albania and western Greece extending up to the island of Cephalonia. This zone of compression is due to the collision between two continental lithospheres (Apulian-Eurasian). The subduction of the African lithosphere under the Aegean results in the occurrence of thrust faulting along the convex side of the Hellenic arc. These two zones of compression are connected via strike-slip faulting observed at the area of Cephalonia island. TheP axis along the convex side of the arc keeps approximately the same strike throughout the arc (210° NNE-SSW) and plunges with a mean angle of 24° to southwest. The broad mainland of Greece as well as western Turkey are dominated by normal faulting with theT axis striking almost NS (with a trend of 174° for Greece and 180° for western Turkey). The intermediate depth seismicity is distributed into two segments of the Benioff zone. In the shallower part of the Benioff zone, which is found directly beneath the inner slope of the sedimentary arc of the Hellenic arc, earthquakes with depths in the range 40–100 km are distributed. The dip angle of the Benioff zone in this area is found equal to 23°. This part of the Benioff zone is coupled with the seismic zone of shallow earthquakes along the arc and it is here that the greatest earthquakes have been observed (M _s 8.0). The deeper part (inner) of the Benioff zone, where the earthquakes with depths in the range 100–180 km are distributed, dips with a mean angle of 38° below the volcanic arc of southern Aegean.     

Sensitivity analysis of the probability distribution of groundwater level series based on information entropy

Information entropy is an effective method to analyze uncertainty in various processes. The principle of maximum entropy (POME) provides a guide line for the parameter estimation of probability density function (PDF). Mutual entropy analysis is well qualified for delineating the nonlinear and complex multivariable relationship. The probability distribution of model output is the element of model uncertainty analysis. In this paper, a synthetic groundwater flow field is build to produce groundwater level series (GLS). The probability distribution of GLS is obtained by the frequency analysis method based on POME and Chi-Squared test. The important uncertainty factors that affect the parameters of PDF of GLS are assessed by the sensitivity analysis methods, which include stepwise regression analysis and mutual entropy analysis. Results of this analysis indicate that most of the GLS follow normal distribution (or log-normal distribution), while a few obey others. The mean and variance of normal GLS are affected differently by the input variables of groundwater model. Mutual entropy analysis is more competitive and appropriate for delineating the nonlinear and nonmonotonic multivariable relationship than stepwise regression analysis.     

Local Tsunamis and Distributed Slip at the Source

—Variations in the local tsunami wave field are examined in relation to heterogeneous slip distributions that are characteristic of many shallow subduction zone earthquakes. Assumptions inherent in calculating the coseismic vertical displacement field that defines the initial condition for tsunami propagation are examined. By comparing the seafloor displacement from uniform slip to that from an ideal static crack, we demonstrate that dip-directed slip variations significantly affect the initial cross-sectional wave profile. Because of the hydrodynamic stability of tsunami wave forms, these effects directly impact estimates of maximum runup from the local tsunami. In most cases, an assumption of uniform slip in the dip direction significantly underestimates the maximum amplitude and leading wave steepness of the local tsunami. Whereas dip-directed slip variations affect the initial wave profile, strike-directed slip variations result in wavefront-parallel changes in amplitude that are largely preserved during propagation from the source region toward shore, owing to the effects of refraction. Tests of discretizing slip distributions indicate that small fault surface elements of dimensions similar to the source depth can acceptably approximate the vertical displacement field in comparison to continuous slip distributions. Crack models for tsunamis generated by shallow subduction zone earthquakes indicate that a rupture intersecting the free surface results in approximately twice the average slip. Therefore, the observation of higher slip associated with tsunami earthquakes relative to typical subduction zone earthquakes of the same magnitude suggests that tsunami earthquakes involve rupture of the seafloor, whereas rupture of deeper subduction zone earthquakes may be imbedded and not reach the seafloor.     

首都圈地区地震时间序列的最大熵谱分析方法及地震危险性预测

利用最大熵谱分析方法和最大熵原理方法,对首都圈（北纬38°～42°,东经113°～120°）1484年以来发生5．0级以上地震的时间序列资料进行了分析,结果表明,首都圈地区历史上5．0级以上地震存在12．9年的卓越周期,并且在今后50年内,发生5．0≤Ms〈6．0和6．0≤Ms〈7．0地震的概率分别是0．9907和0．6916,发生7．0≤Ms〈8．0地震的概率较低,只有0．2564发生Ms≥8．0地震的概率最低。仅为0．0718。     

Seismic wave attenuation in the upper Mantle beneath the Aegean region

A detailed study of P and S waves from earthquakes located along the Hellenic arc and recorded by the Greek seismological network, shows an abnormal distribution of the seismic waves in the central Aegean Sea. The data indicate a zone of anomalously high seismic wave attenuation in the Upper Mantle beneath the Cyclades plateau and the inner part of the volcanic arc. Several independent observations suggest the presence of magma beneath the Cyclades massif.In addition, geophysical data indicate the presence of low-density and rigidity material. Theoretical consideration of the propagation of elastic waves corroborate the observed absence of shear waves.     

Segmentation of Active Faults and Risk Probability Prediction of Strong Earthquakes in Sichuan Province

Based on geometric structure,active strength,and maximum seismic rupture length along the fault in the late Quaternary or Holocene,this paper presents the segmentation of main active faults in Sichuan Province and uses the recurrence probability model to predict the recurrence probabilities of strong earthquakes along each segment during next 30 years.The results indicate that earthquakes with M=7.0 or greater may happen along Qiajiao segment,Qianning segment,and Selaha segment of Xianshuihe fault zone,the segment from Xichang to Mianning and Yejidong segment of Anninghe fault zone; earthquakes with M=6.0 or greater may happen along the segment from Maowen to Caopuo of Longmenshan fault zone and Xiaoyanjing segment of Anninghe fault zone.     

Bayesian probabilities of earthquake occurrences in Greece and surrounding areas

The Bayesian extreme-value distribution of earthquake occurrences has been adopted to estimate the seismic hazard in some seismogenic zones in Greece and surrounding regions. Seismic moment, slip rate, earthquake recurrence rate and magnitude were considered as basic parameters for computing the prior estimates of the seismicity. These estimates are then updated in terms of Bayes' theorem and historical estimates of seismicity associated with each zone.High probabilities for earthquakes withM6.0 have been obtained for the northwestern part of Greece as well as for the southwestern part of the Hellenic arc.     

Maximum entropy-Gumbel-Hougaard copula method for simulation of monthly streamflow in Xiangxi river,China

A maximum entropy-Gumbel-Hougaard copula (MEGHC) method has been proposed for monthly streamflow simulation. The marginal distributions of monthly streamflows are estimated through the maximum entropy (ME) method with the first four non-central moments (i.e. mean, standard deviation, skewness and kurtosis) being the constraints. The Lagrange multipliers in ME-based marginal distributions are determined using the conjugate gradient (CG) method which is of superlinear convergence, simple recurrence formula and less calculation. Then the joint distributions of two adjacent monthly streamflows are constructed using the Gumbel-Hougaard copula (GHC) method. The developed MEGHC method has been applied for monthly streamflow simulation in Xiangxi river, China. The goodness-of-fit statistical tests, consisting of K–S test, A–D test, RMSE and Rosenblatt transformation with Cramér von Mises statistic, show that the MEGHC method can reflect dependence structure in adjacent monthly streamflows of Xiangxi river, China. Comparison between simulated streamflow generated by MEGHC and observations indicates the satisfactory performance of MEGHC with small relative errors.     

A long-term earthquake forecast for the Kuril-Kamchatka arc for the period from September 2011 to August 2016. The likely location,time, and evolution of the next great earthquake with M ≥ 7.7 in Kamchatka

We consider the results from the ongoing 2010–2011 work on long-term earthquake prediction for the Kuril-Kamchatka arc based on the pattern of seismic gaps and the seismic cycle. We develop a forecast for the next 5 years, from September 2011 to August 2016, for all segments of the Kuril-Kamchatka arc earthquake-generating zone. For 20 segments we predict the appropriate phases of the seismic cycle, the normalized rate of small earthquakes (A₁₀), the magnitudes of moderate earthquakes to be expected with probability 0.8, 0.5, and 0.15, and the maximum possible magnitudes and probability of occurrence for great (M ≥ 7.7) earthquakes. This study serves as another confirmation that it is entirely necessary to continue the work in seismic retrofitting in the area of Petropavlovsk-Kamchatskii.     

Recurrence characteristics of late-quaternary strong earthquakes on the major active faults along the northern border of Ordos block

Through study on trenches, analysis of recurrence characteristics and recurrence interval cluster/gap of strong earthquakes along the major active faults on the northern border of Ordos block, we found 62 paleoearthquakes that occurred in the late Quaternary, including 33 earthquakes occurring in the Holocene. The recurrence characteristics of the paleoearthquakes are different at three levels, segments, faults, and fault zones. The strong seismic sequence on the independent segments is mostly characterized by long- and short-interval recurrences, while that on the faults and in fault zone is characterized clearly by random and cluster recurrences. Results of the moving window test indicate that the probabilities of "temporal cluster or gap", caused by random coincidence as opposed to intersegment contagion, are 64% and 70% for the Serteng piedmont fault and for the south-border fault of Wula Mountains, respectively, no clear interaction among the segments of each fault; while the probability is 26.8% for the whole fault zone, suggesting a clear interaction among the faults of this fault zone. These recurrence characteristics may imply an effect of the entire block motion on the recurrence of strong earthquakes. Moreover, the elapsed time for the Wujumeng Pass-Dongfeng Village segment of Serteng piedmont fault and the Tuzuo Banner-Wusutu and the Hohhot segments of Daqingshan piedmont fault has exceeded the average recurrence interval, hence these three segments may be the possible places for future strong earthquakes.     

全球强震与地球自转角加速度变化过程关系统计研究

统计分析了1962—2017年全球强震活动与地球自转角加速度变化过程的关系, 结果显示, 全球8级以上地震发生在地球自转角加速度下降期的概率相对自然概率高出12%, 达到64%, 统计结果具有显著性, 但7.5级和7.8级以上地震的统计结果没有显著性。 分区统计结果表明, 全球强震活动具有明显的区域性特征: 在地球自转角加速度上升期, 高于自然概率的强震主要分布在阿尔卑斯带中西段、 环太平洋地震带的琉球—菲律宾地区以及中国东部; 在地球自转角加速度下降期, 高于自然概率的强震主要分布在环太平洋地震带、 阿尔卑斯带中段(喜马拉雅弧)、 阿尔卑斯带东段(印尼岛弧海沟)以及中亚大陆地区。 分析认为地球自转角加速度变化过程与全球区域地震活动之间存在较强的相关性, 可能与地球自转角加速度变化引起板块间相互作用的强弱有关。