R/S分析法在南水北调西线一期工程调水河流径流趋势预测中的应用

南水北调西线一期工程主要是从雅砻江支流鲜水河的达曲、泥曲和大渡河的支流色曲、杜柯河、玛柯河、阿柯河等6条河流上引水40×10⁸m³·a^-1,约占河道年径流的60%~70%,剩余大约30%~40%的径流主要用于河道的生态环境需水.由此可见,这些河流的径流多少直接关系着调水工程的实施.利用域重标度分析法(R/S分析)对这6条支流附近的水文站的径流趋势进行了初步分析,结果表明:大渡河支流的绰斯甲、足木足、泥曲的朱巴、雅砻江的甘孜等水文站月径流序列的赫斯特系数分别为0.4090、0.3884、0.4487、0.4271,都<0.5,即这些径流序列具有反持续性,甘孜和足木足站的径流量将会增加;朱巴、绰斯甲两站的径流将会减少,这对西线调水工程的实施是不利的.     

河流年径流量的R/S灰色预测

径流过程具有分形和灰色特征。基于此,将R/S分析与灰色系统理论相结合,提出了R/S灰色预测模型以预报河流年径流量。针对黑河正义峡水文站60a(1949~2011年)的年径流量资料,首先进行R/S分析,确定径流量序列的Hurst指数H和平均循环周期T;然后在一个周期内进行年径流量灰色预测。结果表明:R/S灰色预测结果的精度明显高于直接进行灰色预测的精度。该方法拓宽了分形和灰色理论在径流过程研究的应用范围,为河流径流量的科学预测提供了一种新方法。     

成矿元素品位有序数据集自仿射分形方法应用性评价

自仿射分形的Hurst指数是分析地质剖面数据的有利参数。以大尹格庄金矿不同勘探线刻槽取样所得的金品位序列为例，评价Hurst指数的几种估算方法在地质剖面数据分析中的适用性。取相同尺度，全部数据集的增量标准偏差法统计散点呈波状变化，部分数据集的曲线长度变换法统计散点的后半部分呈波状变化,全部数据集的重标极差分析法统计散点线性拟合较好。结果显示增量标准偏差法对尺度要求较为苛刻，适于巨量数据的统计；曲线长度变换法应用性较广，所得Hurst指数反映品位的空间变化强度；重标极差分析法稳定性最好，其Hurst指数反映了品位变化相依性。      

Trend predictions in water resources using rescaled range (R/S) analysis

Based on historical and observational data of wet-and-low water resource changes, this article used the rescaled range (R/S) analysis principle and method to calculate the H index and establish the relation formula of R(i)/S(i) and i. Based on {x _i }, and by using the least squares method, a new time series calculation method was proposed which endows the Brownian motion equation with forecasting abilities. This is a new attempt to forecast trend changes of water resources. Utilizing the time series data of water resources in Jinhua City, China, and the Brownian motion equation, aforecast was made of future trends in wet-and-low water resource changes. Satisfactory validation results were obtained, which indicate that this is an effective method for forecasting water resource changes.     

基于Hurst指数的矿化强度识别－以山东大尹格庄金矿为例

探索成矿元素分布的分形特征是揭示矿化富集程度的重要途径之一。运用重标极差分析（R/S）方法,研究了山东大尹格庄金矿-210 m中段多勘探线Au品位序列随采样尺度变化的趋势,探讨元素序列的Hurst指数与矿化强度的关系。结果显示:具有不同矿化强度的勘探线Au的Hurst指数存在明显差异,且均大于0.5;矿化连续分布或间断出现的勘探线元素品位序列的Hurst指数大于0.65,表明元素序列具有标度不变性和长相关性,序列的持续强度与矿化程度基本一致,可为区域矿化强度定量识别提供一种新的有效方法。     

山东大尹格庄金矿蚀变岩中矿体分布稳定性的动力学控制参量探讨

元素品位分布的相依性指标——赫斯特指数(Hurst指数)是矿体分布稳定性的动力学控制参量,重标极差(R/S)分析是相依性分析的有效方法。利用R/S分析对胶东大尹格庄金矿黄铁绢英岩内不同勘探线金元素品位系列的Hurst指数计算发现,Hurst指数主要介于0.59至0.89之间,均值为0.75,标准差为0.09,均大于随机行走经验Hurst指数的均值与标准差;计算结果说明元素品位分布存在正相关性,但由于受多种因素影响,其空间分布的相依性具有一定波动。元素品位分布的正相依性显示在特定的地质背景内,矿体连续分布或者间断出现,发育相对稳定,其与大尹格庄金矿的地质事实相吻合。     

R／S分析及矿井瓦斯涌出量的分形预测

介绍了分形理论中的时间序列（R／S）分析方法，讨论了赫斯特指数的理论意义和实际计算方法，并将其应用于矿井瓦斯涌出量预测。通过对矿井瓦斯涌出量时间序列的分形处理，根据极差、标准差的结构分维值的大小，对矿井瓦斯涌出量的增量趋势做了分形预测。     

Prediction of rainfall using artificial neural networks for synoptic station of Mashhad: a case study

In this paper, we have utilized ANN (artificial neural network) modeling for the prediction of monthly rainfall in Mashhad synoptic station which is located in Iran. To achieve this black-box model, we have used monthly rainfall data from 1953 to 2003 for this synoptic station. First, the Hurst rescaled range statistical (R/S) analysis is used to evaluate the predictability of the collected data. Then, to extract the rainfall dynamic of this station using ANN modeling, a three-layer feed-forward perceptron network with back propagation algorithm is utilized. Using this ANN structure as a black-box model, we have realized the complex dynamics of rainfall through the past information of the system. The approach employs the gradient decent algorithm to train the network. Trying different parameters, two structures, M₅₃₁ and M₇₄₁, have been selected which give the best estimation performance. The performance statistical analysis of the obtained models shows with the best tuning of the developed monthly prediction model the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) are 0.93, 0.99, and 6.02 mm, respectively, which confirms the effectiveness of the developed models.     

遗传模拟退火的BP算法在冲击地压中的应用

冲击地压的预测、预报的研究,大多数仍停留在简单的统计研究和单因素的预测方面,因而,结果也不十分理想。笔者采用多层前向网络对该问题进行数学建模,网络的训练算法采用基于遗传模拟退火的BP优化算法。该算法是在遗传算法中引入模拟退火机制,将其同BP算法结合,形成一个混合的优化算法。新算法既有神经网络的学习能力和鲁棒性,又有遗传算法的强全局随机搜索能力。同时,利用华丰矿冲击地压的实际监测数据,通过遗传算法的主要性能指标对新算法的参数进行了比较研究,得到优化后的一组参数。利用该参数,对冲击地压的神经网络模型的结构、权值和阈值进行了优化,得到了非全连接的优化神经网络模型。最后,利用该模型对华丰矿冲击地压进行了短期最大震级的预报。预测结果的相对误差率平均为 7.84 %,预测效果比较理想。     

Verhulst滑坡预测预报模型的改进及其应用

Verhulst生物生长模型是一种统计型的滑坡预测预报模型,针对原始Verhulst模型中把第一个数据点作为已知条件的理论依据不存在,可能导致预报精度较低问题,将前人改进Verhulst模型的方法应用到滑坡预测预报中,推导出用改进模型和速度最大值判据预报滑坡发生时间的计算公式。通过分析表明,原始Verhulst模型中以速度最大值作为预报滑坡发生时间的判据缺乏合理性,以加速度和加加速度最大值作为预报判据应更合理,并推导出用加速度和加加速度最大值判据预报的计算公式。基于推导的公式,编写Matlab程序进行计算,将原始和改进的Verhulst模型以及3种判据应用于一些滑坡实例的预报中。结果表明,（1）与原始Verhulst模型相比,改进模型的预报效果较好,其预报滑坡发生的时间更早,且更准确;（2）与速度最大值判据相比,加速度和加加速度最大值判据的预报效果较好,其预报时间较早,且较准确;（3）可把原始模型中单一的时间预报值拓展为一段预报的时间范围,该预报时间范围的上限是加速度最大值时刻,下限是加加速度最大值时刻;（4）用改进模型和该时间段范围判据进行预报能起到提前预报的作用,且预报结果较准确。此外,经讨论认为临近破坏时,裂缝的增多以及动摩擦系数小于静摩擦系数导致抗滑力降低,剩余下滑力增大,是使滑体产生加速度逐渐增大运动的原因。     

Heterogeneities characterization from velocity logs using multifractional Brownian motion

Well logs provide additional information from the borehole that cannot be derived from other subsurface investigations. Their analysis may bring supplementary features about the earth’s heterogeneities. In previous researches, the logs were modeled using fractional Brownian motions indexed by Hurst (or Hölder) exponents quantifying their global regularity degrees. Indeed, these monofractal models, characterized by the same Hurst exponent, do not allow to study the depth-evolution of the local Hurst parameter. In order to overcome this problem, we propose to model the logs using multifractional Brownian motions and suggest an algorithm, developed previously for financial time series, to estimate the local Hurst exponent function. First, the potential of this algorithm is assessed through its application on synthetic sonic log data simulated by the successive random additions method. We note that the estimated Hurst functions (or regularity profiles) are very close to the theoretical Hurst functions. Second, this analysis is extended to sonic logs data from the KTB pilot borehole (Germany). Using the resulted regularity profiles, we carry out a lithological segmentation and fault identification on the geological layers crossed by the well. We derived also a correlation between the Hurst value variation and the lithological changes.     

The probability distributions and fractal dimension of sunspot cycles associated with ENSO phenomena

Various methods have been used to secure the certainty of significant relations among the sunspot cycles and some of the terrestrial climate parameters such as temperature, rainfall, and ENSO. This study investigates the behavior of ENSO cycles and mean monthly sunspot cycles. Sunspot cycles range from 1755 to 2016 whereas, ENSO cycles range from 1866 to 2012. In this regard, the appropriateness of distributions is investigated with the help of Kolmogorov-Smirnov D, Anderson-Darling, and chi-square tests. It is found that most of the sunspot cycle follows generalized Pareto distribution whereas, generalized extreme value distribution was found appropriate for ENSO cycles. Probability distribution is used to analyze the behavior of each sunspot cycle and ENSO cycle separately. Probability distribution indicates the tail behavior of each cycle; tail explored correlation cycles. Furthermore, self-similar and self-affine fractal dimension methods are used to compute Hurst exponents to determine the persistency of the available data. Fractal dimension has an ability to study the complexity involved in sunspot and ENSO cycles. The fractal dimension and Hurst exponent describe persistency (smoothness) and complexity of data. Hurst exponent measures long-term behavior of time series, making it more helpful for forecasting. This is the measure of regularity or irregularity (chaos) of the time function in the form of their persistency or anti-persistency, respectively. Hurst exponents are computed using rescaled range analysis method and box counting methods. Both these methods are suitable for long-term forecasting. The results of this study confirm that during the period 1980–2000, ENSO cycles were very active. Simultaneously, ENSO was active for the periods 1982–1983, 1986–1987, 1991–1993, 1994–1995, and 1997–1998; these periods include two strongest periods of the century viz., 1982–1983 and 1997–1998. Sunspot cycles and ENSO cycles both were found to be persistent. Self-similar fractal dimensions exhibited a better persistency and a better correlation as compared to self-affine fractal dimension. This research is a part of a larger research project investigating the correlation of sunspot cycles and ENSO cycles, and the influence of ENSO cycles on variations of the local climatic parameters which in turn depends on solar activity changes.     

郑州西部山区“7·20”山洪地质灾害成因研究

2021年“7·20”极端暴雨引发河南省郑州市西部山区四市(荥阳、巩义、新密、登封)山洪地质灾害造成251人死亡失踪,分布在44个乡镇140个行政村、组或社区,既具有群发性、分散性,也具有相对集聚性。本次山洪地质灾害分散复杂,流域灾害链和区域灾害群共存,山洪灾害链呈现空间关联、时间接续、动力转换和灾情放大的效应。文章总结了山洪地质灾害时空分布特点,分析了山洪地质灾害的形成因素,探讨了索河流域邢门堂垴跨沟路基阻水溃决-王宗店暴洪冲淹-崔庙村海沟寨公路路基堰塞淹没等山洪灾害链的成因,研究了王宗店村南头组滑坡顺层滑移的地质力学模式及其稳定性与力学参数的关系。初步提出当前期过程或日降雨量达到200 mm,未来1 h预报雨量超过40 mm,或3 h预报雨量超过100 mm,可以作为山洪地质灾害预警响应判据,必须启动红色预警响应。研究结果可为郑州市西部山区预防应对山洪地质灾害提供决策支持,也可供类似的山地丘陵区城乡社区防灾减灾与应急响应参考。     

Seismic moment release data in earthquake catalogue: Application of Hurst statistics in delineating temporal clustering and seismic vulnerability

Sequential cumulative moment release data of macroearthquakes (Mw≥4.3) of seventeen seismic zones (A to Q) belonging to NE-Himalaya, Burmese-Andaman arc and West- Sunda arc are analysed by Hurst analysis, a non-parametric statistical procedure to identify clustering of low and high values in a time series. The moment release in a zone occurs in alternate positive, negative and positive sloping segments forming a wave like pattern with intervening small horizontal segment. The negative sloping segments indicate decelerated moment release pattern or temporal slackening of elastic strain release with high b–value (>0.95). The horizontal segment indicates temporal clustering of moderate magnitude events/seismic moments with moderate b-values (0.8–0.95). The positive segment is characterised by accelerated moment release within a short span of time indicating temporal clustering of larger magnitude earthquakes/seismic moments and exhibit lowest b–value (<0.7). All zones attest moderate to high Hurst K values, range 0.7-0.86. The pattern in Hurst plots, specially a reversal of trend after prolong negative slope is used for earthquake prognostication in the seismic zones. Our analysis shows that most of the zones register a notable reversal of Hurst clustering trend after a prolonged negative slope which is accompanied by a major earthquake near its end. However, South Burma region (Zone-I) and Tripura fold belt and Bangladesh Plain (Zone-K) do not show any moderate or large shock around the end of the negative sloping trend in Hurst plot. Hence, these two zones can be considered more prone to produce moderate to larger earthquakes in future.     

大坝变形监测遗传神经网络模型

在简要介绍遗传神经网络的基本概念及学习步骤的基础上,分别对大坝坝顶径向水平位移、切向水平位移和大坝坝顶沉降量监测数据进行了训练和预测。结果表明,利用遗传算法特有的全局优化能力,可以较好地完成网络的学习,而且还减少了网络训练次数,缩短了网络训练时间。     

Time varying seismicity in Greece: Hurst's analysis and Monte Carlo simulation applied to a new earthquake catalogue for Greece

Hurst's rescaled range analysis is a useful tool in the examination of a time series and is designed to measure memory content and determine its fractal texture. This study applies the Hurst method to a new earthquake catalogue for Greece. The study also adopts Monte Carlo simulations to provide a statistical test underpinning the Hurst analyses. Together these reveal basic temporal fractal characteristics in the earthquake occurrence time-histories' memory. Three regions are considered, approximately: all of Greece and some surrounding areas, and the sub-zones of the Hellenic Arc and the Gulf of Corinth. Three temporal textures are considered: elapsed time between earthquakes, strain energy release, and earthquake frequency. The elapsed temporal textures for the zone whole Greece indicate distinct characteristics in chronological order and possess long memory. These belong to the class non-random pattern. However, these characteristics generally disappear when the sub-zones are considered and become random patterns. The Monte Carlo simulations support this. Therefore, memoryless statistical seismic hazard estimates may not be suitable for whole Greece but could be useful for the sub-zones. The strain energy release temporal textures for whole Greece and for the sub-zones, no matter that these seem to possess long memory at first analysis, are all random patterns. In other words, the Monte Carlo simulations demonstrate that these patterns are much more likely to happen by chance. The seismic frequency textures for whole Greece and for the sub-zones suggest long memory, however, only the texture for the Hellenic Arc zone (M_S ≥ 5.0) and that for whole Greece (M_S ≥ 4.0) approach demonstrable non-random patterns. Except for these, other patterns happen by chance.     

滑坡时间预测预报研究进展

我国是一个深受滑坡灾害困扰的国家，每年由滑坡所造成的经济损失异常惨重。因此，滑坡预测预报已成为人们研究的一个热点问题。对滑坡时间预测预报的研究现状和研究进展作了系统地总结，重点探讨了滑坡预报模型（包括定量预报模型、定性预报模型以及GMD预报模型等）、预报判据研究方面的进展，提出了滑坡综合信息预报的思路及具体的实施技术路线。     

Bias in estimating fractal dimension with the rescaled-range (R/S) technique

Fractal geostatistics are being applied to subsurface geological data as a way of predicting the spatial distribution of hydrocarbon reservoir properties. The fractal dimension is the controlling parameter in stochastic methods to produce random fields of porosity and permeability. Rescaled range (R/S)analysis has become a popular way of estimating the fractal dimension, via determination of the Hurst exponent (H). A systematic investigation has been undertaken of the bias to be expected due to a range of factors commonly inherent in borehole data, particularly downhole wireline logs. The results are integrated with a review of previous work in this area. Small datasets. overlapping samples, drift and nonstationariry of means can produce a very large bias, and convergence of estimates of H around 0.85–0.90 regardless of original fractal dimension. Nonstationarity can also account for H>1, which has been reported in the literature but which is theoretically impossible for fractal time series. These results call into question the validity of fractal stochastic models built using fractal dimensions estimated with the R/Smethod.     

西北江网河区顶端分流比变化特征研究

根据三水、马口水文站1959~2004水文年实测流量资料的月均序列,应用经验模式分解(EMD)方法分析三水站分流比水文年序列的周期变化及趋势变化,应用启发式分割算法(BG)识别变异点,并采用R/S分析方法探讨分流比变化的持续性特征,结果表明:近46年来,三水站分流比序列具有3.2a、6.6a、15.3a、30.7a的波动周期,表现出复杂的多时间尺度性;三水站分流比的变化趋势是显著增加.增加速率为0.0022/a,并在1992年发生了突变,且为均值向上跳跃;该序列具有非常强的状态持续性,存在长期记忆性,未来仍将呈显著的增加趋势.     

基于CI指数的甘肃省黄土高原地区气象干旱的变化趋势分析

基于甘肃省黄土高原区33个气象站1962-2010年气象资料, 利用综合气象干旱指数(CI)对其近50 a的干旱频率和平均持续时间的空间分布、 干旱强度趋势变化和极端干旱事件频次进行了分析, 此基础上应用基于分型理论的R/S方法对干旱强度未来变化趋势进行了预测. 结果表明: 甘肃省黄土高原区干旱发生频率和多年平均持续天数在兰州-靖远一带和庆阳北部属于高值区, 而岷县、 渭源一带属于低值区; 106° E以西"临洮-通渭-天水"一带和庆阳东南部是干旱变幅最大的地方. 20世纪90年代以来, 干旱强度增大的较快, 四季均呈现出干旱强度变大的趋势, 其中春、 秋季干旱强度加剧的趋势明显, 夏季近10 a都处于非常严重的干旱状态, 但未通过0.01的显著性检验; 20世纪60年代至今, 极端干旱事件发生频次快速增多. 四季干旱强度Hurst指数H 均大于0.5, 同时分维数D 均小于1.5, 因此, 未来一段时间干旱强度仍然保持与过去相一致的变化趋势. 研究结果可为相关部门制定相应抗旱对策提供科学依据.