Monofractal and multifractal approaches in investigating scaling properties in temporal patterns of the 1983-2000 seismicity in the western Corinth graben, Greece

Much recent work has been focused on understanding the statistical properties of time-occurrence series of earthquakes. Investigating into the patterns of seismic sequences reveals evidence of scaling features in temporal behavior. This is shown in the clustering properties of seismicity of the western Corinth graben, Greece from 1983 to 2000. Power-law behavior has been found by means of Allan factor analysis and Fourier spectra for the earthquake sequence, with consistent values for the scaling exponents, that decrease with the threshold magnitude. The analysis of the temporal variation of the scaling exponent, performed with different threshold magnitudes, reveals an enhancing of the clusterization in correspondence to larger events. The multifractal analysis of the temporal distribution of the events has shown a decrease of the intermittent character with the threshold magnitude.     

Scaling properties of landslides in the Rif mountains of Morocco

Landslides in the central Rif mountains (Morocco) were analyzed by multifractal analysis. Our results suggest that spatial distribution of landslides in the region is not a homogeneous fractal structure but a heterogeneous one with generalized dimensions D(1)=1.713>D(2)>…>D(12)=1.325. The value of D(12)=D(∞) is the fractal dimension of the most intensive clustering in the heterogeneous fractal set. It is worthwhile to note that we found D(0)<D(1). The analysis of areas affected by sliding from the geological map of Beni Ahmed at a scale 1:50 000 shows the power law size distribution: N(A>a)∝a^−1.57. This confirms the scale invariance of sliding and suggests that real landslides may exhibit a Self-Organized Criticality (SOC) behaviour.     

The solar magnetic flux mid-term periodicities and the solar dynamo

We investigate here the fluctuations in the total, open and closed solar magnetic flux (SMF) for the period 1971–1999 by means of the maximum entropy method in the frequency range 5×10⁻⁹–10⁻⁷ Hz (6 yr to 120 days). We use monthly data for the total, open and closed magnetic solar fluxes. Periodicities found in the series are similar showing that there is some relationship between the fluxes. The most important finding of this work is the existence of fluctuations at around 1.3 and 1.7 yr in the SMF with alternating importance during consecutive even and odd solar cycles. These fluctuations are directly related with variations present in cosmic rays, solar wind parameters and geomagnetic activity indexes. A quasi-triennial periodicity previously found in sunspots and other solar phenomena is also of importance. The SMF is generated by the action of the solar dynamo; therefore, it is through the magnetic flux that the solar dynamo influences several heliospheric phenomena.     

Some notes on entropy measures. II. The relative entropy matrix and the positivity constraint

Based on the maximum entropy concept with the number of bins (class intervals), N, maximized in terms of residual errors in sampling of the system, the residual entropy matrix (REM), which is intrinsically positive definite, is sampled uniformly at N equal intervals in entropy space. The mandatory constraint of positivity shows that the finitely sampled REM then provides estimates on the magnitudes of missing components of the autocorrelation sequence describing REM. If the mandatory constraint is relaxed to its limit, the resulting prediction for REM is identical to Burg's (1967) maximum entropy algorithm. The advantages are that assessments can be made: (i) whether the missing components are known accurately enough that no further measurements are needed; (ii) the N equal intervals of the entropy measure are sufficient to provide resolution on the REM for each and every sample; or (iii) whether finer interval resolution is needed to extract information for a particular sample.     

新疆及其邻区M≥7强震的预测研究

新疆及其邻近地区Ｍ≥７强震活动在时间分布上具有明显的有序性。自１７１６年以来的２１次Ｍ≥７强震存在着时间间隔为１１、２５、３０、４１和６０年的有序值。利用强震活动时间的有序性结构，可对该区７级强震进行预测探索。本文同时还应用熵和经验分布函数，讨论了下次强震发生的地点和概率。     

Revisiting prior distributions,Part II: Implications of the physical prior in maximum entropy analysis

The well-known “Maximum Entropy Formalism” offers a powerful framework for deriving probability density functions given a relevant knowledge base and an adequate prior. The majority of results based on this approach have been derived assuming a flat uninformative prior, but this assumption is to a large extent arbitrary (any one-to-one transformation of the random variable will change the flat uninformative prior into some non-constant function). In a companion paper we introduced the notion of a natural reference point for dimensional physical variables, and used this notion to derive a class of physical priors that are form-invariant to changes in the system of dimensional units. The present paper studies effects of these priors on the probability density functions derived using the maximum entropy formalism. Analysis of real data shows that when the maximum entropy formalism uses the physical prior it yields significantly better results than when it is based on the commonly used flat uninformative prior. This improvement reflects the significance of the incorporating additional information (contained in physical priors), which is ignored when flat priors are used in the standard form of the maximum entropy formalism. A potentially serious limitation of the maximum entropy formalism is the assumption that sample moments are available. This is not the case in many macroscopic real-world problems, where the knowledge base available is a finite sample rather than population moments. As a result, the maximum entropy formalism generates a family of “nested models” parameterized by the unknown values of the population parameters. In this work we combine this formalism with a model selection scheme based on Akaike’s information criterion to derive the maximum entropy model that is most consistent with the available sample. This combination establishes a general inference framework of wide applicability in scientific/engineering problems.     

1961—2016年祁连山区季节性干旱综合指数特征分析

采用Z指数和熵权理论,构建了干旱综合指数作为干旱强度评价标准,对祁连山区季节性干旱特征及其空间分布规律进行了深入剖析。结果表明:1961—2016年季节性干旱强度普遍减弱,其中春秋两季显著减弱,夏季明显减弱;尽管20世纪60—70年代、90年代为季节性干旱频发与重发时段,但从2000年以来夏旱与冬旱却比较频繁,不容忽视。干旱强度由强到弱依次为冬季、夏季、春季和秋季,冬季干旱程度最强;在干旱波动性上秋季最强,冬季次之,春季最弱。春夏秋三季南侧比北侧干旱,冬季北侧比南侧干旱,其中冬季干旱范围最为广泛,尤以酒泉为中心的北侧区域最为显著。在研究时段内祁连山南北两侧干旱强度逐渐减弱,南侧明显减弱,枯草期干旱强度减弱程度尤为显著。本研究为祁连山区干旱评价提供了参考依据。     

Fractal Characteristics of Fault Structures and Their Use for Mapping Ore-prospecting Potential in the Qitianling Area, Southern Hunan Province, China

Quantitative analyses of the spatial distribution of fault structures can provide a theoretical basis for forecasting prospective ore deposits. Characteristics and complexity of fault structure distribution in the Qitianling area, Southern Hunan Province, China, were quantitatively calculated and appraised by fractal and multifractal methods to evaluate the relation between fault structures and ore-prospecting potential. The results show that the lengths of faults can be modeled as multifractals. Multifractal spectra evidently reflect the characteristics of the scaling of fault structures. The boxcounting dimension value(D) of fault structures is equal to 1.656, as indicates complexity of the spatial distribution of faults and favorable structural conditions for the formation of ore deposits. Moreover, the D values of sub-regions were calculated and isopleths of their fractal dimension values were plotted accordingly. Overlay analyses of isopleths of fractal dimension values and distributions of known ore deposits show that areas with the larger fractal dimension values of fault structures have more ore deposits. This spatial coupling relationship between D values and ore deposits can be used to forecast and explore other ore deposits. On the basis of complexity theory for ore-forming systems, three exploration targets with high D values were delineated as prospective ore deposits.     

Estimating the spatial distribution of dredged material disposed of at sea using particle-size distributions and metal concentrations

We present a method to estimate the spatial distribution of dredged material disposed of at sea. Using both dredged sediments and samples of sea-bed sediment from near the Rame Head disposal site, Plymouth, UK, we applied entropy analysis to the <63 μm sediment fraction and combined the results with the trace metal data in the same fraction, to form a series of groups. We interpret the distribution of sediments in one group (F1) to approximate the distribution of material affected by the disposal site. This distribution includes locations close to the disposal site, and also locations <4 km to the SE and SW, <6 km to the NW and <2 km to the N. This approach demonstrates the feasibility of using trace metal analysis of particular grain size fractions to reduce uncertainty in interpreting the spatial distribution of impacts of dredge disposal.     

形变观测数据的多异常形态统一识别

地震前兆数据中的形变观测数据变化复杂,地球物理场变化和环境干扰等信息识别与剔除是与地震相关现象分析的关键.传统的信号识别主要采用回归分析、经验模态分解、频域信号分解等方法,但它们难以统一识别高幅值变化(尖峰、阶跃)与高频变化波形.本文利用信息熵参与形变时序数据的自动化分段构造子序列,一定程度上避免了这两种波形被分割的弊端,然后以统计描述方式表达子序列,最后利用角度异常因子(Angle-Based Outlier Factor,ABOF)和局部异常因子(Local Outlier Factor,LOF)构建对数函数定义离群点,以解决统一识别高幅度变化与高频率变化的问题.实验表明,对于特征向量维度变化的情况,LOF-ABOF算法的计算效率呈线性变化关系;在特征表达策略改变的情况下,该算法对高幅值变化和高频变化的异常识别效果良好.本文所提供方法可以检测出高幅值变化与高频率变化的异常形态,为地震前兆数据中形变观测数据"前兆信号"的识别提供指导与参考,为深入认识地震现象及其产生机理奠定基础.