Acoustic and electromagnetic emissions preceding the earthquake in Kamchatka

In 2013, simultaneous observations of acoustic and electromagnetic emissions ranging from 200 Hz to 11 kHz were carried out in Kamchatka; as a result, abnormal surges of the emissions were registered 1–2 days before seismic events with magnitudes M _LH ≥ 5 at a hypocentral distance up to 200 km. The most likely cause of the occurrence of the abnormal emissions in inherently different fields was activation of deformation processes preceding the earthquakes.     

On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

A review of methods used to determine the fractal dimension of linear features

An in-depth review of the more commonly applied methods used in the determination of the fractal dimension of one-dimensional curves is presented. Many often conflicting opinions about the different methods have been collected and are contrasted with each other. In addition, several little known but potentially useful techniques are also reviewed. General recommendations which should be considered whenever applying any method are made.     

The use of the fractal dimension to quantify the morphology of irregular-shaped particles

For several decades, sedimentologists have had difficulty in obtaining an efficient index of particle form that can be used to specify adequately irregular morphology of sedimentary particles. Mandelbrot has suggested the use of the fractal dimension as a single value estimate of form, in order to characterize morphologically closed loops of an irregular nature. The concept of fractal dimension derives from Richardson's unpublished suggestion that a stable linear relationship appears when the logarithm of the perimeter estimate of an irregular outline is plotted against the logarithm of the unit of measurement (step length). Decreases in step length result in an increase in perimeter by a constant weight (b) for particles whose morphological variations are the same at all measurement scales (self-similarity). The fractal dimension (D) equals 1.0-(b), where b is the slope coefficient of the best-fitting linear regression of the plot. The value of D lies between 1.0 and 2.0, with increasing values of D correlating with increasing irregularity of the outline. In practice, particle outline morphology is not always self-similar, such that two or possibly more fractal elements can occur for many outlines. Two fractal elements reflect the morphological difference between micro-scale edge textural effects (D₁) and macro-scale particle structural effects (D₂) generated by the presence of crenellate-edge morphology (re-entrants). Fractal calibration on a range of regular/irregular particle outline morphologies, plus examination of carbonate beach, pyroclastic and weathered quartz particles indicates that this type of analysis is best suited for morphological characterization of irregular and crenellate particles. In this respect, fractal analysis appears as the complementary analytical technique to harmonic form analysis in order to achieve an adequate specification of all types of particles on a continuum of irregular to regular morphology.     

利用毛管压力曲线分形分维方法研究流动单元

利用取心井铸体薄片获得的图像资料和毛管压力曲线,通过图像分形几何学方法以分维数的形式定量地表征出了复杂的微观孔隙喉道结构特征,发现能够很好地划分和评价孔隙岩石中油、气、水的渗流差异,可以用于储层微观流动单元表征。文中阐述了岩石微观孔隙喉道结构分形的理论基础、计算方法和应用于表征流动单元的依据。建立了中国西部砾岩低渗透油藏微观孔隙喉道分维数与孔隙度、渗透率之间计算图版,据此在油藏中利用常规测井资料获得的孔隙度、渗透率参数计算微观孔隙喉道分维数,开展全油藏流动单元划分与评价,取得了良好的效果。研究结果表明,利用毛管压力曲线分形分维方法研究储层微观流动单元是一种很有效的途径。     

Anomalous electrotelluric residuals prior to a large imminent earthquake in Greece

Periodic anomalies, period 24 h, have been observed in the electrotelluric field prior to a large imminent earthquake in Greece. The periodic anomaly is modulated by an exponential term which implies that successive peaks increase toward the time of the impending earthquake. It is shown that the amplitudes of the periodic variations are much bigger than those accompanying changes of the geomagnetic field.     

Determination of the fractal dimension of a shore platform profile

Morphological studies of shore platforms have focused on elements like width, gradient and elevation, while mostly ignoring the surface roughness as a morphometric attribute. This paper uses the Roughness-length method to show how the Fractal Dimension of a shore platform profile can be obtained. The higher the value of the fractal dimension, the higher is the roughness of the platform. The studied profile is situated in Houghton Bay on the south coast of Wellington, New Zealand. The fractal dimension of the profile under consideration was found to be 1.314. However, one profile is not sufficient to provide information about the surface roughness of a shore platform. Therefore, a number of profiles should be taken to have an idea about surface roughness.     

Estimating fractal dimension of profiles: A comparison of methods

This paper examines the characteristics of four different methods of estimating the fractal dimension of profiles. The semi-variogram, roughness-length, and two spectral methods are compared using synthetic 1024-point profiles generated by three methods, and using two profiles derived from a gridded DEM and two profiles from a laser-scanned soil surface. The analysis concentrates on the Hurst exponent H,which is linearly related to fractal dimension D,and considers both the accuracy and the variability of the estimates of H.The estimation methods are found to be quite consistent for Hnear 0.5, but the semivariogram method appears to be biased for Happroaching 0 and 1, and the roughness-length method for Happroaching 0. The roughness-length or the maximum entropy spectral methods are recommended as the most suitable methods for estimating the fractal dimension of topographic profiles. The fractal model fitted the soil surface data at fine scales but not at broad scales, and did not appear to fit the DEM profiles well at any scale.     

自然水系的计算机处理与分维计算

自然水系的分维值能够反映某一地区一定的地质构造和地壳运动性质,但目前的分维算法大都采用人工完成。本文通过VB编程实现了自然水系的计算机处理与分维计算,并以中国三大水系为例,求得黄河、长江、珠江水系的分维值以及各水系主河道的分维值。该方法快速精确,并能适用于各种线性构造。     

Water quality index and fractal dimension analysis of water parameters

Statistical analysis of water quality parameters were analyzed at Harike Lake on the confluence of Beas and Sutlej rivers of Punjab (India). Mean, median, mode, standard deviation, kurtosis, skewness, coefficient of variation, regression lines, correlation coefficient, Hurst exponent, fractal dimension and predictability index were estimated for each water parameter. Monthly variation of water quality index using month-wise and parameter-wise value of quality rating and actual value present in water sample was calculated and compared with World Health Organization/Environmental Protection Agency standard value of these parameters. It was observed that Brownian time series behavior exists of potential of hydrogen with total dissolved solids, hardness, alkalinity, sulfate, chloride and conductance parameters; biochemical oxygen demand with total dissolved solids, hardness, alkalinity, sulfate, chloride, conductance and calcium parameters; dissolved oxygen with total dissolved solids, hardness, alkalinity, sulfate, chloride, conductance and calcium parameters; ferrous with total dissolved solids, hardness, alkalinity, sulfate, conductance and calcium parameters; chromium with total dissolved solids, hardness, alkalinity, sulfate, chloride, conductance and zinc parameters; zinc with total dissolved solids, hardness, sulfate, chloride, conductance and calcium parameters; fluoride with total dissolved solids, hardness, alkalinity, sulfate, chloride and conductance parameters; nitrate with total dissolved solids, sulfate and conductance parameters; nitrite with potential of hydrogen, total dissolved solids, hardness, alkalinity, sulfate, chloride, conductance and calcium parameters. Also, using water quality index, it was observed that water of the lake was severely contaminated and became unfit for drinking and industrial use.     

Geomorphometry and fractal dimension of a riverine badland in Maharashtra

One of the most serious limitations in studying the surface morphometry of a badland landscape is the nonavailability of a very fine resolution data which is essential for such types of studies. Local relief of most of the badlands in India and also from other parts of the world exhibit limited relief amplitude, often within a few meters. The paper reports a case study carried out in a riverine badland formed along the Western Deccan Trap Region. An attempt has been made in the present paper to extract the morphometric variables of the landscape from the DEMs derived from a high resolution field generated data, because the accuracy of the DEM derived values are dependent on the pixel resolution of the DEM from which they are generated. The size of the pixel resolution should be fixed differently for different landscapes depending on the landscape process in the area. The local relief of the area is around 10 m and for such types of landscapes the topographical maps and also the web-available DEMs are of very coarse resolutions which are not suitable for the analysis. Therefore two well defined tributary catchments were chosen from the area under investigation and theodolite surveys were carried out, contours were generated with 10 cm interval, DEMs were derived by using Arc GIS software. SRTM (Shuttle Radar Topography Mission) 90 m resolution data were utilized to generate DEM for the whole basin. Hypsometric and the drainage basin parameters were extracted from these data by using the same software. Fractal dimension of the whole basin and the sample basins were also obtained for the same data. The morphometric data generated were used to understand the geomorphic processes operating in the area.     

Study of directivity effect on electromagnetic emissions in the HF band as earthquake precursors: Preliminary results on field observations

This work focuses on the use of electromagnetic emissions (EM) in the HF band as a warning event for earthquakes. EM at HF components 41 MHz and 46 MHz were monitored and recorded from eight field stations in Greece and correlated with seismological events. Directivity effect raised since EM emissions at specific station locations were correlated to earthquake events from prescribed regions. EM recordings during 1999 were used and by visual inspection were associated to most of the earthquake events greater than 5R. Using these observations a novel algorithm based on the ratio of short term to long term signal average, together with a prediction rules set derived from 1999's EM emissions study were developed to combine results from several field stations. Performance of the system was promising, but was dependent on the geographic area of interest. Overall performance for earthquakes events of magnitude greater than 5.7 R was 75% of seismic events were correctly predicted by EM activity, while 25% were not predicted.     

基于孔隙分形维数的土壤大孔隙流水力特征参数研究

根据数字图像制备分析技术得到大孔隙数目、大小和形状等特征数据,用分形理论计算孔隙分形维数,并对两类不同质地土壤的孔隙分形维数进行分析比较,应用基于孔隙分形维数的大孔隙分形模型,建立了土壤水分特征曲线和非饱和导水率的预测模型。结果表明,孔隙分形维数D_v可定量描述不同质地土壤结构,其模型预测精度优于颗粒大小分布估计的分形模型,可用于实际问题的研究。     

The strength and fractal dimension characteristics of alum–kaolin flocs

Flocs generated by various shear forces exhibit different characteristics of size, strength and structure. These properties were investigated by employing a continuous optical monitoring and a microscope with CCD camera to directly monitor aggregation under six different shear intensities. The floc structure was characterized by the fractal dimension. The results showed that the flocculation index (FI) decreased from 1.16 at 20 rpm to 0.25 at 250 rpm and the floc size decreased from 550 μm to 150 μm, meantime, the FI value showed a good correlation with floc size. In order to determine the floc strength, two methods were used. One was the strength factor, ranging from 18.3% to 62.5%, calculated from FI curve, and the other was a theoretical value between 0.005 N/m² and 0.240 N/m², estimated by calculation. The floc strength increased with the G value in both cases. Furthermore, the fractal dimension increased with G and its value was between 1.30 and 1.63. The relation between fractal dimension and strength was also obtained.     

波形长度分形维数在结构振动诊断中的应用

在Hausdorff 维数和分配维数的基础上,采用拓扑映射技术,提出了振动波形长度分形维数的定义和计算公式,并对其数学严密性进行了证明.结合工程实例探讨了基于振动波形长度分形维数计算的结构振动诊断技术:模型增长法和滑动窗法.该技术对于波形异常检测表现出精度高、抗噪能力强及自动快捷等优势,构成了一条分形理论用于结构振动诊断的有效技术路线,具有良好的应用价值.     

河流形态的分维及与洪水关系的探讨--以长江中下游为例

河流水系形态特征可以通过河流的分形特征来反映,分形维数则是河流分形特征的量化表示,其与河流洪水之间存在着一定的关系。以长江中下游为例,利用网格覆盖法计算出长江中下游河流分维,分析了长江中下游河流的分形特性,并在此基础上结合长江中下游洪水分析不同水系特征下洪水的特点。研究结果表明,一般来说河道分维越大、河网分维越小,洪水发生可能性则越高。     

锦州台文安5.1级地震前体应变变化观测报告

2006年7月4日河北文安发生MS5.1地震。此次地震前,6月28日开始,辽宁锦州台钻孔应变仪观测到异常变化,持续4天。本文报告了变化情况,同时给出了水位和气压变化。     

中国花岗岩类化学元素组成的分维数特征

将各种化学元素的丰度集合视为一组丰度序列,首次将分维数(盒维数)应用于研究中国花岗岩类的化学元素组成及演化特征。原理上,分形的遍在性源于随机性的遍在性,分维数的取值可表征丰度序列的内部结构性及演化的方向性,为矿产资源勘查提供重要信息;实践上,以观测元素相容性序列为基础分析其地球化学行为,采用盒维数以不失观测变量的整体性。详细探讨了分维数与成岩序列上的演化趋势或分异程度与研究对象地球化学特征间的相互关系及作用机制,据以解释为何在组分、时间与空间上同属花岗岩类却呈现出截然相异的成矿专属性与含矿性;确立了从频数特征角度探讨化学元素组成研究的新思路。研究结果表明：中国花岗岩类化学元素在丰度序列演化中均存有某种形式的结构性演化,即在组成、时间及空间上的有序结构,传统的(对数)正态分布模型难以描述其频数规律。然而,累加(差)的频数却是服从分形分布的,分维数与聚类分析的结果十分接近,且其递减序列可作为研究体系演化程度的判据,具有相当重要的地球化学意义。     

紫色泥岩水热条件下崩解过程的分维特性

以马头山组（K2m）、妥甸组（J3t）和下禄丰组（J1l）自然风干的紫色泥岩为研究对象,分别进行干湿、冷热和干湿冷热3种处理,并运用分维方法分析不同处理下紫色泥岩的崩解特性,发现分维数能比较准确地表征紫色泥岩的崩解过程：分维数越大,岩石破碎程度越高;分维数越小,岩石破碎程度越低。3种紫色泥岩在不同处理方式下崩解的分维数大小都是干湿冷热 干湿 冷热,可见,水热共同作用对母岩崩解的影响明显大于仅有水或热的作用。相同处理方式下3种泥岩的分维数大小为J3t J1l K2m,且在干湿和干湿冷热条件下J3t的崩解分维数与K2m和J1l的差异显著,这主要是由这3种泥岩的物理特性、元素组成以及其风化成度所决定的。     

基于关联维数的地质灾害空间分布特征分析

通过分形理论中关联维数及其动态变化来揭示黑水河流域地质灾害的时空分布特征,并探讨了影响区内地质灾害空间分布的相关因素。研究表明:区内不同规模地质灾害点系统空间分布具有分形特征,崩塌灾害点的分布最为集中,滑坡次之,泥石流则最为分散;近十年来区内每年所发生灾害的空间分布集中程度变化剧烈,呈现强集中、弱分散的特点;近五年来每年所发生的灾害呈逐渐分散趋势,但灾害的累积却有逐渐集中的趋势;影响区内地质灾害空间分布异同的主要因素为地形坡度、地层岩性、河流、降雨、人类工程活动、高程、断裂。