Multifractal filtering method for extraction of ocean from remotely sensed imagery

Traditional methods of extracting the ocean wave eddy information from remotely sensed imagery mainly use the edge detection technology such as Canny and Hough operators. However, due to the complexities of ocean eddies and image itself, it is sometimes difficult to successfully detect ocean eddies using these methods. A mnltifractal filtering technology is proposed for extraction of ocean eddies and demonstrated using NASA MODIS, SeaWiFS and NOAA satellite data set in the typical area, such as ocean west boundary current. Results showed that the new method has a superior performance over the traditional methods.     

Change of multifractal thermal characteristics in the western Philippine sea upper layer during internal wave-soliton propagation

The upper layer (above 140 m depth) temperature in the western Philippine Sea near Taiwan was sampled using a coastal monitoring buoy (CMB) with 15 attached thermistors during July 28–August 7, 2005. The data were collected every 10 min at 1, 3, 5, 10, 15, and 20 m using the CMB sensors, and every 15 sec at 15 different depths between 25 m and 140 m. Internal waves and solitons were identified from the time-depth plot of the temperature field. Without the internal waves and solitons, the power spectra, structure functions, and singular measures (representing the intermittency) of temperature field satisfy the power law with multi-scale characteristics at all depths. The internal waves do not change the basic characteristics of the multifractal structure. However, the internal solitons change the power exponent of the power spectra drastically, especially in the low wave number domain; they also break down the power law of the structure function and increase the intermittency parameter. The physical mechanisms causing these different effects need to be explored further.     

Spatial analysis of elements in soils from Chengdu City

Three kinds of spatial analysis methods （geostatistics, concentration-area fractal model and the multifractal analysis called the moment method） were used for almost 50 elements, including heavy metals, disperse elements, rare elements and even others, in 6586 top soil （0-20 cm） samples and 1833 deep soil （150-200 cm） samples from Chengdu metropolitan area of 12400 km^2, southwestern China. The ranges of spatial correlation revealed by variograms are quite different for different kinds of elements in the top and deep soils. The most interest is the fact that the multifractal spectra of environmentally important elements such as Pb, Cr, Cd and Ni in top soils in the metropolitan area show systematic change from those in the deep soils, revealing a strong anthropogenic addition, while Hg, Zn, As, Cu and all common elements show no such kind of addition. In terms of multifractal properties based on the multifractal spectrum curves, those disperse and rare elements show great deviation from other major and trace elements, which is also of great interest.     

Multifractal modeling and spatial statistics

In general, the multifractal model provides more information about measurements on spatial objects than a fractal model. It also results in mathematical equations for the covariance function and semivariogram in spatial statistics which are determined primarily by the second-order mass exponent. However, these equations can be approximated by power-law relations which are comparable directly to equations based on fractal modeling. The multifractal approach is used to describe the underlying spatial structure of De Wijs 's example of zinc values from a sphalerite-bearing quartz vein near Pulacayo, Bolivia. It is shown that these data are multifractal instead of fractal, and that the second-order mass exponent (=0.979±0.011 for the example) can be used in spatial statistical analysis.     

A New Model for Quantifying Anisotropic Scale Invariance and for Decomposition of Mixing Patterns

A new power–law function has been derived to represent the relationship between area of the set consisting of wave numbers with spectral energy density above S (A(>S)) on the two-dimensional frequency plane and S. The power–law relation holds if the field concerned possessing isotropic scale invariance or generalized scaling invariance involves rotational and ratio-scale changing transforms. The equation is valid for dealing with common exploration geophysical and geochemical fields encountered in mineral exploration and environmental assessment. This power–law function not only provides a new model for characterizing anisotropic scaling invariance for generalized scaling field, for example, estimating the power exponent of power spectrum of generalized scale invariance measure in frequency domain, but also forms a theoretical base for the S–A filtering technique developed for decomposing a mixing field into components on the basis of distinct scaling properties in the frequency domain. It is demonstrated that the method has potential to become a general technique for image processing and pattern recognition.     

Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China

Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.     

普朗斑岩型铜矿床成矿元素多重分形特征及其矿化强度指示

成矿元素品位的变化受控于长期地质作用过程,具有较强的非线性特征,定量刻画其变化特征有助于深入理解成矿过程,并为找矿预测提供理论依据。运用多重分形去趋势移动均值（MFDMA） 法,分析云南普朗斑岩型铜矿床4号勘探线钻孔Cu元素品位的多重分形特征及其对矿化强度的指示意义。结果显示：所有钻孔Cu元素品位具有多重分形特征,且不同矿化等级的元素分布存在局部奇异性差异,多重分形强度随矿化强度等级减弱而增加;这些特征指示在钾硅化带—带内侧强矿化钻孔的高品位相对聚集,而带外侧角岩化—青磐岩化带的高品位相对分散;通过数据随机重排技术推测Cu品位多重分形结构奇异性差异是由其分布概率密度和长相关性共同作用引起,后者的作用贡献大于前者。     

城市地理研究中的单分形、多分形和自仿射分形

分形几何学在城市地理研究中具有广泛的应用,然而很多基本概念却让初学者感到迷惑。如何区分单分形、自仿射分形与多分形,是一个基本而重要的问题。简单分形容易理解,而真实的地理现象很少是单分形的。城市生长过程具有自仿射特征,而城市空间格局却具有多分形性质。作者发现,各种分形的共性在于三个方面：标度律、分数维和熵守恒。论文基于标度、分维和熵守恒公式,借助隐喻城市生长的规则分形来区分单分形、多分形和自仿射分形,讨论分形系统演化的机理、分形与空间自相关和空间异质性的联系,同时澄清一些在地理分形研究中的常见错误概念。最后以城市位序-规模分布为例,说明并对比单分形和多分形在城市地理研究中的建模与应用思路。     

京津冀城镇体系与水系结构的时空关系研究

京津冀地区人水关系矛盾突出,分形可以有效描述城镇体系和水系时空演化特征,从而揭示两者演化关系,为城市问题的解决提供一些理论和经验依据。论文采用分形理论中的网格维数和多分维谱,首先分别刻画了两者的时空演化特征,其次探讨了城镇体系和水系结构之间的时空关系,最后探究了水系结构退化的影响因素。主要结论有：① 1990—2010年,京津冀地区建设用地的网格维数升高、自相似性增强、从集聚向分散转变,意味着建设用地朝着空间填充程度增强、有序、分散的方向发展,而水系反之,证明两者具有不同的时空演化方向;② 21世纪10年代,京津冀的人水关系十分紧张,南水北调虽然缓和了京津冀用水问题,改善了大尺度上的水系结构,但在小尺度上改善有限;③ 越靠近城市中心,建设用地分形形态发育越成熟,结构越有序,越靠近外围越混乱无序;④ 京津冀地区水系退化,由自然和人为两方面因素造成,21世纪以后人为因素的影响较为显著。针对京津冀地区水系退化,提出如下政策建议：在城市建设过程中,一方面科学规划城市水系,重视低等级水系的保护;另一方面节约集约利用水资源,完善水资源管理机制。未来,需要进一步探索城市发展和水系的非线性关系,为城市可持续发展提供依据。     

板内与板间地震活动时空分布的多重分形特征研究

利用多重分形分析方法,考察了中国大陆和台湾地区以及新西兰的地震活动广义应变释放时间和空间分布的多重分形特征. 结果表明,地震活动时空分布的多重分形特征与不同地球动力学环境关系密切. 强震活动时间分布在板间地区具有比板内地区更明显的丛集性, 对中小地震这种丛集性差异较小;强震活动空间分布在板内地区具有比板间地区更强的丛集性,但对中小地震则相反.