广义自相似性原理与模型  

Generalized Self-Similarity Theory and Models

作　　者：曹黎[1] 成秋明[2] 陈志军[2] 严光生[1] 

机构地区：[1]中国地质调查局,北京100037 [2]中国地质大学地质过程与矿产资源国家重点实验室,湖北武汉430074

出　　处：《地球科学（中国地质大学学报）》2009年第2期270-274,共5页Earth Science-Journal of China University of Geosciences

基　　金：中国地质调查局项目“重要矿产资源三维预测评价方法与示范”(No.1212010633810);教育部创新团队基金(No.IRT0755);国家自然科学基金项目(Nos.40638041,40502029);地质过程与矿产资源国家重点实验室科技部专项经费资助

摘　　要：为了理解各式各样的具有广义自相似性特征的尺度不变性系统,提出了1个称之为GSI(generalized scale invariance)的理论体系.它阐述了大小尺度可以相互关联而不需要引入任何1个特有(具体)尺度的最普通情形.在二维线性GSI理论的基础上,形成了2个重要的各向异性尺度不变性量化模型:SIG(scale invariant generator)模型和S-A(spectrum-area)模型.SIG模型通过在频率域中估计GSI理论中代表旋转和层化程度的尺度不变性生成元的参数来量化各向异性尺度不变性.而S-A模型通过从二维频率域中能谱密度大于P元素集的面积与P之间关系的非参数模型对各向异性尺度不变性进行量化.如果研究的对象是1个混合模式(多个不同尺度的过程或作用叠加而形成的),S-A模型不仅可以对异性尺度不变性进行量化,还可以对该混合模式进行分解.系统阐述了GSI理论、SIG模型和S-A模型,并将SIG模型和S-A模型结合提出了既能对混合模式进行分解又能对分解后模式的各向异性尺度不变性进行量化的模型.In order to understand various anisotropic scale invariance systems, the generalized scale invariance （GSI） concept was brought forward to present a formalism stating the most general conditions under which large and small scales can be related. Two different anisotropic scale invariance quantification models were developed： the scale invariant generator （SIG） model quantifies anisotropies by estimating the GSI generator in frequency domain, a form Of scale transformation defined in GSI representing how the scaling field is stratified and how it rotates, and the family of balls that best describes the scaling field; the spectrum-area （S-A） model quantifies anisotropies by estimating the anisotropic scaling exponent defined in GSI through a power-law function representing the relationship between area of the set with spectral energy density above P on the 2D frequency domain and P. S-A is not only an anisotropic scale invariance quantification technique but also a mixing data decomposition technique, which can decompose mixing data into multiple components based on anisotropic scaling properties in frequency domain. This paper introduces the GSI concept, the SIG model and S-A model systematically and proposes an idea to combine the SIG model and S-A model so that the new combined model can not only decompose mixing data into multiple components but also quantify the decomposed components ＇ anisotropic scale invariance as well.

关 键 词：广义自相似性(各向异性尺度不变性) GSI SIG S-A 

分 类 号：P628[天文地球—地质矿产勘探]