特征尺度、标度与地理空间分析
Characteristic Scales, Scaling, and Geospatial Analysis
AI总结：
本文通过数学模型比较有尺度与无尺度地理系统，提出用分形几何等标度理论研究无尺度现象，并给出四种区分方法，强调复杂地理系统需针对不同方面采用不同方法论。
摘要：
地理现象可分为两类：有尺度现象与无尺度现象。前者具有特征尺度，后者没有特征尺度。传统的定量与数学方法只能有效应用于有尺度地理现象，而不能有效应用于无尺度地理现象。本文借助简单的地理数学模型，对有尺度地理系统与无尺度地理系统进行了比较。主要观点如下。第一，有尺度现象可以用传统数学方法研究，而无尺度现象应当使用基于标度的理论（如分形几何）来研究；第二，有尺度现象属于基于距离的地理空间，而无尺度现象属于基于维数的地理空间；第三，提出了四种区分无尺度现象与有尺度现象的方法，包括标度变换、概率分布、自相关与偏自相关函数以及ht指数。在实践中，一个复杂地理系统通常同时具有有尺度方面与无尺度方面。对于不同类型的地理系统或同一地理系统的不同方面，必须采用不同的方法论。
英文摘要：
Geographical phenomena fall into two categories: scaleful phenomena and scale-free phenomena. The former bears characteristic scales, and the latter has no characteristic scale. The conventional quantitative and mathematical methods can only be effectively applied to scaleful geographical phenomena rather than the scale-free geographical phenomena. In this paper, a comparison between scaleful geographical systems and scale-free geographical systems are drawn by means of simple geographical mathematical models. The main viewpoints are as below. First, the scaleful phenomena can be researched by conventional mathematical methods, while the scale-free phenomena should be studied using the theory based on scaling such as fractal geometry; Second, the scaleful phenomena belong to distance-based geo-space, while the scale-free phenomena belong to dimension-based geo-space; Third, four approaches to distinguish scale-free phenomena from scaleful phenomena are presented, including scaling transform, probability distribution, autocorrelation and partial autocorrelation functions, and ht-index. In practice, a complex geographical system usually possesses scaleful aspects and scale-free aspects. Different methodologies must be adopted for different types of geographic systems or different aspects of the same geographic system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
