论文标题
地理分析：从基于距离的空间到基于维度的空间
Geographical Analysis: from Distance-based Space to Dimension-based Space
论文作者
论文摘要
地理空间的传统概念是基于距离的概念。如果进行空间分析，则进行距离测量。但是，有效的基于距离的空间的前提是地理系统具有特征性量表。对于无标度地理系统，无法用纯距离进行有效描述空间结构，因此基于距离的空间无效地理位置建模。在真正的地理世界中，无处不在的模式和过程无处不在。我们需要新的地理空间概念。使用分形和扩展关系的想法，我提出了一个基于维度的空间概念，用于无限制地理分析。如果地理现象具有特征性的尺度，我们可以使用距离测量值对其进行建模。如果地理现象没有特征性尺度，我们将使用分形维度来描述它，该尺寸基于距离变量和相应测量值之间的缩放关系。简而言之，地理空间分为两种类型：规模空间和无尺度空间。这项研究显示了一种新的空间建模和无特征性地理系统定量分析的方法。
The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical systems have characteristic scales. For a scale-free geographical system, the spatial structure cannot be validly described with pure distance, and thus the distance-based space is ineffective for geographical modelling. In the real geographical world, scale-free patterns and processes are everywhere. We need new notion of geographical space. Using the ideas from fractals and scaling relations, I propose a dimension-based concept of space for scale-free geographical analysis. If a geographical phenomenon bears characteristic scales, we can model it using distance measurement; if a geographical phenomenon has no characteristic scale, we will describe it using fractal dimension, which is based on the scaling relations between distance variable and the corresponding measurements. In short, geographical space fall into two types: scaleful space and scale-free space. This study shows a new way of spatial modeling and quantitative analyses for the geographical systems without characteristic scale.
