Abstract: Distance decay issue of spatial interactions in geography was described and analyzed, and a number of approaches were summarized to solve the gravity model. Firstly, many spatial interactions are governed by the distance decay effect, and the distance decay function quantitatively represents the distance effect. Among kinds of distance decay functions such as power law, exponential and other equations, the power law function reveals the inherent distance impacts behind spatial interactions so that the interaction formula becomes the gravity model, which is widely used in geography and regional economics. Secondly, the authors summarize some methods to quantify the distance decay function according to an interaction matrix and a distance matrix. The simulation results show that fitting the gravity model to estimate nodal attractions as well as the distance decay parameter is an appropriate way to apply the model.

Key words: spatial interactions, distance decay, gravity model, analytic approach, simulation approach

摘要： 对地理学研究中空间交互问题的距离衰减现象进行描述和分析, 并总结重力模型的求解方法。首先, 大部分空间交互都受到距离衰减效应的影响, 距离衰减函数定量表示交互中距离的作用。对比幂律、指数等多种形式的距离衰减函数, 认为幂律形式能够更好地刻画距离影响的本质特征, 并且可以在不同交互中进行比较, 其对应的交互模型即为在地理学和区域经济学中广泛应用的重力模型。然后, 在重力模型的基础上, 总结解析法和模拟法两大类基于给定交互矩阵和距离矩阵定量计算距离衰减函数及衰减系数的方法。由于难以先验确定交互公式中节点规模的数值, 因此拟合重力模型, 同时估计距离衰减系数, 是应用重力模型的恰当方式。

关键词: 空间交互, 距离衰减, 重力模型, 解析法, 模拟法