基于最大熵原理的黄土丘陵区地质灾害规模频率分布研究

在分析地质灾害规模分布的基础上,基于最大熵原理在理论上推导出崩塌、滑坡和不稳定斜坡灾害长、宽和厚等参数规模频率负指数分布关系,提出了规模参数频率分布简单而有效的计算公式。最后以黄土丘陵区宝塔区为例,对所提出的公式进行验证,结果表明:(1)宝塔区地质灾害以中型滑坡和中型崩塌为主,但大型地质灾害在控制着滑坡崩塌总面积和总体积中起着重要的作用;(2)滑坡、崩塌和不稳定斜坡规模等级指数主要集中于(5.5,6]级、(4,4.5]级和(5,5.5]级;(3)崩塌、滑坡和不稳定斜坡的长、宽和厚规模频率分布符合更简单的指数关系,且用指数关系拟合的规模频率曲线不会产生偏转效应;(4)对面积和体积取算术平方根和立方根后,它们的规模-频率分布也呈现出负指数分布,并且拟合效果良好(决定系数R2>0.9,概率P<0.05)。

Distribution of frequency-size of geological disaster base on principle of maximum entropy in loess plateau

This study investigates the principles of frequency-size of geological disaster in loess hilly region. Baota district in Yan’an city in Shaanxi province is chosen as the typical geological disaster region in loess plateau. The database of geological disaster in Baota district is built through 3S technology, field survey and remote sensing interpretation. In the view of the holism and in the base of scale distribution analysis and maximum entropy principle, the theory that the parameters of frequency-size such as the length, width and thickness of collapse, landslide and unstable slope accorded with negative exponential distribution is come up for the first time using mathematical statistic method. As a result, a simple and effective formula about frequency- size distribution is put forward. At the end, the formula is verified by the example of Baota district. (1) The results mainly show that the geological disaster of Baota district is mainly middle-scale landslide and collapse; however, large-scale disaster plays important role in the control of total area and volume of collapse. (2) Then this study defines the grade index of volume size for researching size distribution of geological disaster. The results show that the size grade index of landslide, collapse and unstable slope is mainly in (5.5, 6], (4, 4.5] and (5, 5.5], respectively. (3) The frequency-size distribution of collapse, landslide, and the length, width and thickness of unstable slope accord with the exponential relation; furthermore, the curve would not have rollover effect. (4) One of simple methods to solve the frequency-size distribution is to get the square root of area and cube root of volume. The results show that they present negative exponential distribution with a good fitting effect (R2>0.9, P<0.05). Thus the formula plays important role in the prediction of the occurrence frequency of landslide in any size.