A Stochastic Differential Equation Approach to Studying Landslide Failure and Size Distributions

地貌学中一个尚未解决的主要问题是：当一个斜坡开始崩塌时，随之而来的滑坡会有多大？ 可能的滑坡规模跨度巨大，潜在的故障规模从米到公里不等-所以不幸的是，特别是对于灾害评估，我们仍然无法预测这样的规模。尽管我们现在在区域范围内对山体滑坡的规模和频率分布有相当好的限制，但这种能力仍然存在。该项目采用了一种新的理论方法，其中包括使用随机微分方程，以解决个别滑坡传播和整体滑坡sizedistribution的问题。 我们已经发现，一个简单的，随机演算模型的斜坡故障可以解释完整的尺寸频率分布的滑坡，包括平均滑坡的大小和幂律比例和非比例分量的分布。 我们正在发展这个理论，以解决以下关键问题：（1）如何平均滑坡规模在合奏分布与现实？- 如果它不是制图分辨率的人为因素，那么它是否与土壤的物理性质（如土壤深度、粘聚力和岩性）有关，还是仅仅是平均山坡比例的函数？(2)随机理论的物理假设是否被实地观察所证实？ (3)我们是否可以更精确地分析数据和模拟不同的边坡破坏机制？(4)落石是由一个完全不同的随机过程和一个完全不同的大小-频率分布发生的吗？ 我们的努力的结果将是一个更深入的了解随机行为的山坡破坏和滑坡灾害。

A major unsolved problem in geomorphology is this: when a slope begins to fail, how big will the ensuing landslide be? The span of possible landslide sizes is enormous, with potential failures ranging in scale from meters to kilometers - so it's unfortunate, particularly for hazard assessment, that we remain unable to predict such sizes. This inability persists despite the fact that we now have rather good constraints on the size-frequency distribution of landslides at a regional scale. This project takes a new theoretical tack, one that involves the use of stochastic differential equations, to address in concert the issues of individual landslide propagation and ensemble landslide sizedistribution. We have found that a simple, stochastic calculus model for slope failure can explain the full size-frequency distribution of landslides, including the mean landslide size and both the power-law scaling and non-scaling components of the distribution. We are developing this theory in order to address the following key questions: (1) how does the mean landslide size in an ensemble distribution relate to reality? - if it is not an artifact of mapping resolution, does it relate to physical properties such as soil depth, cohesion, and lithology, or is it simply a function of mean hillslope scale? (2) are the physical assumptions of the stochastic theory borne out by field observations? (3) can we be more precise in our data analysis and modeling of different slope failure mechanisms? (4) do rockfalls occur by an entirely different stochastic process with an altogether different size-frequency distribution? The outcome of our efforts will be a deeper understanding of the stochastic behavior of hillslope failure and landslide hazard.