This paper presents a learning-based stochastic simulation method that incorporates high-order spatial statistics at multiple scales from sources with different resolutions. Regarding the simulation of a certain spatial attribute, the high-order spatial information from different sources is encapsulated as aggregated kernel statistics in a spatial Legendre moment kernel space, and the probability distribution of the underlying random field model is derived by a statistical learning algorithm, which matches the high-order spatial statistics of the target model to the observed ones. In addition, a related software is developed as the SGeMS plugin. Case studies are conducted with a known data set and a gold deposit, demonstrating reproduction of high-order spatial statistics from the available data, as well as practical aspects in mining applications.

本文提出了一种基于学习的随机模拟方法，该方法结合了来自不同分辨率来源的多尺度高阶空间统计信息。关于特定空间属性的模拟，将来自不同来源的高阶空间信息封装为空间Legendre矩内核空间中的聚合内核统计信息，并通过统计学习算法推导基础随机场模型的概率分布，将目标模型的高阶空间统计信息与观察到的信息进行匹配。此外，还开发了相关软件作为SGeMS插件。案例研究使用已知的数据集和金矿床进行，展示了从可用数据中再现的高阶空间统计数据以及采矿应用中的实际情况。