Learning high-order spatial statistics at multiple scales: A kernel-based stochastic simulation algorithm and its implementation

Abstract

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.