Modern approaches for the spatial simulation of categorical variables are largely based on multi-point statistical methods, where a training image is used to derive complex spatial relationships using relevant patterns. In these approaches, simulated realizations are driven by the training image utilized, while the spatial statistics of the actual sample data are ignored. This paper presents a data-driven, high-order simulation approach based on the approximation of high-order spatial indicator moments. The high-order spatial statistics are expressed as functions of spatial distances that are similar to variogram models for two-point methods, while higher-order statistics are connected with lower-orders via boundary conditions. Using an advanced recursive B-spline approximation algorithm, the high-order statistics are reconstructed from the available data and are subsequently used for the construction of conditional distributions using Bayes’ rule. Random values are subsequently simulated for all unsampled grid nodes. The main advantages of the proposed technique are its ability to (a) simulate without a training image to reproduce the high-order statistics of the data, and (b) adapt the model’s complexity to the information available in the data. The practical intricacies and effectiveness of the proposed approach are demonstrated through applications at two copper deposits.

分类变量空间模拟的现代方法主要基于多点统计方法，其中使用训练图像使用相关模式推导出复杂的空间关系。在这些方法中，模拟实现由所使用的训练图像驱动，而忽略实际样本数据的空间统计。本文提出了一种基于高阶空间指标矩近似的数据驱动的高阶模拟方法。高阶空间统计表示为空间距离的函数，类似于两点方法的变异函数模型，而高阶统计通过边界条件与低阶统计联系起来。使用高级递归 B 样条近似算法，高阶统计数据从可用数据中重建，随后用于使用贝叶斯规则构建条件分布。随后为所有未采样的网格节点模拟随机值。所提出的技术的主要优点是它能够 (a) 在没有训练图像的情况下模拟以重现数据的高阶统计数据，以及 (b) 使模型的复杂性适应数据中可用的信息。通过在两个铜矿床的应用证明了所提出方法的实际复杂性和有效性。所提出的技术的主要优点是它能够 (a) 在没有训练图像的情况下模拟以重现数据的高阶统计数据，以及 (b) 使模型的复杂性适应数据中可用的信息。通过在两个铜矿床的应用证明了所提出方法的实际复杂性和有效性。所提出的技术的主要优点是它能够 (a) 在没有训练图像的情况下模拟以重现数据的高阶统计数据，以及 (b) 使模型的复杂性适应数据中可用的信息。通过在两个铜矿床的应用证明了所提出方法的实际复杂性和有效性。