Assessing spatial uncertainty over an arbitrary volume is usually done by generating multiple simulations of the random function and averaging the property over each realization to build its uncertainty distribution. However, this is a cumbersome process for practitioners, as they need to compute and process a large number of realizations. Multi-Gaussian kriging provides a simpler alternative, by directly computing the conditional probability density functions of the random variables. In this work, we revisit the multi-Gaussian framework and present the implementation details to determine the conditional distribution at any support, by numerical integration of the conditional probabilities, using an importance sampling approach. We demonstrate the use of this approach and assess its accuracy in the lognormal and exponential cases with synthetic data. We also apply it to a real three-dimensional mining case, where the uncertainty over scheduled production volumes is determined. The ability to assess this uncertainty may prove valuable, as it enables schedule changes to be made in a mining setting in order to ensure the smooth running of downstream processes.

评估任意体积上的空间不确定性通常是通过生成随机函数的多个模拟并平均每个实现的属性以建立其不确定性分布来完成的。但是，对于从业者来说，这是一个麻烦的过程，因为他们需要计算和处理大量的实现。通过直接计算随机变量的条件概率密度函数，多高斯克里金法提供了一种更简单的选择。在这项工作中，我们将重新审视多高斯框架，并提出实施细节，以通过使用重要性抽样方法对条件概率进行数值积分来确定任何支持下的条件分布。我们演示了这种方法的使用，并在对数正态和指数情况下使用综合数据评估了其准确性。我们还将其应用于真实的三维采矿案例，其中确定了计划产量的不确定性。评估这种不确定性的能力可能证明是有价值的，因为它可以在采矿环境中进行进度更改，以确保下游流程的顺利进行。