The spatial modeling of geo-domains has become ubiquitous in many geoscientific fields. However, geo-domains’ spatial modeling poses real challenges, including the uncertainty assessment of geo-domain boundaries. Geo-domain models are subject to uncertainties due mainly to the inherent lack of knowledge in areas with little or no data. Because they are often used for impactful decision-making, they must accurately estimate the geo-domain boundaries’ uncertainty. This paper presents a geostatistical implicit modeling method to assess the uncertainty of 3D geo-domain boundaries. The basic concept of the method is to represent the underlying implicit function associated with each geo-domain as a sum of a random implicit trend function and a residual random function. The conditional simulation of geo-domains is performed through a step-by-step approach. First, implicit trend function realizations and optimal covariance parameters associated with the residual random function are generated through the probability perturbation method. Then, residual function realizations are generated through classical geostatistical unconditional simulation methods and added to implicit trend function realizations to obtain unconditional implicit function realizations. Next, the conditioning of unconditional implicit function realizations to hard data is performed via principal component analysis and randomized quadratic programming. Finally, conditional implicit function simulations are transformed to conditional geo-domain simulations by applying a truncation rule. The proposed method is constructed to honor hard data and stated rules of how geo-domains interact spatially. It is applied to a lithological dataset from a porphyry copper deposit. A comparison with the classical sequential indicator simulation (SIS) method is carried out. The results indicate that the proposed approach can provide a more reliable and realistic uncertainty assessment of 3D geo-domain boundaries than the traditional sequential indicator simulation (SIS) approach.

地理域的空间建模已在许多地球科学领域中无处不在。然而，地理域的空间建模带来了真正的挑战，包括地理域边界的不确定性评估。地理域模型容易受到不确定性的影响，这主要是由于在数据很少或没有数据的地区内在缺乏知识。因为它们经常用于有影响力的决策，所以它们必须准确估计地理域边界的不确定性。本文提出了一种地统计隐式建模方法来评估 3D 地理域边界的不确定性。该方法的基本概念是将与每个地理域相关联的潜在隐函数表示为随机隐趋势函数和残差随机函数之和。地理域的条件模拟是通过逐步方法执行的。首先，通过概率扰动方法生成与残差随机函数相关的隐式趋势函数实现和最优协方差参数。然后，通过经典地统计无条件模拟方法生成残差函数实现，并添加到隐式趋势函数实现中以获得无条件隐函数实现。接下来，通过主成分分析和随机二次规划执行无条件隐函数实现对硬数据的调节。最后，通过应用截断规则将条件隐函数模拟转换为条件地理域模拟。所提出的方法旨在尊重硬数据和地理域如何在空间上相互作用的规定规则。它应用于来自斑岩铜矿床的岩性数据集。与经典的序列指标模拟 (SIS) 方法进行了比较。结果表明，与传统的顺序指标模拟 (SIS) 方法相比，所提出的方法可以提供更可靠、更现实的 3D 地理域边界不确定性评估。