Implicit methods for modeling geological structures such as stratigraphy and faults have been developed for more than a decade, and they have made automatic model construction feasible. The implicit potential field method is such a method that is capable of incorporating multiple types of data including contact points for geological boundaries and their measured orientations. The implicit potential field method relies on the solution of a co-kriging system. However, applying the method to 3D modeling of large-scale geological structures constrained to dense data and strict geological rules remains challenging. Due to the non-stationary and complex nature of large-scale geological structures, and difficulty in estimating an adequate variogram model, performing global interpolation with all dense data together may create geologically unrealistic artifacts. We propose a framework that uses a divide-and-conquer strategy. The core idea is to create intermediate 3D geological models that match subsets of data and then recombine them into a single large 3D geological model, while maintaining data and geological rule constraints. We also prove that linear combinations of potential fields preserve properties of conditioning. The paper presents an application of the framework in modeling the stratigraphy model of a large banded iron formation in Western Australia with dense boreholes, but scarce orientation measurements.

用于模拟地层和断层等地质结构的隐式方法已经发展了十多年，它们使自动模型构建成为可能。隐式势场法是这样一种方法，它能够合并多种类型的数据，包括地质边界的接触点及其测量方向。隐式势场方法依赖于协同克里金系统的解决方案。然而，将该方法应用于受限于密集数据和严格地质规则的大型地质结构的 3D 建模仍然具有挑战性。由于大尺度地质构造的非平稳性和复杂性，难以估计出合适的变差函数模型，将所有密集数据一起执行全局插值可能会产生地质上不切实际的工件。我们提出了一个使用分而治之策略的框架。核心思想是创建与数据子集匹配的中间 3D 地质模型，然后将它们重新组合成单​​个大型 3D 地质模型，同时保持数据和地质规则约束。我们还证明了势场的线性组合保留了条件反射的特性。本文介绍了该框架在模拟西澳大利亚大型带状铁层地层模型中的应用，该地层具有密集的钻孔，但方向测量稀少。核心思想是创建与数据子集匹配的中间 3D 地质模型，然后将它们重新组合成单​​个大型 3D 地质模型，同时保持数据和地质规则约束。我们还证明了势场的线性组合保留了条件反射的特性。本文介绍了该框架在模拟西澳大利亚大型带状铁层地层模型中的应用，该地层具有密集的钻孔，但方向测量稀少。核心思想是创建与数据子集匹配的中间 3D 地质模型，然后将它们重新组合成单​​个大型 3D 地质模型，同时保持数据和地质规则约束。我们还证明了势场的线性组合保留了条件反射的特性。本文介绍了该框架在模拟西澳大利亚大型带状铁层地层模型中的应用，该地层具有密集的钻孔，但方向测量稀少。