3D Modeling of Large-Scale Geological Structures by Linear Combinations of Implicit Functions: Application to a Large Banded Iron Formation

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.

Automated summary

Implicit methods for modeling geological structures, such as the implicit potential field method, have been developed for over a decade, allowing for automatic model construction by incorporating various types of data. However, applying this method to large-scale 3D modeling of geological structures remains challenging due to complex nature and difficulty in estimating an adequate variogram model. A divide-and-conquer strategy is proposed to address this challenge, creating intermediate 3D geological models matching subsets of data and then recombining them while preserving data and geological rule constraints.