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<p>The three-dimensional geological model of fold structures can facilitate a better understanding of the complex underground fold structures and provide guidance for resource exploration. To address the inability of traditional arc-segment cutting methods to construct three-dimensional geological models of upright and inclined fold structures that satisfy fold element constraints, this study proposes an integrated explicit–implicit regional modeling method that combines nonuniform rational B-splines (NURBS) and Hermite radial basis functions (HRBFs) based on fold element constraints. The specific procedures include (1) restoring the fold layers based on the NURBS with the fold elements as constraints, (2) performing cutting modeling by implicitizing the NURBS surface to construct a three-dimensional fold model that conforms to the laws of structural geology, and (3) completing the modeling of other geological structures and the implicit integration of the entire geological map based on the implicit HRBF modeling method. This study selects the Yeyahu area in Beijing and the typical fold structure areas in the northwest of China as the research objects to validate the three-dimensional modeling method for fold structures. A comparative study with the traditional arc-segment cutting method shows that the method proposed in this paper integrates mathematical parameters and fold elements for modeling. The modeling process is reasonable, the degree of automation is high, and it can accurately construct the three-dimensional geological models of various upright and inclined fold structures in regional geological survey maps.</p> Graphical Abstract <p></p>

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A Method for Integrated Explicit and Implicit Regional Modeling of Fold Structures Combining NURBS and HRBF Based on the Constraints of Fold Elements

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Jiateng Guo,
  • Long Gao,
  • Ziming Xiong,
  • Luyuan Wang,
  • Xulei Wang,
  • Zhibin Liu,
  • Yiming Liu

摘要

The three-dimensional geological model of fold structures can facilitate a better understanding of the complex underground fold structures and provide guidance for resource exploration. To address the inability of traditional arc-segment cutting methods to construct three-dimensional geological models of upright and inclined fold structures that satisfy fold element constraints, this study proposes an integrated explicit–implicit regional modeling method that combines nonuniform rational B-splines (NURBS) and Hermite radial basis functions (HRBFs) based on fold element constraints. The specific procedures include (1) restoring the fold layers based on the NURBS with the fold elements as constraints, (2) performing cutting modeling by implicitizing the NURBS surface to construct a three-dimensional fold model that conforms to the laws of structural geology, and (3) completing the modeling of other geological structures and the implicit integration of the entire geological map based on the implicit HRBF modeling method. This study selects the Yeyahu area in Beijing and the typical fold structure areas in the northwest of China as the research objects to validate the three-dimensional modeling method for fold structures. A comparative study with the traditional arc-segment cutting method shows that the method proposed in this paper integrates mathematical parameters and fold elements for modeling. The modeling process is reasonable, the degree of automation is high, and it can accurately construct the three-dimensional geological models of various upright and inclined fold structures in regional geological survey maps.

Graphical Abstract