# Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Modeling Elements

#### 3.1. Attitudes

#### 3.2. Boundaries

## 4. Modeling Workflow

- (1)
- (2)
- A fundamental body that contains all of the regional geological bodies was constructed.
- (3)
- Using the attitude constraints, the geological interfaces were constructed from the geological boundaries’ arcs.
- (4)
- Using face-body Boolean calculation, the geological bodies were extracted from the fundamental body.
- (5)
- The top surfaces of the geological bodies were matched to the surface entities that were created in step 4 through their boundaries.

## 5. Top Surface Models

- (1)
- A triangulated irregular network (TIN) was constructed from the DEM points and the points along the boundaries.
- (2)
- The boundary was substituted into the TIN model, and the triangles that intersected the boundary were constructed until they were distributed on both sides of the boundary.
- (3)
- The triangles above the body’s top surface were deleted, and the top surface was acquired.

## 6. HRBF Body-Extraction Method

#### 6.1. HRBF Interfaces

#### 6.2. Fundamental Model

#### 6.3. Face-Body Boolean

#### 6.4. Extraction of the Geological Model

## 7. Surface Intersection

#### 7.1. Surface-Segment Intersection

_{1}to surface $\overline{{P}_{1}{H}_{1}}$ is |f (P

_{1})|, and the distance from P

_{2}to surface $\overline{{P}_{1}{H}_{2}}$ is |f (P

_{2})|. The perpendicular feet H

_{1}and H

_{2}of P

_{1}and P

_{2}, respectively, and the intersection point K are approximately collinear. Under these circumstances, triangle △P

_{1}H

_{1}K is similar to triangle △P

_{2}H

_{2}K. From the characteristics of similar triangles, vertex $\overrightarrow{{P}_{1}K}$ could be calculated as

#### 7.2. Surface–Triangle Intersection

_{1}) = 0, f(P

_{2}) < 0 and f(P

_{3}) > 0, the triangle was divided into △P

_{1}KP

_{3}and △P

_{1}KP

_{2}; △P

_{1}KP

_{3}was in the positive field, and △P

_{1}KP

_{2}was in the negative field.

_{1}) > 0, f(P

_{2}) < 0, and f(P

_{3}) < 0, and the triangle was divided as △P

_{1}K

_{1}K

_{2}, △P

_{2}K

_{1}K

_{2}and △P

_{2}P

_{3}K

_{2}. Triangle △P

_{1}K

_{1}K

_{2}was in the positive field, and △P

_{2}K

_{1}K

_{2}and △P

_{2}P

_{3}K

_{2}were in the negative field.

## 8. Results and Analysis

#### 8.1. Simulation of Strata

#### 8.2. Simulation of Folds

#### 8.3. Simulation of Faults

#### 8.4. Realistic Geological Mapping

^{(R)}Core

^{(TM)}i5-4210U, 8 GB of RAM memory, and an Intel HD graphics card).

## 9. Conclusions and Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 4.**Geological interface created by the geological boundary through HRBF and the fundamental body divided by the geological interface.

**Figure 6.**Surface-related intersections. (

**a**) The segment intersects the HRBF surface; (

**b**) a triangle with one point on the surface intersects the surface; and (

**c**) a triangle with no points on the surface intersects the surface.

**Figure 7.**Simulated strata: (

**a**) conformable strata and sections perpendicular to the strata and (

**b**) unconformable strata and cross-sections describing the conformable and unconformable parts.

**Figure 9.**Fold models from a geological map: (

**a**) the 2D geological map with attitudes that describe the geological conditions; (

**b**) 3D geological model; and (

**c**) exploded view of the model.

**Figure 11.**Fault models from a geological map: (

**a**) 2D geological map containing two faults; (

**b**) 3D geological model; and (

**c**) exploded view of the geological model divided by the faults.

**Figure 12.**Realistic geological model: (

**a**) 2D geological map of the study area; (

**b**) 3D geological model, the three main parts of the model and the constraining attitudes’ displayed as arrows; (

**c**) cross-sections of the geological model; and (

**d**) exploded view of the models.

**Figure 13.**Geological models constrained by Drill-hole data: (

**a**) virtual drill-hole data constructed in the area containing stratum; (

**b**) the geological model that extended vertically was modified by the drill-holes; and (

**c**) the stratum model constrained by the drill-holes.

**Figure 14.**Terrain surface modeling time with respect to the DEM point count. The modeling time was linear dependent to the point count.

**Figure 15.**Plumb scanning implicit construction time with respect to the reciprocal of the quadratic of the grid length. The modeling time was nearly proportional to the reciprocal of the quadratic of the grid length.

Point Count | Time/s |
---|---|

5000 | 8 |

10,000 | 15 |

20,000 | 30 |

50,000 | 81 |

100,000 | 147 |

200,000 | 293 |

Grid Length/m | Time/s |
---|---|

50 | 698 |

70 | 324 |

80 | 256 |

90 | 215 |

100 | 172 |

200 | 87 |

300 | 64 |

400 | 61 |

500 | 60 |

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**MDPI and ACS Style**

Guo, J.; Wu, L.; Zhou, W.; Jiang, J.; Li, C.
Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes. *ISPRS Int. J. Geo-Inf.* **2016**, *5*, 17.
https://doi.org/10.3390/ijgi5020017

**AMA Style**

Guo J, Wu L, Zhou W, Jiang J, Li C.
Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes. *ISPRS International Journal of Geo-Information*. 2016; 5(2):17.
https://doi.org/10.3390/ijgi5020017

**Chicago/Turabian Style**

Guo, Jiateng, Lixin Wu, Wenhui Zhou, Jizhou Jiang, and Chaoling Li.
2016. "Towards Automatic and Topologically Consistent 3D Regional Geological Modeling from Boundaries and Attitudes" *ISPRS International Journal of Geo-Information* 5, no. 2: 17.
https://doi.org/10.3390/ijgi5020017