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物探与化探  2025, Vol. 49 Issue (2): 349-359    DOI: 10.11720/wtyht.2025.2573
  方法研究信息处理仪器研制 本期目录 | 过刊浏览 | 高级检索 |
基于标量坐标的复杂地质表面模型隐式生成方法
刘培刚1(), 袁昊1, 薛开欣1, 李兆亮2,3, 李宗民1
1.中国石油大学(华东) 计算机科学与技术学院,山东 青岛 266580
2.中国自然资源航空物探遥感中心,北京 100083
3.自然资源部 航空地球物理与遥感地质重点实验室,北京 100083
Implicit generation of complex geological surface models based on scalar coordinates
LIU Pei-Gang1(), YUAN Hao1, XUE Kai-Xin1, LI Zhao-Liang2,3, LI Zong-Min1
1. College of Computer Science and Technology, China University of Petroleum (East China), Qingdao 266580, China
2. China Aero Geophysical Survey and Remote Sensing Center for Natural Resources, Beijing 100083, China
3. Key Laboratory of Airborne Geophysics and Remote Sensing Geology, Ministry of Land and Resources, Beijing 100083, China
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摘要 

地质模型的构建和呈现是三维地质建模领域的研究热点和难点之一。针对规模庞大、表面复杂、地质约束信息不足的地质体数据,本文采用基于域分解的隐式生成方法,实现大规模地质表面模型的快速构建。以径向基函数为核函数来构建隐式方程;利用重叠域分解策略,并行求解每个域内的分布函数,降低时空成本,加快求解速度;提取法向量生成控制点,构建表面波动约束,实现对模型边界的良好控制。实验结果表明,本文提出的方法能够在保证模型较高质量的前提下显著提升分布函数的求解效率。本研究有效解决地质建模中效率与精度的平衡难题,为地质表面精细化重构提供了方法理论支持。

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刘培刚
袁昊
薛开欣
李兆亮
李宗民
关键词 地质表面模型隐式建模径向基函数域分解    
Abstract

The construction and presentation of a geological modelprove to be ahot topic and challenge in research on 3D geological modelling. Given the large scale, involvement of complex surfaces, and insufficient geological constraints of geological body data, this study achieved the rapid construction of a large-scale geological surface model using the domain decomposition-based implicit generation method. Initially, implicit functionswere constructed by taking radial basis functions as the kernel functions.Then, the distribution functions of various domainswere solved in parallel usinganoverlapping domain decompositionmethod, reducing the spatiotemporalcost and accelerating the solving process.Subsequently, normal vectors were extracted to generate control pointsand formconstraints on surface fluctuation, thereby effectively controlling the model boundaries. The experimental results indicate that the method proposed in this study can significantly improve the efficiency associated with the solving of distribution functionswhile ensuring the high quality of the model. This study effectively solves the problem of balance between efficiency and precision in geological modeling and provides methodological support for the refinement of geological surfaces.

Key wordsgeological surface model    implicit modelling    radial basis function    domain decomposition
收稿日期: 2023-12-27      修回日期: 2024-05-14      出版日期: 2025-04-20
ZTFLH:  TP391  
基金资助:国家重点研发计划项目(2019YFF0301800);国家自然科学基金项目(61379106)
作者简介: 刘培刚(1979-),男,2017年毕业于北京大学,理学博士,主要从事人工智能、图形图像处理、数据科学及应用的研究工作。Email:dongfangwy@upc.edu.cn
引用本文:   
刘培刚, 袁昊, 薛开欣, 李兆亮, 李宗民. 基于标量坐标的复杂地质表面模型隐式生成方法[J]. 物探与化探, 2025, 49(2): 349-359.
LIU Pei-Gang, YUAN Hao, XUE Kai-Xin, LI Zhao-Liang, LI Zong-Min. Implicit generation of complex geological surface models based on scalar coordinates. Geophysical and Geochemical Exploration, 2025, 49(2): 349-359.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2025.2573      或      https://www.wutanyuhuatan.com/CN/Y2025/V49/I2/349
Fig.1  模型构建流程
Fig.2  法向校正方法
Fig.3  控制点二维示意(红色代表模型内部控制点,蓝色代表模型外部控制点)
Fig.4  域重叠示意
(ρ表示域重叠部分)
Fig.5  纵截面
Fig.6  横截面
Fig.7  固定视点的法向量
(a~e为法向量指向模型外部的区域放大效果)
Fig.8  固定视点的法向量切面示意
Fig.9  校正的法向量
(a~e为图7对应区域校正法向后的放大效果)
Fig.10  校正的法向量切面示意
Fig.11  法向量随机筛选
(a~e为法向量随机筛选的区域放大效果)
Fig.12  法向量随机筛选切面示意
Fig.13  法向量极值筛选
(a~e为法向量极值筛选的区域放大效果)
Fig.14  法向量极值筛选切面示意
Fig.15  5个法向量随机筛选和极值筛选区域内法向量数量
方法 矩阵阶数
Surfe (4×N)2
本文方法 (N/10)2
Table 1  矩阵复杂度对比
方法 不同数据量的运行时间
1000 3200 5000 11000 50000
Surfe 90 s 40 min 2.5 h 22 h
本文方法
(非并行)
0.91 s 19.45 s 29.72 s 67.58 s 268.3 s
本文方法
(并行)
0.35 s 3.3 s 5.2 s 15.8 s 120.6 s
Table 2  运行时间对比
Fig.16  法向量随机筛选和极值筛选结果对比
(a~c为局部放大区域)
参数 数据量
1000 3200 5000 11000
运行时间/s 0.35 3.3 5.2 15.8
平均曲率/10-4 8.921 4.972 3.519 1.377
Table 3  不同数据量下模型的平均曲率
Fig.17  1 000个数据的模型效果
Fig.18  3 200个数据的模型效果
Fig.19  5 000个数据的模型效果
Fig.20  11 000个数据的模型效果
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