Articles | Volume 16, issue 13
https://doi.org/10.5194/gmd-16-3651-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-16-3651-2023
© Author(s) 2023. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development and technical paper
| 
05 Jul 2023
Development and technical paper |
| 05 Jul 2023
| 05 Jul 2023
AdaHRBF v1.0: gradient-adaptive Hermite–Birkhoff radial basis function interpolants for three-dimensional stratigraphic implicit modeling
Baoyi Zhang
Key laboratory of Metallogenic Prediction of Nonferrous Metals and
Geological Environment Monitoring (Ministry of Education), Central South University, Changsha 410083,
China
School of
Geosciences and Info-Physics, Central South University, Changsha 410083,
China
Linze Du
Key laboratory of Metallogenic Prediction of Nonferrous Metals and
Geological Environment Monitoring (Ministry of Education), Central South University, Changsha 410083,
China
School of
Geosciences and Info-Physics, Central South University, Changsha 410083,
China
Umair Khan
Institute of Deep-Sea Science and Engineering, Chinese Academy of
Sciences, Sanya 572000, China
Yongqiang Tong
Key laboratory of Metallogenic Prediction of Nonferrous Metals and
Geological Environment Monitoring (Ministry of Education), Central South University, Changsha 410083,
China
School of
Geosciences and Info-Physics, Central South University, Changsha 410083,
China
Wuhan ZGIS Science and Technology Co. Ltd., Wuhan 430074, China
Lifang Wang
Wuhan ZGIS Science and Technology Co. Ltd., Wuhan 430074, China
School of Geomatics and Geography, Hunan Vocational College of
Engineering, Changsha 410151, China
Hao Deng
CORRESPONDING AUTHOR
Key laboratory of Metallogenic Prediction of Nonferrous Metals and
Geological Environment Monitoring (Ministry of Education), Central South University, Changsha 410083,
China
School of
Geosciences and Info-Physics, Central South University, Changsha 410083,
China
Viewed
Total article views: 5,716 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 23 Jan 2023)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 3,207 | 2,318 | 191 | 5,716 | 211 | 274 |
- HTML: 3,207
- PDF: 2,318
- XML: 191
- Total: 5,716
- BibTeX: 211
- EndNote: 274
Total article views: 3,395 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 05 Jul 2023)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 2,097 | 1,183 | 115 | 3,395 | 142 | 186 |
- HTML: 2,097
- PDF: 1,183
- XML: 115
- Total: 3,395
- BibTeX: 142
- EndNote: 186
Total article views: 2,321 (including HTML, PDF, and XML)
Cumulative views and downloads
(calculated since 23 Jan 2023)
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 1,110 | 1,135 | 76 | 2,321 | 69 | 88 |
- HTML: 1,110
- PDF: 1,135
- XML: 76
- Total: 2,321
- BibTeX: 69
- EndNote: 88
Viewed (geographical distribution)
Total article views: 5,716 (including HTML, PDF, and XML)
Thereof 5,637 with geography defined
and 79 with unknown origin.
Total article views: 3,395 (including HTML, PDF, and XML)
Thereof 3,338 with geography defined
and 57 with unknown origin.
Total article views: 2,321 (including HTML, PDF, and XML)
Thereof 2,299 with geography defined
and 22 with unknown origin.
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
1
Cited
13 citations as recorded by crossref.
- Three-Dimensional Stratigraphic Structure and Property Collaborative Modeling in Urban Engineering Construction B. Zhang et al. https://doi.org/10.3390/math13030345
- CurvRBF: Mean Curvature-Controllable Radial Basis Functions for Implicit Geological Modeling Y. Chen et al. https://doi.org/10.1007/s11004-025-10226-0
- Deep Subsurface Pseudo-Lithostratigraphic Modeling Based on Three-Dimensional Convolutional Neural Network (3D CNN) Using Inversed Geophysical Properties and Shallow Subsurface Geological Model B. Zhang et al. https://doi.org/10.2113/2024/lithosphere_2023_273
- A domain-decomposition-based parallel approach for 3D geological modeling using radial basis functions interpolation on GPUs H. Li et al. https://doi.org/10.1007/s12145-024-01588-w
- Semantic rule-guided three-dimensional reservoir modeling method using an improved multiple-point geostatistics simulation Q. Chen et al. https://doi.org/10.3389/feart.2026.1766398
- Rapid Implicit 3D geological modelling from a large quantity of boreholes via a divide-and-conquer strategy based on Voronoi diagrams and R-functions X. Wang et al. https://doi.org/10.1016/j.enggeo.2025.108348
- Iterative 3D Implicit Orebody Modeling Based on Automatic Refinement of Off-Surface Points X. Mao et al. https://doi.org/10.1007/s11053-026-10727-7
- Integrated Three-Dimensional Structural and Petrophysical Modeling for Assessment of CO2 Storage Potential in Gas Reservoir S. Shah et al. https://doi.org/10.2113/2024/lithosphere_2024_222
- A geology-informed graph neural network solution for addressing the data sparsity challenge in 3D geological modeling M. Liao et al. https://doi.org/10.1016/j.enggeo.2026.108859
- A lightweight convolutional neural network with end-to-end learning for three-dimensional mineral prospectivity modeling: A case study of the Sanhetun Area, Heilongjiang Province, Northeastern China B. Zhang et al. https://doi.org/10.1016/j.oregeorev.2023.105788
- A deep learning-driven three-dimensional geological modeling method using sparse borehole sampling data Z. He et al. https://doi.org/10.1016/j.measurement.2025.118461
- Multi-Scale 3D Convolution Neural Network with Lightweight Attention Mechanisms for Mineral Prospectivity Mapping in Pulang Porphyry Deposit, Yunnan Province, Southwest China X. Wang et al. https://doi.org/10.1007/s11053-026-10726-8
- Implicit 3D Orebody Boundary Modeling Based on Adaptive Finite Difference Method Z. Wang et al. https://doi.org/10.3390/min16050541
13 citations as recorded by crossref.
- Three-Dimensional Stratigraphic Structure and Property Collaborative Modeling in Urban Engineering Construction B. Zhang et al. https://doi.org/10.3390/math13030345
- CurvRBF: Mean Curvature-Controllable Radial Basis Functions for Implicit Geological Modeling Y. Chen et al. https://doi.org/10.1007/s11004-025-10226-0
- Deep Subsurface Pseudo-Lithostratigraphic Modeling Based on Three-Dimensional Convolutional Neural Network (3D CNN) Using Inversed Geophysical Properties and Shallow Subsurface Geological Model B. Zhang et al. https://doi.org/10.2113/2024/lithosphere_2023_273
- A domain-decomposition-based parallel approach for 3D geological modeling using radial basis functions interpolation on GPUs H. Li et al. https://doi.org/10.1007/s12145-024-01588-w
- Semantic rule-guided three-dimensional reservoir modeling method using an improved multiple-point geostatistics simulation Q. Chen et al. https://doi.org/10.3389/feart.2026.1766398
- Rapid Implicit 3D geological modelling from a large quantity of boreholes via a divide-and-conquer strategy based on Voronoi diagrams and R-functions X. Wang et al. https://doi.org/10.1016/j.enggeo.2025.108348
- Iterative 3D Implicit Orebody Modeling Based on Automatic Refinement of Off-Surface Points X. Mao et al. https://doi.org/10.1007/s11053-026-10727-7
- Integrated Three-Dimensional Structural and Petrophysical Modeling for Assessment of CO2 Storage Potential in Gas Reservoir S. Shah et al. https://doi.org/10.2113/2024/lithosphere_2024_222
- A geology-informed graph neural network solution for addressing the data sparsity challenge in 3D geological modeling M. Liao et al. https://doi.org/10.1016/j.enggeo.2026.108859
- A lightweight convolutional neural network with end-to-end learning for three-dimensional mineral prospectivity modeling: A case study of the Sanhetun Area, Heilongjiang Province, Northeastern China B. Zhang et al. https://doi.org/10.1016/j.oregeorev.2023.105788
- A deep learning-driven three-dimensional geological modeling method using sparse borehole sampling data Z. He et al. https://doi.org/10.1016/j.measurement.2025.118461
- Multi-Scale 3D Convolution Neural Network with Lightweight Attention Mechanisms for Mineral Prospectivity Mapping in Pulang Porphyry Deposit, Yunnan Province, Southwest China X. Wang et al. https://doi.org/10.1007/s11053-026-10726-8
- Implicit 3D Orebody Boundary Modeling Based on Adaptive Finite Difference Method Z. Wang et al. https://doi.org/10.3390/min16050541
Saved (final revised paper)
Latest update: 29 Jul 2026
Short summary
We propose a Hermite–Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D stratigraphic potential field (SPF) modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolants constrained by the scattered on-contact attribute points and off-contact attitude points of a set of strata in 3D space, we add a novel optimization term to iteratively obtain the true gradient magnitude.
We propose a Hermite–Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an...
