Articles | Volume 16, issue 13
Development and technical paper
05 Jul 2023
Development and technical paper |  | 05 Jul 2023

AdaHRBF v1.0: gradient-adaptive Hermite–Birkhoff radial basis function interpolants for three-dimensional stratigraphic implicit modeling

Baoyi Zhang, Linze Du, Umair Khan, Yongqiang Tong, Lifang Wang, and Hao Deng

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Cited articles

Basson, I. J., Creus, P. K., Anthonissen, C. J., Stoch, B., and Ekkerd, J.: Structural analysis and implicit 3D modelling of high-grade host rocks to the Venetia kimberlite diatremes, Central Zone, Limpopo Belt, South Africa, J. Struct. Geol., 86, 47-61,, 2016. 
Basson, I. J., Anthonissen, C. J., McCall, M. J., Stoch, B., Britz, J., Deacon, J., Strydom, M., Cloete, E., Botha, J., Bester, M., and Nel, D.: Ore-structure relationships at Sishen Mine, Northern Cape, Republic of South Africa, based on fully-constrained implicit 3D modelling, Ore Geol. Rev., 86, 825–838,, 2017. 
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Calcagno, P., Chilès, J. P., Courrioux, G., and Guillen, A.: Geological modelling from field data and geological knowledge: Part I. Modelling method coupling 3D potential-field interpolation and geological rules, Phys. Earth Planet. In., 171, 147–157,, 2008. 
Caumon, G., Gray, G., Antoine, C., and Titeux, M.-O.: Three-Dimensional Implicit Stratigraphic Model Building From Remote Sensing Data on Tetrahedral Meshes: Theory and Application to a Regional Model of La Popa Basin, NE Mexico, IEEE T. Geosci. Remote, 51, 1613–1621, 2013. 
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.