Preprints
https://doi.org/10.5194/egusphere-2022-1304
https://doi.org/10.5194/egusphere-2022-1304
 
23 Jan 2023
23 Jan 2023
Status: this preprint is open for discussion.

AdaHRBF v1.0: Gradient-Adaptive Hermite-Birkhoff Radial Basis Function Interpolants for Three-dimensional Stratigraphic Implicit Modeling

Baoyi Zhang1, Linze Du1, Umair Khan2, Yongqiang Tong1,3, Lifang Wang3,4, and Hao Deng1 Baoyi Zhang et al.
  • 1Key laboratory of Metallogenic Prediction of Nonferrous Metals & Geological Environment Monitoring (Ministry of Education)/School of Geosciences & Info-Physics, Central South University, Changsha 410083, China
  • 2Institute of Deep-Sea Science and Engineering, Chinese Academy of Sciences, Sanya 572000, China
  • 3Wuhan ZGIS Science & Technology Co. Ltd., Wuhan 430074, China
  • 4School of Geomatics and Geography, Hunan Vocational College of Engineering, Changsha 410151, China

Abstract. Three-dimensional (3D) stratigraphic modelling is capable of modeling the shape, topology, and other properties of strata in a digitalized manner. The implicit modeling approach is becoming the mainstream approach for 3D stratigraphic modelling, which incorporates both the off-contact attitudes and the on-contact occurrence information of stratigraphic interface to estimate the stratigraphic potential field (SPF) to represent the 3D architectures of strata. However, the magnitudes of SPF gradient controlling variation trend of SPF values cannot be directly derived from the known stratigraphic attribute or attitude data. In this paper, we propose an Hermite-Birkhoff radial basis function (HRBF) formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D SPF modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolant 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 optimizing term to iteratively obtain the true gradient magnitude. The case study shows that the HRBF interpolants can consistently establish accurate multiple stratigraphic interfaces and fully express the internal stratigraphic attribute and attitude. To ensure harmony of the variation of stratigraphic thickness, we adopt the relative burial depth of stratigraphic interface to the Quaternary as the SPF attribute value and propose a new stratigraphical thickness index (STI) to represent the variation trend of stratigraphic thickness in SPF. In addition, the proposed stratigraphic potential field modeling by HRBF interpolants can provide a suitable basic model for subsequent geosciences numerical simulation.

Baoyi Zhang et al.

Status: open (until 20 Mar 2023)

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Baoyi Zhang et al.

Data sets

AdaHRBF Zhang et al. https://github.com/csugeo3d/AdaHRBF

Model code and software

AdaHRBF Zhang et al. https://doi.org/10.5281/zenodo.7340093

Baoyi Zhang et al.

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Short summary
We propose an HRBF formulation, AdaHRBF, with an adaptive gradient magnitude for continuous 3D SPF modeling of multiple stratigraphic interfaces. In the linear system of HRBF interpolant 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 optimizing term to iteratively obtain the true gradient magnitude.