AdaHRBF v1.0: gradient-adaptive Hermite–Birkhoff radial basis function interpolants for three-dimensional stratigraphic implicit modeling
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Published:2023-07-05
Issue:13
Volume:16
Page:3651-3674
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ISSN:1991-9603
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Container-title:Geoscientific Model Development
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language:en
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Short-container-title:Geosci. Model Dev.
Author:
Zhang BaoyiORCID, Du Linze, Khan Umair, Tong Yongqiang, Wang Lifang, Deng Hao
Abstract
Abstract. Three-dimensional (3D) stratigraphic modeling 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 modeling, which incorporates both
the off-contact strike and dip directions 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 the SPF gradient controlling the variation trend of SPF values
cannot be directly derived from the known stratigraphic attribute or strike
and dip data. In this paper, we propose a 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 interpolants constrained by the scattered on-contact
attribute points and off-contact strike and dip points of a set of strata in
3D space, we add a novel optimizing term to iteratively obtain the optimized
gradient magnitude. The case study shows that the HRBF interpolants can
consistently and accurately establish multiple stratigraphic interfaces and fully
express the internal stratigraphic attribute and orientation. To ensure
harmony of the variation in stratigraphic thickness, we adopt the relative
burial depth of the stratigraphic interface to the Quaternary as the SPF
attribute value. In addition, the proposed stratigraphic-potential-field
modeling by HRBF interpolants can provide a suitable basic model for
subsequent geosciences' numerical simulation.
Funder
National Natural Science Foundation of China China Geological Survey National Key Research and Development Program of China
Publisher
Copernicus GmbH
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