基于多尺度CSRBFs的地层三维地质建模

基于矿山多源数据实现地层三维地质建模是数字矿山研究中的一项重要工作，其成果有助于矿山资源评估、生产规划编制等工作的有序进行。采用插值方法对离散采样的非均匀点状数据进行处理，是精准构建矿体模型的关键。然而，矿体建模常用的插值方法在处理数据时，很少有效顾及数据的非均匀性。基于多尺度CSRBFs插值方法，提出了一种可以处理非均匀数据的地层三维建模技术。首先从多源数据中提取非均匀的地质离散点数据集。然后，使用多尺度CSRBFs插值构建地层表面模型，插值步骤包括：①样品点获取与单位法向量计算；②通过八叉树空间索引构建层次点集；③使用多尺度CSRBFs方法在样品点集上由粗到细逐层插值，计算地层表面隐式函数；④地层隐式曲面可视化。最后，使用提出的断层建模方法在连续地层表面构建正断层、逆断层和交叉断层模型。研究表明：多尺度CSRBFs（Multi-scale CSRBF， MsCSRBF）插值方法通过十折交叉验证获得的平均误差为0.943 m，精度优于反距离加权法（Inverse Distance Weighted， IDW）和普通克里金法（Ordinary Kriging， OK），且MsCSRBF方法相比于IDW和OK方法插值运算效率更高。上述分析表明：多尺度CSRBFs差值方法能够针对非均匀数据进行地层表面模型的高精度、快速重建。

Three-dimensional Geological Modeling of Stratum Based on Multi-scale CSRBFs

It is an important work in digital mine research to construct the three-dimensional （3D） geological models of strata based on multi-source data of mines，and these models will facilitate the mine resource assessment and production planning process.The processing of discrete sampling of non-uniform point data by interpolation method is the key to accurately construct the strata model.However，the interpolation methods commonly used in geological modeling do not consider the non-uniformity of the data.Based on the multi-scale CSRBFs interpolation method，a 3D stratum modeling process that can employ non-uniform data is proposed. The process is divided into three steps.Firstly，non-uniform geological discrete points are extracted from multi-source data.Then，the multi-scale CSRBFs interpolation is used to construct the stratum surface model，including four steps:①sample points and unit normal vectors acquisition；②construction of hierarchical point sets by octree；③ multi-scale CSRBFs method is used to interpolate layer by layer from coarse to fine on the hierarchical point sets；④visualization of the implicit surface of the stratum.Finally，the proposed fault modeling method is used to construct normal，reverse and cross-fault models on the continuous stratum surface.The stduy results show that the average error obtained by multi-scale CSRBFs interpolation method （Multi-scale CSRBF，MsCSRBF） through ten-fold cross-validation is 0.943 m，which is lower than the error obtained by inverse distance weighted （IDW） and ordinary kriging （OK）.And the MsCSRBF method is also more time-efficient than the IDW and OK interpolation methods.The above stduy results further indicated that multi-scale CSRBF interpolation method proposed in this paper can carry out high-precision and rapid reconstruction of the formation surface model for non-uniform data.