起伏地表下的复杂三维地质模型建立与重力异常计算

Complex 3D Model Establishment Under Undulating Surface and Gravity Anomaly Calculation

由于地质体和矿体的形态非常复杂,使用长方体网格离散建立正演模型时可能和真实情况有很大差别,因此计算结果可靠性差。本文提出一种基于约束Delaunay网格剖分的方法对地质体进行离散并进行重力建模,在模型边界等复杂区域使用网格自适应加密技术,将三维地质体离散为有限个四面体;并详细推导出针对四面体网格的重力正演公式,实现了基于约束Delaunay网格剖分技术的三维重力数值模拟;最后,针对一个合成数据模型,将计算解与解析解对比。结果表明,细化网格的模拟结果比粗糙网格更好,满足数值模拟的精度要求。将该方法应用到金川矿区实际地质体建模中,根据局部需要,建立各处网格密度不均匀的三维模型,并计算该模型的地表重力场,而后对比模拟数据与实测数据,结果表明Delaunay网格建模方法具有很强的适用性,能够模拟复杂的地质体重力异常。

Because of the complicated shape of the actual geological bodies, it may be quite different from the real situation when using the cuboid grid to establish the forward model, and the reliability of the calculation results is poor. In this paper, a constrained Delaunay meshing method is proposed to discretize the geological bodies and perform gravity modeling. The grid adaptive cryptography is used in the complex region such as a model boundary to discretize a three-dimensional geological body into a finite tetrahedron;then, the gravity forward formula of the tetrahedral mesh is derived in detail;and finally,the three-dimensional gravity numerical simulation based on the constrained Delaunay meshing technique is realized. For a composite data model, the calculated solution is compared to the analytical solution. And the simulation results of fine mesh are better than that of coarse mesh, and meet the accuracy requirements of numerical simulation. The method was applied to the actual geological body modeling in Jinchuan mining area. According to the local needs, a three-dimensional model with uneven mesh density was built, the surface gravity field of the model was calculated, and the simulation data was compared with the measured data. The results show that the unstructured mesh modeling method is strongly applicable and can simulate the gravity anomalies of complex geological bodies.