基于顶点中心有限元算法的重力场矢量和重力梯度张量高精度模拟  

High-accuracy gravity field and gravity gradient forward modelling based on 3 D vertex-centered finite-element algorithm

作　　者：童孝忠 孙娅 黄基文 柳建新 TONG Xiao-zhong;SUN Ya;HUANG Ji-wen;LIU Jian-xin(School of Geosciences and Info-physics,Central South University,Changsha 410083,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals of Ministry of Education,Central South University,Changsha 410083,China)

机构地区：[1]School of Geosciences and Info-physics,Central South University,Changsha 410083,China [2]Key Laboratory of Metallogenic Prediction of Nonferrous Metals of Ministry of Education,Central South University,Changsha 410083,China

出　　处：《Journal of Central South University》2024年第5期1659-1670,共12页中南大学学报（英文版）

基　　金：Project(42274083) supported by the National Natural Science Foundation of China;Project(2023JJ30659) supported by Hunan Provincial Natural Science Foundation of China。

摘　　要：密度非均质性引起的重力异常由三维泊松方程控制,而目前大多数正演模拟方法都依赖于其积分解和以单元为中心的数值方法。当利用重力位计算重力场时,这些数值策略将不可避免地失去准确性。为了缓解这一问题,本文提出了一种高效、准确的高阶顶点中心有限元方法来模拟三维重力异常。首先,通过具有六面体网格的顶点中心有限元来建立正演算法,并选用ILU-BICGSTAB迭代方法求解大型对称稀疏线性方程组。其次,为了获得重力位的一阶导数和二阶导数,采用了高阶拉格朗日插值技术。最后,采用三维立方体密度模型测试了顶点中心有限元算法的准确性,并利用薄垂直矩形棱镜模型和实测模型测试了算法的灵活性。数值结果表明,高阶顶点中心有限元算法能获得高精度的重力场矢量和重力梯度张量。与精确积分解和顶点中心算法相比,高阶顶点中心有限元格式在模拟三维重力异常方面表现出更高的效率和准确性。同时,相较于单元中心数值解,高阶顶点中心有限元算法在模拟三维重力异常表现出更高的效率和准确性。Gravity anomalies generated by density non-uniformity are governed by the 3D Poisson equation.Most existing forward methods for such anomalies rely on integral techniques and cell-centered numerical approaches.Once the gravitational potential is calculated,these numerical schemes will inevitably lose high accuracy.To alleviate this problem,an accurate and efficient high-order vertex-centered finite-element scheme for simulating 3D gravity anomalies is presented.Firstly,the forward algorithm is formulated through the vertex-centered finite element with hexahedral meshes.The biconjugate gradient stabilized algorithm can solve the linear equation system combined with an incomplete LU factorization(ILU-BICSSTAB).Secondly,a high-degree Lagrange interpolating scheme is applied to achieve the first-derivate and second-derivate gravitational potential.Finally,a 3D cubic density model is used to test the accuracy of the vertex-centered finite-element algorithm,and thin vertical rectangular prisms and real example for flexibility.All numerical results indicate that our high-order vertex-centered finite-element method can provide an accurate approximation for the gravity field vector and the gravity gradient tensor.Meanwhile,compared to the cell-centered numerical algorithm,the high-order vertex-centered finite element scheme exhibits higher efficiency and accuracy in simulating 3D gravity anomalies.

关 键 词：重力异常 三维泊松方程 顶点中心有限元算法 数值模拟 ILU-BICGSTAB迭代法 

分 类 号：P631.1[天文地球—地质矿产勘探] TB115[天文地球—地质学]