起伏地形下基于非结构网格模型降维的重力三维密度反演

3D density inversionof gravity based on unstructured grid and model dimension reduction under undulating terrain

复杂起伏地形以及剖分方式对重力反演解释具有重要影响.目前重力密度反演研究主要基于直立长方体模型,这显著降低了对起伏地形和复杂地质体的拟合程度,对重力反演解释易产生较大影响.四面体非结构网格能够更加精细地模拟起伏地形及复杂地质体,为此本文研究了起伏地形条件下基于四面体非结构网格剖分的重力三维密度反演.首先基于Delaunay方法将地下区域剖分为四面体非结构网格,引入垂向导数和相关系数两种方法进行模型降维技术从而减小解的空间,通过添加最小长度约束,深度加权约束,物性范围约束构建目标函数,并采用预条件共轭梯度法求解.为了提高反演效率在计算过程引入OpenMP并行算法.并研究了各项约束以及两种模型降维方法在四面体非结构网格正则化反演中的效果.通过不同深度直立长方体模型以及起伏地形下组合模型试验,基于四面体非结构网格的重力密度反演可以清晰地反映异常体位置.将本文提出的方法应用于美国密苏里州东南部的氧化铁矿床,反演结果与已知岩体具有较好的一致性,进一步证明该方法的正确性和有效性.

Complex undulating topography and mesh generation method have important influence on gravity inversion and interpretation.At present,the density inversion of gravity is mainly based on vertical cuboid model,which significantly reduces the degree of fitting for undulating terrain and complex geological bodies,and is easy to have a great impact on the gravity inversion and interpretation.The tetrahedral unstructured grid can more accurately simulate the undulating terrain and complex geological bodies.Therefore,this paper studies the 3D density inversion of gravity based on tetrahedral unstructured grid under the undulating terrain.Firstly,the underground area is divided into tetrahedral unstructured grids based on Delaunay′s method,and two methods of vertical derivative and correlation coefficient are introduced to model dimension reduction so as to reduce the space of the solution.The objective function is constructed using the minimum length constraint,the depth weighted constraint and the physical range constraint,and solved by the preconditioned conjugate gradient method.In order to improve the inversion efficiency,OpenMP parallel algorithm is introduced.The effects of various constraints and two model dimension reduction methods on the regularized inversion of tetrahedral unstructured meshes are studied.The density inversion of gravity based on tetrahedral unstructured grid can clearly reflect the position of the geological bodies through the experiments of vertical cuboid models at different depths and combined models under undulating terrain.The method proposed in this paper is applied to the iron oxide deposit in Southeast Missouri,USA.The inversion results are in great agreement with the known rock masses,which further proves the correctness and effectiveness of the method.