【作者】 李端；

【导师】 陈超；

【作者基本信息】 中国地质大学 ， 地球物理学， 2018， 博士

【摘要】 重力场和地磁场的空间特性及其变化是重力学和地磁学研究中的重要内容。基于本构关系以及有限的观测数据,采用数学物理方法可重构(reconstruction)或重建重力场和地磁场,并应用于重力场和地磁场的空间延拓、梯度计算、分量转换以及插值和网格化等方面,可以得到更丰富、更完整的重磁场三维空间信息。而且,重磁场观测数据通常是离散的,对离散观测数据进行重构,不仅可以提高数据转换的质量,还有利于准确认识场源特征,进而有助于叠加场的有效分离。事实上,离散位场观测数据的重构技术早已广泛应用于不同领域,但随着位场观测技术与计算机科技水平的提高,对位场重构技术提出了新的要求。因此,发展位场重构技术具有重要的学术意义和实用价值。等效源方法是一种常用的重磁场重构方法。该方法基于位场的等效性原理,利用一组简单的等效场源代替真实场源,通过充分拟合观测数据建立等效源模型,进而利用等效源模型正演实现场的重构和转换;具有适用性广、稳定性强和计算精度高的优势,受到国内外学者的广泛关注。但是,目前的等效源方法仍存在一些不足,如重构过程中会出现低频段信号的“泄露”、等效源模型设置方案缺少针对性等。本论文针对传统等效源方法中存在的问题,通过理论模型试验和分析,开展了等效源优化设置和反演算法等方面的研究。论文从等效源方法理论出发,讨论了等效源单元体形状、等效源深度、等效层展布形态、等效源磁化方向(针对地磁异常而言)和等效单元网格密度等参数的选取对重构效果的影响。通过分析产生信号“泄露”的原因,认为利用多层等效源代替单层等效源能够有效抑制信号的“泄露”;并根据理论模型试验,从重构精度、低频段信号恢复情况以及计算效率等方面进行对比,表明三层等效源方案具有最佳的重构效果。基于以上研究工作,本文提出了一种构建三层等效源模型的技术方案,即将第一层等效源布设在近地表约1~6倍离散数据点距深处;第二层等效源深度结合场源深度估计方法进行设置;第三层则设置在基底深度附近。其中第一层和第二层等效源可以随地形起伏或沿水平面进行空间展布;而为减少设置难度,第三层等效源选择沿水平面展布。等效源单元体选用长方体能较好地保留多频段位场信息,且其几何尺寸随着设置深度增加而加大,以保证各单元体相应的敏感度并控制单元体总数量。该方案所构建的三层等效源,在观测面之下呈正梯形分布,有效地减小了数据区域边部效应。论文针对等效源物性反演算法进行了讨论。对比了各反演算法的优劣,并结合三层等效源方案,选择预优共轭梯度算法用于反演,获取等效源物性分布。该算法可通过设置预优因子使深层等效源发挥作用,以减小“趋肤效应”的影响,并使计算效率得到有效提高。此外,我们引入重构重磁场的梯度值拟合误差作为评价重构效果的参数,以提高重构的准确度。论文通过大量二维与三维理论模型试验表明,本文提出的方法不仅可以高精度重构空间重磁场数据,而且能够获得高精度的异常梯度和分量等转换结果,同时可以很好地实现重磁场数据的插值、网格化及多源数据融合等应用,与传统方法相比有显著的优势。最后,论文利用实测重磁资料验证了该方法的稳定性和实用性。更多还原

【Abstract】 The characteristics and changes of gravity and geomagnetic field are very important for the exploration and research of potential field.Based on the constitutive relation and the limited observation data,the mathematical and physical methods can be used to reconstruct the gravity and geomagnetic field.These methods could be applied to spatial continuation,gradient calculation,component conversion,gridding and so on.So that,a richer and more complete three-dimensional information of the potential field can be obtained.Moreover,the reconstruction of data on discrete positions not only improve conversion accuracy,but also recove the characteristics of source accurately,which is helpful to the effective separation of superposition field.The reconstruction techniques of discrete potential field data has been widely utilized in many areas.However,with the improvement of observation technology and computer technique,new requirements have been put forward for the reconstruction of potential field.Therefore,it is of great academic significance and practical value to develop potential field reconstruction technique.The equivalent source technique is widely used for restoring potential field.Based on the equivalence principle of potential field,the equivalent(virtual)sources are constructed to replace the actual sources through fitting the observed data.Then anomaly data would be produced at any other points in passive region by forward calulation of these equivalent sources.With the advantages of concision,stabilization,precision and flexibility,equivalent source method has still been the interest of geoscientists.However,the current researches still have some deficiencies,i.e.,low-frequency signal “leak” during reconstruction processing and lacking pertinence in equivalent source construction schemes.In this thesis,through synthesis experiments and analysis,we research the optimal structure of equivalent source and inversion algorithms,for solving the problems of traditional equivalent source method.Based on the theory of equivalent source method,we discuss the parameters setting of equivalent sources,which could impact calculation results significantly.These parameters include depth,spatial distribution,magnetization direction,cell type and mesh spacing of equivalent source.By analyzing the causes of signal leakage,we hold the opinion that using multi-layer equivalent source can effectively suppress the leakage of signal.Furthermore,through comparison of reconstruction accuracy,low-frequency signal recovery and computational efficiency,the results of synthetic experiments show that three-layer equivalent source scheme has the best reconstruction effect.According to above research results,we propose a technical scheme of three-layer equivalent source.In this scheme,the first layer is located at the depth of 1~6 times average interval of discrete data;the depth of second layer is determined by source depth estimation method;and the third layer is set near the depth of substrate.The equivalent sources on the first and second layer can be distributed with terrain or horizontal plane;the equivalent sources of third layer is placed along a horizontal plane.Rectangular prism is selected as cell of equivalent source to better retain multi-frequency field information.And the geometry size of cell increases with its setting depth,so as to ensure corresponding sensitivity of each cells and control the total number of cells.The threelayer equivalent source constructed by this scheme is distributed in a trapezoidal region under observation surface,which effectively reduces the edge effect over the study region.We discuss inversion algorithms for density or susceptibility of equivalent sources.By comparing advantages of each inversion algorithms and combining the three-layer equivalent source scheme,we select the preconditioned conjugate gradient method for solving inverse problem to obtain equivalent source property distribution.This method could make deep equivalent sources contributing by setting preoptimization factor,and it can reduce the skin effect and improve computational efficiency.In addition,we introduce the error of gradient of reconstructed potential field as a parameter for evaluating reconstruction quality,to improve the computational accuracy.The results of 2D and 3D syntheic experiments show that the proposed method can not only reconstruct gravity and magnetic field with high precision,but also obtain high precision gradients and components of anomaly.Furthermore,the data gridding and multi-source data fusion can be implemented well.Therefore,there are significant advantages over traditional equivalent source method.Finally,real data examples are used to illustrate the stability and practicality of the three-layer equivalent source method.更多还原