On the Non-uniqueness of Gravitational and Magnetic Field Data Inversion (Survey Article)
On the Non-uniqueness of Gravitational and Magnetic Field Data Inversion (Survey Article)
复制标题
论重磁场数据反演的非唯一性（调查文章）
DOI：
10.1007/978-3-319-57181-2_15
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
R. Telschow
中科院分区：
文献类型：
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作者：
S. Leweke;V. Michel;R. Telschow
地球的引力和磁场代表了地球系统中一些最重要的可观测物。这些磁场的反转揭示了地球（或其他天体）表面或内部隐藏的结构和动力学。然而，这两个场的反转都存在严重的解的非唯一性。在本文中，我们提出了一种广义的方法，其中包括重力和磁场数据的反演。其中，提出并比较了唯一性约束。这包括表面密度分析（也称为薄层假设）。我们通过适当的标准正交基系统刻画了所考虑的一类逆问题的零空间。进一步，我们利用标准正交基和再现核的方法扩展了解的可重构部分。结果之一是，关于解的径向依赖性的信息在可观测值中丢失了。为了说明非唯一性，我们展示了一些从重力数据反演中无法揭示的异常例子。本文旨在为地球引力和磁场数据的反演提供理论参考。
The gravitational and the magnetic field of the Earth represent some of the most important observables of the geosystem. The inversion of these fields reveals hidden structures and dynamics at the surface or in the interior of the Earth (or other celestial bodies). However, the inversions of both fields suffer from a severe non-uniqueness of the solutions. In this paper, we present a generalized approach which includes the inversion of gravitational and magnetic field data. Amongst others, uniqueness constraints are proposed and compared. This includes the surface density ansatz (also known as the thin layer assumption). We characterize the null space of the considered class of inverse problems via an appropriate orthonormal basis system. Further, we expand the reconstructable part of the solution by means of orthonormal bases and reproducing kernels. One result is that information on the radial dependence of the solution is lost in the observables. As an illustration of the non-uniqueness, we show examples of anomalies which cannot be disclosed from the inversion of gravitational data. This paper is intended to be a theoretical reference work on the inversion of gravitational but also magnetic field data of the Earth.