大地测量反演解非唯一性的处理方法研究
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摘要
由于地球物理场的等效性和大地测量观测资料的局限性,大地测量反演解的非唯一性是反演不可避免的问题,同时能否求得问题的最优解是关系到反演结果能否成功进行相关地学解释的关键,因此当今反演问题研究的热点和难点就是如何求得反演问题的最优解。本文主要从非线性反演问题的求解方法、反演模型检验以及反演模型建立(先验信息即不等式约束的应用)等几个方面系统地研究了大地测量反演解非唯一性的处理方法,具体从以下几个方面进行了研究:
(1)从反演解的存在性、反演模型构制、解的非唯一性和解的评价四个方面将大地测量反演问题的研究进行了统一,给出了大地测量反演解的存在性、大地测量反演模型构制、大地测量非线性反演以及反演解的评价问题的定义;
(2)从定义、理论组成及求解方法和应用领域等方面对比分析了回归分析、测量平差与大地测量反演,使它们之间的关系更加明确;
(3)研究了目前常用的非线性反演问题的解算方法,将量子退火法引入到大地测量反演中来,提出了基于三次样条的大地测量半线性反演方法;
(4)给出了大地测量反演模型的准外部检验方法,提出了观测数据的划分方法以及准外部检验的质量控制标准;
(5)提出了利用先验信息处理反演解非唯一性问题的附不等式约束的大地测量反演理论,讨论利用该理论的关键问题和难点,提出该反演方法的分类和实施,给出了其应用前景。
Because of the equality of geophysical field and localization of geodetic observations, the un-uniqueness of estimated parameter is one of the most important and unavoidable problems in geodetic and geophysical inversion. At the sametime, getting the optimization is a critical problem to the explanation to relative geoscience. So how to get the optimization of inversion problems is the hotspot and nodus in geodetic and geophysical inversion. From how to get the optimization of non-linear inversion, external detection of geodetic inversion model, and the establishment of inversion model (application of inequality constraint), the methds of disposing un-uniqueness of estimate parameter are discussed in this paper. This thesis involves the aspects as following:
1. At the base of R.Parker's theory, the research of geodetic inversion of thirty years is unified at four aspects: the existence of settlement; the foundation of inverse model; the non-uniqueness of settlement; the appraisement of settlement. The definitions of existence of settlement, foundation of inverse model, non-linear geodetic inversion and appraisement of settlement are given.
2. For the first time, regression analysis, survey adjustment and geodetic inversion are compared with each other in definition, theory composing, resolving methods, applied areas and so on. Their differences and affiliation are summarized.
3. Studies are concentred on the methods of non-linear inversion problems. Quantum Annealing is introduced in geodetic inversion. Hemi-linear inversion method of geodesy based on cubic spline is put forward.
4. Hemi-outer testing method is given for geodetic inversion model. The divide method of observation and the standard of Hemi-outer testing method of geodetic inversion model are put forward.
5. The Inequality Constraints Geodetic Inversion Theory is given to solve the un-uniqueness problem with the prior information. At the same time, the advantages, key point and difficulty of this theory are discussed. At last, the realization, classification method, and applied foregrounds of the theory are given.
(1)从反演解的存在性、反演模型构制、解的非唯一性和解的评价四个方面将大地测量反演问题的研究进行了统一,给出了大地测量反演解的存在性、大地测量反演模型构制、大地测量非线性反演以及反演解的评价问题的定义;
(2)从定义、理论组成及求解方法和应用领域等方面对比分析了回归分析、测量平差与大地测量反演,使它们之间的关系更加明确;
(3)研究了目前常用的非线性反演问题的解算方法,将量子退火法引入到大地测量反演中来,提出了基于三次样条的大地测量半线性反演方法;
(4)给出了大地测量反演模型的准外部检验方法,提出了观测数据的划分方法以及准外部检验的质量控制标准;
(5)提出了利用先验信息处理反演解非唯一性问题的附不等式约束的大地测量反演理论,讨论利用该理论的关键问题和难点,提出该反演方法的分类和实施,给出了其应用前景。
Because of the equality of geophysical field and localization of geodetic observations, the un-uniqueness of estimated parameter is one of the most important and unavoidable problems in geodetic and geophysical inversion. At the sametime, getting the optimization is a critical problem to the explanation to relative geoscience. So how to get the optimization of inversion problems is the hotspot and nodus in geodetic and geophysical inversion. From how to get the optimization of non-linear inversion, external detection of geodetic inversion model, and the establishment of inversion model (application of inequality constraint), the methds of disposing un-uniqueness of estimate parameter are discussed in this paper. This thesis involves the aspects as following:
1. At the base of R.Parker's theory, the research of geodetic inversion of thirty years is unified at four aspects: the existence of settlement; the foundation of inverse model; the non-uniqueness of settlement; the appraisement of settlement. The definitions of existence of settlement, foundation of inverse model, non-linear geodetic inversion and appraisement of settlement are given.
2. For the first time, regression analysis, survey adjustment and geodetic inversion are compared with each other in definition, theory composing, resolving methods, applied areas and so on. Their differences and affiliation are summarized.
3. Studies are concentred on the methods of non-linear inversion problems. Quantum Annealing is introduced in geodetic inversion. Hemi-linear inversion method of geodesy based on cubic spline is put forward.
4. Hemi-outer testing method is given for geodetic inversion model. The divide method of observation and the standard of Hemi-outer testing method of geodetic inversion model are put forward.
5. The Inequality Constraints Geodetic Inversion Theory is given to solve the un-uniqueness problem with the prior information. At the same time, the advantages, key point and difficulty of this theory are discussed. At last, the realization, classification method, and applied foregrounds of the theory are given.
引文
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