多源地壳形变场数据的总体最小二乘联合反演研究

The crustal deformation analysis by multi-source data GPS and InSAR and the total least squares adjustment theory and method are the research hotspots in geodetic inversion and surveying data processing respectively. But the interdisciplinary research of multi-source data and TLS method have not been published simultaneously in crustal deformation analysis at home and abroad. The time-varying information of 3-dimensions deformation field can be effectively revealed by the combination of multi-source data. In the deformation analysis model, not only the observations contain noise, but also the coefficient matrix is contaminated by some noise from data sampling and measurement which also can not be ignored. The errors of observation and coefficient matrix can be treated by TLS method, and the reasonable and credible geophysical parameter estimations can be obtained. In the project, the multi-source data GPS and InSAR and TLS method will be used to inverse the parameters of crustal deformation field and obtain the geophysical explanations. The main research contents are the model construction of TLS joint inversion, its corresponding algorithm, the determination of relative weight ratio factors, inequality constraint inversion, and so on. And then the theory and methods will be used in the applications on the crustal strain parameters inversion, the earthquake fault parameters inversion, the earthquake slip distribution inversion, and so on. The project is focused on the TLS joint inversion of multi-source deformation data. The geodetic inversion theory will be further improved and perfected and the multidisciplinary and interdisciplinary research will be pushed forward through all these studies.

联合GPS、InSAR等多源数据分析地壳形变及总体最小二乘（TLS）平差理论与方法已分别成为大地测量反演和测量数据处理领域的研究热点，然而同时基于多源数据和TLS方法交叉研究地壳形变在国内外还未见相关研究成果发表。联合多源数据可有效揭示三维形变场的时变信息，但形变分析模型中不仅观测值含有误差，系数矩阵往往由于数据采样、观测等同样含有不可忽略的误差；TLS方法可同时处理观测值和系数矩阵存在的误差，得到合理可靠的地球物理参数估值。本项目将利用GPS、InSAR等多源形变场数据和TLS方法研究地壳形变场的参数反演及其物理解释，深入研究TLS联合反演模型的建立、求解算法、不同类观测值相对权比的确定、附有不等式约束方法等，并研究这些理论和方法在地壳应变参数、地震断层参数及滑动分布反演等问题中的应用。本项目着眼于多源形变场数据的TLS联合反演研究，将进一步完善大地测量反演理论、推动多学科的交叉。

联合多源数据分析地壳形变及总体最小二乘平差理论与方法已分别成为大地测量反演和测量数据处理领域的研究热点，将二者结合起来进行的研究较少。本项目研究了多源形变场数据的总体最小二乘联合反演（平差）以及相关理论问题，主要研究内容如下：（1）提出了总体最小二乘联合反演（平差）方法，并用于L’Aquila地震断层滑动分析中；（2）研究了地壳应变参数反演的总体最小二乘方法，并用于川滇地区地壳应变率参数的反演；（3）采用LN-1范数算法和加上模拟污染正态分布粗差的InSAR数据反演了2008年大柴旦Mw6.3级地震断层位错模型参数；（4）提出了病态总体最小二乘问题的虚拟观测法、谱修正迭代法以及共轭梯度法，并用于火山地壳形变分析的Mogi模型参数反演；（5）研究了总体最小二乘的随机模型，提出了基于PEIV模型的赫尔默特方差分量估计迭代算法、附有相对权比的PEIV模型总体最小二乘平差算法以及加权总体最小二乘平差随机模型的验后估计方法；（6）系统研究了总体最小二乘研究进展及解的相关特性；（7）提出了复数域总体最小二乘平差、PEIV模型的新解法、多元总体最小二乘问题的牛顿解法、混合总体最小二乘的迭代解算算法、附有等式约束的加权总体最小二乘平差方法、GPS高程转换的总体最小二乘方法以及相关方法在测边网坐标平差、变异函数模型回归、坐标转换、点云数据拟合等测量数据处理中的应用。项目的研究成果将进一步充实大地测量反演和测量平差与数据处理理论，对于系数矩阵含有误差、多类（源）数据的联合平差以及地壳形变分析具有重要价值。