地球物理导航中位场下延的迭代正则化方法研究

地磁、重力数据下延是制备地球物理导航基准图的重要内容,而它通常是一个不适定问题,采用常规代数方法求解并不奏效;对此,结合航空地球物理测量和地球物理导航的特点,研究了迭代正则化方法(包括迭代Tikhonov法、Landweber迭代法和截断奇异值分解(TSVD)法)在位场下延中的应用.首先给出了位场下延和迭代正则化的基本理论,然后采用理论位场模型验证了迭代正则化方法在位场下延中的应用可行性,最后分析了迭代正则化方法的下延精度、计算时间和边界效应等性能.由分析结果可知,迭代Tikhonov方法具有最好的综合下延性能,应优先在实际的位场下延中使用.

Study of Iterative Regularization Methods for Potential Field Downward Continuation in Geophysical Navigation

Downward continuation of potential field data is an important part in preparing reference map for geophysical navigation, but it's usually an ill-posed problem, thus traditional algebraic methods are not applicable to it. In this paper,based on characteristics of airborne geophysical survey and geophysical navigation, the application of iterative regularization including iterative Tikhonov regularization, Landweber iterative regularization and truncated singular value decomposition (TSVD), in downward continuation of potential field data is studied. First, basic principles of potential field downward continuation and iterative regularization are introduced. Second, these three iterative regularization methods for downward continuation of potential field data are validated by using a theoretical potential field model. Finally including downwardcontinued accuracy, computing time and edge effect, the performances of these three iterative regularization methods are analyzed. It will be seen from the analysis that iterative Tikhonov regularization has the best downward-continued performance, and should be used firstly in practical downward continuation of potential field data.