基于拟最优正则化因子组的航空重力向下延拓迭代求解方法

刘猛, 王正涛

刘猛, 王正涛. 基于拟最优正则化因子组的航空重力向下延拓迭代求解方法[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20230127
引用本文: 刘猛, 王正涛. 基于拟最优正则化因子组的航空重力向下延拓迭代求解方法[J]. 武汉大学学报 ( 信息科学版). DOI: 10.13203/j.whugis20230127
LIU Meng, WANG Zheng-tao. Downward Continuation Iterative Regularization Solution Based on Quasi Optimal Regularization Factor Set[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20230127
Citation: LIU Meng, WANG Zheng-tao. Downward Continuation Iterative Regularization Solution Based on Quasi Optimal Regularization Factor Set[J]. Geomatics and Information Science of Wuhan University. DOI: 10.13203/j.whugis20230127

基于拟最优正则化因子组的航空重力向下延拓迭代求解方法

基金项目: 

国家自然科学基金(42274003,41974007,41774019)

详细信息
    作者简介:

    刘猛,硕士,主要从事固体地球物理学研究。meng.liu@whu.edu.cn

    通讯作者:

    王正涛,博士生导师,教授,主要从事物理大地测量学、卫星大地测量学、地磁学等方面的研究。ztwang@whu.edu.cn

Downward Continuation Iterative Regularization Solution Based on Quasi Optimal Regularization Factor Set

  • 摘要: 迭代Tikhonov正则化法和迭代Landweber正则化法是有效解决向下延拓不适定问题的两种迭代正则化算法。针对迭代正则化法中迭代次数和正则化参数选取问题,构建拟最优正则化因子组概念,对拟最优正则化因子组中迭代次数和正则化参数分布进行了分析,提出了迭代正则化法中迭代次数和正则化参数最优组合的选取依据,给出了利用L曲线法求取与迭代次数对应最优正则化参数的公式,采用EGM08和EIGEN-6C4重力场模型设计了仿真实验,与传统Tikhonov正则化法进行了比较分析,验证了选取迭代正则化法正则化因子组依据的可靠性。
    Abstract: Objectives: Iterative Tikhonov regularization and iterative Landweber regularization are currently the two most commonly used iterative regularization algorithms, which can effectively solve the ill-posed problem during the continuation process. However, their optimal combination of iteration times and regularization parameters has not yet been determined, which limits their practicality. Methods: This paper constructs the concept of quasi-optimal regularization factor set and analyzes the distribution of iteration numbers and regularization parameters in the quasi-optimal regularization factor set. Based on this, a selection criterion for the optimal combination of iteration number and regularization parameter in iterative regularization algorithms is proposed, and a formula for using the L-curve method to obtain the optimal regularization parameter corresponding to the number of iterations is provided. Results: The study on the relationship between the extension error of iterative regularization algorithms and the variation of regularization factor sets shows that there is a significant correlation between the optimal regularization parameters and the number of iterations in the quasi optimal regularization factor set. When the number of iterations exceeds 10, the extension solutions corresponding to each quasi optimal regularization factor set are basically identical. When the number of iterations is large enough, any quasi optimal regularization factor set can be considered as the optimal regularization factor set. The iterative regularization algorithm based on the selected strategy in this article has a smoother extension solution and smaller error compared to the traditional Tikhonov regularization method. However, in areas with significant data changes, some high-frequency signals are filtered out as noise, and the extension effect is not significantly improved. Conclusions: The iterative regularization algorithm based on the selected strategy in this article has a smoother and smaller error extension solution compared to the traditional Tikhonov regularization method, which shows reliability and practicality.
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出版历程
  • 收稿日期:  2023-10-30
  • 网络出版日期:  2024-05-12

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