Downward continuation of airborne gravity data based on iterative methods

Abstract

The downward continuation (DWC) of airborne gravity data usually adopts the Poisson integral equation, which is the first kind Fredholm integral equation. To improve the stability and accuracy of the DWC, based on the traditional regularization methods and Landweber iteration method, we introduce two other iterative algorithms, namely Cimmino and component averaging (CAV). In order to cooperate with the use of the iterative algorithms, in response to the discrepancy principle (DP) stopping rule, we further investigate the monotone error (ME) rule and normalized cumulative periodogram (NCP) in this paper. The numerically simulated experiments are conducted by using the EGM2008 to simulate airborne gravity data in the western United States, which is a mountainous area. The statistical results validate that Cimmino and CAV are comparable to Landweber, and iterative methods are better than generalized cross validation and least squares in the test examples. Furthermore, the results also show that three stopping rules succeed in stopping the iterative process, when the resolution of gravity anomalies grid is 5′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5^{\\prime }$$\\end{document}. When the resolution is 2′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2^{\\prime }$$\\end{document}, DP fails to stop the iteration, and ME is unstable, and only NCP performs well.