Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions  

作　　者：Yihao Wu Bo Zhong Zhicai Luo 

机构地区：[1]MOE Key Laboratory of Fundamental Physical Quantities Measurement,School of Physics,Huazhong University of Science and Technology [2]School of Geodesy and Geomatics,Wuhan University [3]Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,Wuhan University

出　　处：《Journal of Earth Science》2018年第6期1349-1358,共10页地球科学学刊（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos.41374023,41131067,41474019);the National 973 Project of China (No.2013CB733302);the China Postdoctoral Science Foundation (No.2016M602301);the Key Laboratory of Geospace Envi-ronment and Geodesy,Ministry of Education,Wuhan University (No.15-02-08);the State Scholarship Fund from Chinese Scholarship Council (No.201306270014)

摘　　要：The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.The application of Tikhonov regularization method dealing with the ill-conditioned problems in the regional gravity field modeling by Poisson wavelets is studied. In particular, the choices of the regularization matrices as well as the approaches for estimating the regularization parameters are investigated in details. The numerical results show that the regularized solutions derived from the first-order regularization are better than the ones obtained from zero-order regularization. For cross validation, the optimal regularization parameters are estimated from L-curve, variance component estimation（VCE） and minimum standard deviation（MSTD） approach, respectively, and the results show that the derived regularization parameters from different methods are consistent with each other. Together with the firstorder Tikhonov regularization and VCE method, the optimal network of Poisson wavelets is derived, based on which the local gravimetric geoid is computed. The accuracy of the corresponding gravimetric geoid reaches 1.1 cm in Netherlands, which validates the reliability of using Tikhonov regularization method in tackling the ill-conditioned problem for regional gravity field modeling.

关 键 词：regional gravity field modeling Poisson wavelets radial basis functions Tikhonov regularization method L-CURVE variance component estimation（VCE） 

分 类 号：P631.1[天文地球—地质矿产勘探]