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

Yihao Wu; Bo Zhong; Zhicai Luo

doi:10.1007/s12583-017-0771-3

Volume 29 Issue 6

Nov 2018

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Journal of Earth Science > 2018 > 29(6): 1349-1358.

Yihao Wu, Bo Zhong, Zhicai Luo. Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions. Journal of Earth Science, 2018, 29(6): 1349-1358. doi: 10.1007/s12583-017-0771-3

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Yihao Wu, Bo Zhong, Zhicai Luo. Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions. Journal of Earth Science, 2018, 29(6): 1349-1358. doi: 10.1007/s12583-017-0771-3

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

doi: 10.1007/s12583-017-0771-3

Yihao Wu¹,
Bo Zhong^{2,3
,
,},
Zhicai Luo¹

1.
MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
2.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
3.
Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China

Funds:

the China Postdoctoral Science Foundation 2016M602301

the National Natural Science Foundation of China 41374023

the National 973 Project of China 2013CB733302

the State Scholarship Fund from Chinese Scholarship Council 201306270014

the Key Laboratory of Geospace Envi-ronment and Geodesy, Ministry of Education, Wuhan University 15-02-08

the National Natural Science Foundation of China 41131067

the National Natural Science Foundation of China 41474019

More Information

Corresponding author: Bo Zhong
Received Date: 19 Jul 2016
Accepted Date: 05 Dec 2016
Publish Date: 01 Dec 2018

Abstract

Abstract

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 inves-tigated 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 first-order 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.
- regional gravity field modeling,
- Poisson wavelets radial basis functions,
- Tikhonov regularization method,
- L-curve,
- variance component estimation (VCE)

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References(33)

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