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

Abstract

The application of Tikhonov regularization method for 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 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.

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Acknowledgments

Thanks go to the three anonymous reviewers, who gave constructive comments and beneficial suggestions which help us to improve this manuscript. Thanks also go to Prof. Roland Klees from Delft University of Technology for kindly providing the gravity data. This research was mainly 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 Environment and Geodesy, Ministry of Education, Wuhan University (No. 15-02-08), and the State Scholarship Fund from Chinese Scholarship Council (No. 201306270014). The final publication is available at Springer via https://doi.org/10.1007/s12583-017-0771-3.

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Correspondence to Bo Zhong.

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Wu, Y., Zhong, B. & Luo, Z. Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions. J. Earth Sci. 29, 1349–1358 (2018). https://doi.org/10.1007/s12583-017-0771-3

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Key words

  • regional gravity field modeling
  • Poisson wavelets radial basis functions
  • Tikhonov regularization method
  • L-curve
  • variance component estimation (VCE)