Investigation of the Tikhonov Regularization Method in Regional Gravity Field Modeling by Poisson Wavelets Radial Basis Functions
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.
Key wordsregional gravity field modeling Poisson wavelets radial basis functions Tikhonov regularization method L-curve variance component estimation (VCE)
Unable to display preview. Download preview PDF.
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.
- Andersen, O. B., 2010. The DTU10 Gravity Field and Mean Sea Surface. Second International Symposium of the Gravity Field of the Earth (IGFS2). Fairbanks, AlaskaGoogle Scholar
- Guo, D. M., Bao, L. F., Xu, H. Z., 2015. Tectonic Characteristics of the Tibetan Plateau Based on EIGEN-6C2 Gravity Field Model. Earth Science—Journal of China University of Geosciences, 40(10): 1643–1652. https://doi.org/10.3799/dqkx.2015.148 (in Chinese with English Abstract)CrossRefGoogle Scholar
- Heiskanen, W. A., Moritz H., 1967. Physical Geodesy, WH Freeman and Co., San FranciscoGoogle Scholar
- Koch, K. R., 1987. Bayesian Inference for Variance Components. Manuscr. Geod., 12: 309–313Google Scholar
- Tikhonov, A. N., 1963. Regularization of Incorrectly Posed Problems. Sov. Math. Dokl., 4(1): 1624–1627Google Scholar
- Wittwer, T., 2010. Regional Gravity Field Modelling with Radial Basis Functions: [Dissertation]. Delft University of Technology, DelftGoogle Scholar
- Wu, Y. H., Luo, Z. C., 2016. The Approach of Regional Geoid Refinement Based on Combining Multi-Satellite Altimetry Observations and Heterogeneous Gravity Data Sets. Chinese J. Geophys., 59(5): 1596–1607. https://doi.org/10.6038/cjg20160505 (in Chinese with English Abstract)Google Scholar
- Wu, Y. H., Luo, Z. C., Chen, W., et al., 2017. High-Resolution Regional Gravity Field Recovery from Poisson Wavelets Using Heterogeneous Observational Techniques. Earth, Planets and Space, 69(34): 1–15. https://doi.org/10.1186/s40623-017-0618-2Google Scholar
- Wu, Y. H., Luo, Z. C., Zhou, B. Y., 2016. Regional Gravity Modelling Based on Heterogeneous Data Sets by Using Poisson Wavelets Radial Basis Functions. Chinese J. Geophys., 59(3): 852–864. https://doi.org/10.6038/cjg20160308 (in Chinese with English Abstract)Google Scholar
- Xu, P. L., Rummel, R., 1994. Generalized Ridge Regression with Applications in Determination of Potential Fields. Manuscr. Geod., 20: 8–20Google Scholar
- Xu, S. F., Chen, C., Du, J. S., et al., 2015. Characteristics and Tectonic Implications of Lithospheric Density Structures beneath Western Junggar and Its Surroundings. Earth Science—Journal of China University of Geosciences, 40(9): 1556–1565. https://doi.org/10.3799/dqkx.2015.140 (in Chinese with English Abstract)CrossRefGoogle Scholar