Abstract
A new method of GNSS gravity leveling is introduced to determine precisely normal height differences, Both the principle and application of the method are elaborated. Leveling surveying, gravity measurements, and GNSS measurements are carried out in a special region (including slopes, valleys and mountain ridges) to verify its accuracy by combining with gravity potential model. The results show that the precision by this method is mainly influenced by ellipsoidal height differences, gravity potential models, and gravity observations. However, the error by this method exhibits a clear linear relationship with the height difference, while it is independent of the length of the survey line. Within a specific range of height differences (within 360 m), the precision of the GNSS gravity leveling can reach the level of ± 10 mm. This method can, to some extent, provides a modern solution for height measurement which can replace the high-precision leveling surveying. The advantages of GNSS gravity leveling include high precision and high efficiency. It has a promising application prospect in geodesy, hydraulic engineering, earthquake and volcano monitoring.
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References
Anh The Hoang, Shen, Z., Shen, W., Cai, C., Xu, W., Ning, A., & Wu, Y. (2021). Determination of the orthometric height difference based on optical fiber frequency transfer technique. Geodesy and Geodynamics, 126, 405–412. https://doi.org/10.1016/j.geog.2021.08.003
Betti, B., Biagi, L., Crespi, M., & Riguzzi, F. (1999). GPS sensitivity analysis applied to non- permanent deformation control networks. Journal of Geodesy, 73, 158–167. https://doi.org/10.1007/s001900050231
Brian, B., Kristian, B., Christian, G., Irwan, G., Vegard, O., & Eko, J. W. (2023). Geodetic/gravimetric evidence for mass loss in the subsidence area of Bandung, Indonesia. Journal of Geodynamics, 157, 0264–3707. https://doi.org/10.1016/j.jog.101987
Chang, C., Wang, S., Wang, Q., Jia, L., & Liang, W. (2015). Analysis of truncation error based on degree variance of the gravity anomaly of high-order earth gravity model. Science of Surveying and Mapping, 40, 31–33. https://doi.org/10.16251/j.cnki.1009-2307.2015.12.007.
Cheng, P., Shen, W., Sun, X., Cai, C., Wu, K., & Shen, Z. (2021). Measuring height difference using two-way satellite time and frequency transfer. https://doi.org/10.48550/arXiv.2112.10292.
Duan, H., Kang, M., Yan, Q., Wu, S., & Xie, L. (2020). Extraction of high-precision repeated relative gravity observation value. Journal of Geodesy and Geodynamic, 40(10), 1088–1091. https://doi.org/10.14075/j.jgg.2020.10.018.
Filmer, M. S., Featherstone, W. E., & Kuhn, M. (2010). The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network. Journal of Geodesy, 88, 501–503. https://doi.org/10.1007/s00190-010-0388-0
Foroughi, I., Afrasteh, Y., Ramouz, S., & Safari, A. (2017). Local evaluation of Earth Gravitational Models, case study: Iran. Geodesy and Cartography, 43, 1–13. https://doi.org/10.3846/20296991.2017.1299839
Foroughi, I., Vaníček, P., Kingdon, R. W., Goli, M., Sheng, M., Afrasteh, Y., Novák, P., & Santos, M. C. (2019). Sub-centimetre geoid. Journal of Geodesy, 93, 849–868. https://doi.org/10.1007/s00190-018-1208-1
Förste, C., Bruinsma, S., Abrikosov, O., Flechtner, F., Marty, J. C., Lemoine, J. M., Dahle, C., Neumayer, H., Barthelmes, F., König, R., & Biancale, R. (2014). EIGEN-6C4: The latest combined global gravity field model including GOCE data up to degree and order 1949 of GFZ Potsdam and GRGS Toulouse. EGU General Assembly Conference Abstracts. p. 16. https://doi.org/10.1007/978-3-642-32135-1_20.
He, T., & Wen, K. (2023). Theories and applications of earthquake-induced gravity variation: advances and perspectives. Earthquake Science, 36, 376–415. https://doi.org/10.1016/j.eqs.2023.09.001
Heiskanen, W. A., & Moritz, H. (1967). Physical geodesy. Bulletin Géodésique, 86, 491–492. https://doi.org/10.1007/BF02525647
Klokočník, J., Kostelecký, J., & Bezděk, A. (2018). The putative Saginaw impact structure, Michigan, Lake Huron, in the light of gravity aspects derived from recent EIGEN 6C4 gravity field model. Journal of Great Lakes Research, 45, 12–20. https://doi.org/10.1016/j.jglr.2018.11.013
Klokočník, J., Kostelecký, J., Bezděk, A., Cílek, V., Kletetschka, G., & Staňková, H. (2020). Support for two subglacial impact craters in northwest Greenland from Earth gravity model EIGEN 6C4 and other data. Tectonophysics, 780, 228396. https://doi.org/10.1016/j.tecto.2020.228396
Li, J. (2012). The Recent Chinese Terrestrial Digital Height Datum Model: Gravimetric Quasi-Geoid CNGG2011. Acta Geodaetica et Cartographica Sinica, 41:651–660. https://aap.semanticscholar.org/CorpusID:131655626
Meng, Q., Qu, J., Li, X., Zhang, W., Meng, X., & Zhang, H. (2017). Compensating method of the height anomalies for ultra-high Earth’s gravity field model. Wireless Personal Communications, 97, 75–94. https://doi.org/10.1007/s11277-017-4493-8
Nagy, D. (1999). Theoretical gravity formulae and a mean gravity value. Acta Geodaetica Et Geophysica Hungarica, 34, 23–31. https://doi.org/10.1007/BF03325554
Nahavandchi, H. (2002). Two different methods of geoidal height determinations using a spherical harmonic representation of the geopotential, topographic corrections and the height anomaly–geoidal height difference. Journal of Geodesy, 76, 345–352. https://doi.org/10.1007/s00190-002-0253-x
Pavlis, N. K., Holmes, S. A., Kenyon, S. C., Factor, J. K. (2012). The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research: Solid Earth, 117. https://doi.org/10.1029/2011JB008916.
Persson, L. E., Rafeiro, H., & Wall, P. (2017). Historical synopsis of the Taylor remainder. Note di Matematica, 37(1), 1–22. https://doi.org/10.1285/i15900932v37n1p1
Pick, M. (1990). On the normal gravity formulae. Studia Geophysica Et Geodaetica, 34, 289–312. https://doi.org/10.1007/BF02316951
Polcari, M., Borgstrom, S., Gaudio, D. C., Martino, D. P., Ricco, C., Siniscalchi, V., & Trasatti, E. (2022). Thirty years of volcano geodesy from space at Campi Flegrei caldera (Italy). Scientific Data, 9, 728. https://doi.org/10.1038/s41597-022-01849-7
Santos, M. C., Vanicek, P., Featherstone, W. E., Kingdon, R., Ellmann, A., Martin, B. A., Kuhn, M., & Tenzer, R. (2006). The relation between rigorous and Helmert’s definitions of orthometric heights. Journal of Geodesy, 80, 691–704. https://doi.org/10.1007/s00190-006-0086-0
Seda, C., Cuneyt, A., & Ugur, D. (2018). Comparing GPS positioning errors derived from GAMIT/GLOBK and Bernese GNSS software packages: a case study in CORS-TR in Turkey. Survey Review, 51, 1–11. https://doi.org/10.1080/00396265.2018.1505349
Shen, W., Ning, J., Liu, J., Li, J., & Chao, D. (2011). Determination of the geopotential and ortho-metric height based on frequency shift equation. Natural Science, 35, 388–396. https://doi.org/10.4236/ns.2011.35052
Tammaro, U., Obrizzo, F., Riccardi, U., Rocca, A., Pinto, S., Brandi, G., Vertechi, E., & Capuano, P. (2021). Neapolitan volcanic area tide gauge network (Southern Italy): ground displacements and sea-level oscillations. Advances in Geosciences, 52, 105–118. https://doi.org/10.5194/adgeo-52-105-2021
Teng, L., Yuan, Y., Zhang, B., Wang, N., Tan, B., & Chen, Y. (2016). Multi-GNSS precise point positioning (MGPPP) using raw observations. Journal of Geodesy, 91, 1–16. https://doi.org/10.1007/s00190-016-0960-3
Vu, D. T., Bruinsma, S., Bonvalot, S., Remy, D., & Vergos, G. S. (2020). A Quasigeoid-derived transformation model accounting for land subsidence in the Mekong delta towards height system unification in Vietnam. Remote Sensing, 12, 817. https://doi.org/10.3390/rs12050817
Wang, Q., Zhou, R., & Sun, W. (2011). Precision analysis of gravity vertical gradient measurement based on CG-5 relative gravimeter. Advanced Materials Research, 301, 1036–1041. https://doi.org/10.4028/www.scientific.net/AMR.301-303.1036
Wei, Z. (2003). Normal gravity formulae. Acta Geodaetica Et Cartographic Sinica, 32, 95–102.
Wei Z. (2009). GPS gravity-potential leveling. Springer, p 134. https://doi.org/10.1007/978-3-642-00860-3_43.
Wei, Z., & Wang, G. (2003). Determination of Quasi-geoid in Mainland China using geopotential model and GPS/leveling data. Acta Geodaetica Et Cartographica Sinica, 32, 1–5. https://doi.org/10.3321/j.issn:1001-1595.2003.01.001
Wessel, P., Smith, W. H. F., Scharroo, R., Luis, J., & Wobbe, F. (2013). Generic mapping tools: Improved version released. EOS. Transactions of the American Geophysical Union, 94, 409–410. https://doi.org/10.1029/98EO00426
Xing, L. L., Li, H., Li, J. G., Zhang, W. M., & He, Z. T. (2016). Establishment of absolute gravity datum in CMONOC and its application. Acta Geodaetica Et Cartographica Sinica, 45(5), 538–543. https://doi.org/10.11947/j.AGCS.2016.20140653
Xing, L. L., Bai, L., Niu, X. W., & Sang, P. (2020). A new and high-precision gravity base network in the south of the Tibetan Plateau. Geodesy and Geodynamics, 11(4), 258–264. https://doi.org/10.1016/j.geog.2020.05.001
Yang, D., & Zou, J. (2021). Precise levelling in crossing river over 5 km using total station and GNSS. Scientific Reports, 11, 1–12. https://doi.org/10.1038/s41598-021-86929-1
Younis, G. (2017). The integration of GNSS/leveling data with global geopotential models to define the height reference system of Palestine. Arabian Journal for Science and Engineering, 43, 3639–3645. https://doi.org/10.1007/s13369-017-2912-5
Acknowledgements
This work was supported by the National Natural Science Foundation of China [Grant No. 41304013] and the State Key Laboratory of Geodesy and Earth’s Dynamics [Grant No. SKLGED2022-5-2]. We extend our gratitude to Professor Chuanyin Zhang of the Chinese Academy of Surveying and Mapping for providing the geophysical geodetic scientific computation software (https://www.zcyphygeodesy.com/) and figures were plotted with the Generic Mapping Tool (Wessel et al. 2013). Thanks to all field workers involved in GNSS observations, leveling surveys, and gravity observations. Special thanks to Heting jian, Jiaying chen, and Rui wu for their hard work in gravity measurements! Also, our thanks to the two anonymous reviewers for their valuable comments on this manuscript.
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Hurong Duan: Conceptualization, Methodology, Participate in the experiment and writing Yerui Zhang: Calculation analysis, Editing and partial writing Lelin Xing: GMT ploting and Writing-Reviewing Weifeng Liang: Participate in the experiment.
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Duan, H., Zhang, Y., Xing, L. et al. GNSS Gravity Leveling. Pure Appl. Geophys. (2024). https://doi.org/10.1007/s00024-024-03492-2
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DOI: https://doi.org/10.1007/s00024-024-03492-2