Abstract
One important procedure in gravity data processing is making tidal corrections. Sound tidal corrections rely on accurate tidal gravimetric factors. The present study selects data from 12 gPhone gravimeter stations and three superconducting gravimeter stations for the period between 2009 and 2015, distributed across mainland China. Based on these data, the distribution of M2 tidal gravimetric factors over China is obtained. We also estimate the corresponding theoretical values of the M2 wave provided by the DDW99 solid Earth tide model (Dehant et al. in J Geophys Re Solid Earth 104:1035–1058, 1999) and the CSR4.0 ocean tide model (Eanes and Bettadpur in The CSR3. 0 global ocean tide model: diurnal and semi-diurnal ocean tides from TOPEX/POSEIDON altimetry, The University of Texas Center for Space Research, 1996). The results suggest that the measurements and theoretical values of the M2 wave are similar, with an average misfit no greater than 0.6% for most regions of China’s mainland, although the misfit is relatively large, about 1.1%, in northeast China. According to the latest three-dimensional tidal theory and the correction effects on the M2 gravimetric factors at Lhasa, Lijiang, and Wuhan, where the three superconducting gravimeters are located, we select the best-fitting three-dimensional Earth model, GyPSuM (Simmons et al. in J Geophys Res Solid Earth 115:B12, 2010), for mainland China. The theoretical values of the tidal gravimetric factors while considering three-dimensional inhomogeneities are calculated. The results show that the variation in gravimetric factors caused by lateral inhomogeneity across China is from −0.07 to 0.09%.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/10.1109/TAC.1974.1100705
Akaike, H. (1998). Likelihood and the Bayes procedure. Selected Papers of Hirotugu Akaike (pp. 309–332). Springer.
Boy, J. P., Llubes, M., Hinderer, J., & Florsch, N. (2003). A comparison of tidal ocean loading models using superconducting gravimeter data. Journal of Geophysical Research Solid Earth, 108, B4. https://doi.org/10.1029/2002JB002050
Calvo, M., Hinderer, J., Rosat, S., Legros, H., Boy, J. P., Ducarme, B., & Zürn, W. (2014). Time stability of spring and superconducting gravimeters through the analysis of very long gravity records. Journal of Geodynamics, 80, 20–33. https://doi.org/10.1016/j.jog.2014.04.009
Carrère, L., Lyard, F., Cancet, M., Guillot, A., & Picot, N. (2016). FES 2014, a new tidal model—validation results and perspectives for improvements. In Proceedings of the ESA living planet symposium (pp. 9–13)
Chang, S. J., Ferreira, A. M., Ritsema, J., van Heijst, H. J., & Woodhouse, J. H. (2015). Joint inversion for global isotropic and radially anisotropic mantle structure including crustal thickness perturbations. Journal of Geophysical Research Solid Earth, 120(6), 4278–4300. https://doi.org/10.1002/2014JB011824
Chen, X. D., & Sun, H. P. (2002). New method for pre-processing and analyzing tidal gravity observations. Journal of Geodesy and Geodynamics (in Chinese), 22(3), 83–87. https://doi.org/10.14075/j.jgg.2002.03.021
Cheng, Y., & Andersen, O. B. (2011). Multimission empirical ocean tide modeling for shallow waters and polar seas. Journal of Geophysical Research Oceans, 116, C11. https://doi.org/10.1029/2011JC007172
Crossley, D., Hinderer, J., & Riccardi, U. (2013). The measurement of surface gravity. Reports on Progress in Physics, 76(4), 046101. https://doi.org/10.1088/0034-4885/76/4/046101
Dehant, V., Defraigne, P., & Wahr, J. M. (1999). Tides for a convective Earth. Journal of Geophysical Research Solid Earth, 104(B1), 1035–1058. https://doi.org/10.1029/1998JB900051
Durand, S., Debayle, E., Ricard, Y., Zaroli, C., & Lambotte, S. (2017). Confirmation of a change in the global shear velocity pattern at around 1000 km depth. Geophysical Journal International, 211(3), 1628–1639. https://doi.org/10.1093/gji/ggx405
Eanes, R. J., & Bettadpur, S. (1996). The CSR3. 0 global ocean tide model: Diurnal and semi-diurnal ocean tides from TOPEX/POSEIDON altimetry. The University of Texas Center for Space Research.
Egbert, G. D., & Erofeeva, S. Y. (2002). Efficient inverse modeling of barotropic ocean tides. Journal of Atmospheric and Oceanic Technology, 19(2), 183–204. https://doi.org/10.1175/1520-0426(2002)019%3c0183:EIMOBO%3e2.0.CO;2
Farrell, W. E. (1972). Deformation of the Earth by surface loads. Reviews of Geophysics, 10(3), 761–797. https://doi.org/10.1029/RG010i003p00761
Fok, H. S. (2012). Ocean tides modeling using satellite altimetry (Doctoral dissertation, The Ohio State University). https://geodesy.geology.ohio-state.edu/oceantides/OSU12v1.0/readme1st.dat.
Fores, B., Champollion, C., Moigne, N. L., Bayer, R., & Chery, J. (2016). Assessing the precision of the iGrav superconducting gravimeter for hydrological models and karstic hydrological process identification. Geophysical Journal International, 396, 269–280. https://doi.org/10.1093/gji/ggw396
Forte, A. M., & Mitrovica, J. X. (2001). Deep-mantle high-viscosity flow and thermochemical structure inferred from seismic and geodynamic data. Nature, 410(6832), 1049–1056. https://doi.org/10.1038/35074000
Fu, G., & Sun, W. (2007). Effects of lateral inhomogeneity in a spherical Earth on gravity Earth tides. Journal of Geophysical Research Solid Earth, 112, B6. https://doi.org/10.1029/2006JB004512
Ghosh, A., Holt, W. E., & Flesch, L. M. (2009). Contribution of gravitational potential energy differences to the global stress field. Geophysical Journal International, 179(2), 787–812. https://doi.org/10.1111/j.1365-246X.2009.04326.x
Ishiguro, M., Akaike, H., Ooe, M., & Nakai, S. (1998). A Bayesian approach to the analysis of earth tides. Selected papers of Hirotugu Akaike (pp. 361–370). Springer. https://doi.org/10.1007/978-1-4612-1694-0_28
He, J., Yang, K., Tang, W., Lu, H., Qin, J., Chen, Y., & Li, X. (2020). The first high-resolution meteorological forcing dataset for land process studies over China. Scientific Data, 7(1), 1–11. https://doi.org/10.1038/s41597-020-0369-y
Lau, H. C., Mitrovica, J. X., Davis, J. L., Tromp, J., Yang, H. Y., & Al-Attar, D. (2017). Tidal tomography constrains Earth’s deep-mantle buoyancy. Nature, 551(7680), 321–326. https://doi.org/10.1038/nature24452
Liu, Z. W., Li, H., Wei, J., Hao, H. T., & Wu, Y. L. (2011). Accurate determination of calibration factor of gPhone spring gravimeters by using M2 tidal wave amplitude factor. Journal of Geodesy and Geodynamics (in Chinese), 31(5), 146–150. https://doi.org/10.14075/j.jgg.2011.05.004
Longman, I. M. (1963). A Green’s function for determining the deformation of the Earth under surface mass loads: 2 computations and numerical results. Journal of Geophysical Research, 68(2), 485–496. https://doi.org/10.1029/JZ068i002p00485
Love, A. E. H. (1909). The yielding of the Earth to disturbing forces. Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences, 82(551), 73–88. https://doi.org/10.1098/rspa.1909.0008
Lu, Z., & Wen, L. (2017). Abnormally strong daily-cycle S1 strain tide: Observation and physical mechanism. Journal of Geophysical Research Solid Earth, 122(10), 8525–8537. https://doi.org/10.1002/2017JB014383
Luthcke, S. B., Zwally, H. J., Abdalati, W., Rowlands, D. D., Ray, R. D., Nerem, R. S., & Chinn, D. S. (2006). Recent Greenland ice mass loss by drainage system from satellite gravity observations. Science, 314(5803), 1286–1289. https://doi.org/10.1126/science.1130776
Matsumoto, K., Takanezawa, T., & Ooe, M. (2000). Ocean tide models developed by assimilating TOPEX/POSEIDON altimeter data into hydrodynamical model: A global model and a regional model around Japan. Journal of Oceanography, 56(5), 567–581. https://doi.org/10.1023/A:1011157212596
Molodenskiy, S. M. (1977). The influence of horizontal inhomogeneities in the mantle on the amplitude of tidal oscillations. Izvestiya Physics of the Solid Earth, 13, 77–80.
Molodenskiy, S. M. (1980). The effect of lateral heterogeneities upon the tides. BIM Fevrier, 80, 4833–4850.
Munk, W. H., & Cartwright, D. E. (1966). Tidal spectroscopy and prediction. Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences, 259(1105), 533–581. https://doi.org/10.1098/rsta.1966.0024
Ooe, M., & Sato, T. (1983). An extended response method for analysis of disturbed earth tide data. In Proceeding 9th International symposium on earth tides, New York City, August 17–22, 1981 (pp. 299–310)
Panet, I., Mikhailov, V., Diament, M., Pollitz, F., King, G., De Viron, O., & Lemoine, J. M. (2007). Coseismic and post-seismic signatures of the Sumatra 2004 December and 2005 March earthquakes in GRACE satellite gravity. Geophysical Journal International, 171(1), 177–190. https://doi.org/10.1111/j.1365-246X.2007.03525.x
Panning, M. P., Lekić, V., & Romanowicz, B. A. (2010). Importance of crustal corrections in the development of a new global model of radial anisotropy. Journal of Geophysical Research Solid Earth, 115, B12. https://doi.org/10.1029/2010JB007520
Ray, R. D. (2013). Precise comparisons of bottom-pressure and altimetric ocean tides. Journal of Geophysical Research Oceans, 118(9), 4570–4584. https://doi.org/10.1002/jgrc.20336
Riccardi, U., Berrino, G., Corrado, G., & Hinderer, J. (2008). Strategies in the processing and analysis of continuous gravity record in active volcanic areas: The case of Mt. Vesuvius. Annals of Geophysics, 51(1), 57–85. https://doi.org/10.4401/ag-3039
Riccardi, U., Rosat, S., & Hinderer, J. (2011). Comparison of the Micro-g LaCoste gPhone-054 spring gravimeter and the GWR-C026 superconducting gravimeter in Strasbourg (France) using a 300-day time series. Metrologia, 48(1), 28. https://doi.org/10.1088/0026-1394/48/1/003
Rosat, S., & Hinderer, J. (2018). Limits of detection of gravimetric signals on Earth. Scientific Reports, 8(1), 1–8. https://doi.org/10.1038/s41598-018-33717-z
Saito, M. (1967). Excitation of free oscillations and surface waves by a point source in a vertically heterogeneous Earth. Journal of Geophysical Research, 72(14), 3689–3699. https://doi.org/10.1029/JZ072i014p03689
Savcenko, R., & Bosch, W. (2012). EOT11a-empirical ocean tide model from multi-mission satellite altimetry. Deutsches Geodätisches Forschungsinstitut (DGFI) Report No. 89
She, Y., Fu, G., & Wei, J. (2015). Analysis of instrument performance and hydrology response of gPhone meters at Shisanling seismic station. Journal of Geodesy and Geodynamics (in Chinese), 35(5), 901–905. https://doi.org/10.14075/j.jgg.2015.05.039
Simmons, N. A., Forte, A. M., Boschi, L., & Grand, S. P. (2010). GyPSuM: A joint tomographic model of mantle density and seismic wave speeds. Journal of Geophysical Research Solid Earth, 115, B12. https://doi.org/10.1029/2010JB007631
Sun, H. P., Hsu, H. T., Jentzsch, G., & Xu, J. Q. (2002). Tidal gravity observations obtained with a superconducting gravimeter at Wuhan/China and its application to geodynamics. Journal of Geodynamics, 33(1–2), 187–198. https://doi.org/10.1016/S0264-3707(01)00063-1
Sun, H., Zhang, H., Xu, J., Chen, X., Zhou, J., & Zhang, M. (2019). Influences of the Tibetan plateau on tidal gravity detected by using SGs at Lhasa, Lijiang and Wuhan Stations in China. Terrestrial, Atmospheric and Oceanic Sciences, 30(1), 139–149. https://doi.org/10.3319/TAO.2019.02.14.01
Taguchi, E., Stammer, D., & Zahel, W. (2014). Inferring deep ocean tidal energy dissipation from the global high-resolution data-assimilative HAMTIDE model. Journal of Geophysical Research Oceans, 119(7), 4573–4592. https://doi.org/10.1002/2013JC009766
Takeuchi, H., & Saito, M. (1972). Seismic surface waves. Methods in Computational Physics Advances in Research and Applications, 11, 217–295. https://doi.org/10.1016/B978-0-12-460811-5.50010-6
Tamura, Y., Sato, T., Ooe, M., & Ishiguro, M. (1991). A procedure for tidal analysis with a Bayesian information criterion. Geophysical Journal International, 104(3), 507–516. https://doi.org/10.1111/j.1365-246X.1991.tb05697.x
Tanaka, T., Miyajima, R., Asai, H., Horiuchi, Y., Kumada, K., Asai, Y., & Ishii, H. (2013). Hydrological gravity response detection using a gPhone below-and aboveground. Earth, Planets and Space, 65(2), 59–66. https://doi.org/10.5047/eps.2012.06.012
Tesoniero, A., Auer, L., Boschi, L., & Cammarano, F. (2015). Hydration of marginal basins and compositional variations within the continental lithospheric mantle inferred from a new global model of shear and compressional velocity. Journal of Geophysical Research Solid Earth, 120(11), 7789–7813. https://doi.org/10.1002/2015JB012026
Trabant, C., Hutko, A. R., Bahavar, M., Karstens, R., Ahern, T., & Aster, R. (2012). Data products at the IRIS DMC: Stepping stones for research and other applications. Seismological Research Letters, 83(5), 846–854. https://doi.org/10.1785/0220120032
van Camp, M., & Vauterin, P. (2005). Tsoft: Graphical and interactive software for the analysis of time series and Earth tides. Computers and Geosciences, 31(5), 631–640. https://doi.org/10.1016/j.cageo.2004.11.015
van Dam, T. M., & Wahr, J. M. (1987). Displacements of the Earth’s surface due to atmospheric loading: Effects on gravity and baseline measurements. Journal of Geophysical Research Solid Earth, 92(B2), 1281–1286. https://doi.org/10.1029/JB092iB02p01281
Venedikov, A. P., Arnoso, J., & Vieira, R. (2003). VAV: A program for tidal data processing. Computers and Geosciences, 29(4), 487–502. https://doi.org/10.1016/S0098-3004(03)00019-0
Wahr, J. M. (1981). Body tides on an elliptical, rotating, elastic and oceanless Earth. Geophysical Journal International, 64(3), 677–703. https://doi.org/10.1111/j.1365-246X.1981.tb02690.x
Wang, X., Holt, W. E., & Ghosh, A. (2015). Joint modeling of lithosphere and mantle dynamics: Evaluation of constraints from global tomography models. Journal of Geophysical Research Solid Earth, 120(12), 8633–8655. https://doi.org/10.1002/2015JB012188
Wei, J., Li, H., Liu, Z. W., Kang, K. X., & Hao, H. T. (2012). Observation of superconducting gravimeter at Jiufeng seismic station. Chinese Journal of Geophysics (in Chinese), 55(6), 1894–1902. https://doi.org/10.6038/j.issn.0001-5733.2012.06.010
Wenzel, H. G. (1996). The nanogal software: Earth tide data processing package ETERNA 3.30. Bulletin D’information Des Marées Terrestres, 124, 9425–9439.
Xu, J., Chen, X., Zhou, J., & Sun, H. (2012). Characteristics of tidal gravity changes in Lhasa, Tibet, China. ChinEse Science Bulletin, 57(20), 2586–2594. https://doi.org/10.1007/s11434-012-5130-2
Zetler, B. D., Schuldt, M. D., Whipple, R. W., & Hicks, S. D. (1965). Harmonic analysis of tides from data randomly spaced in time. Journal of Geophysical Research, 70(12), 2805–2811. https://doi.org/10.1029/JZ070i012p02805
Zhang, P., Deng, Q., Zhang, G., Ma, J., Gan, W., Min, W., & Wang, Q. (2003). Active tectonic blocks and strong earthquakes in the continent of China. Science in China Series D Earth Sciences, 46(2), 13–24. https://doi.org/10.1360/03dz0002
Zhao, D. (2001). Seismic structure and origin of hotspots and mantle plumes. Earth and Planetary Science Letters, 192(3), 251–265. https://doi.org/10.1016/S0012-821X(01)00465-4
Zhou, J. C., Xu, J. Q., & Sun, H. P. (2009). Accurate correction models for tidal gravity in Chinese continent. Chinese Journal of Geophysics (in Chinese), 52(3), 575–584. https://doi.org/10.1002/cjg2.1379
Acknowledgements
We thank two anonymous reviewers and the Editor for their helpful comments and suggestions. The ocean tide modes in Table 2 are downloadable from the OSO website via http://holt.oso.chalmers.se/loading/. The Earth models in Table 3 are downloadable from the IRIS website via http://ds.iris.edu/ds/products/emc-Earthmodels/ (Trabant et al. 2012). The atmospheric pressure data are downloadable from the TPDC website via http://www.tpdc.ac.cn/zh-hans/data/8028b944-daaa-4511-8769-965612652c49/. The WPARICET program is downloadable from the ICET website via https://www.astro.oma.be/en/. The SPOTL software is downloadable from the website of https://igppweb.ucsd.edu/~agnew/Spotl/spotlmain.html. This work is supported by the National Natural Foundation of China (Grant no. 41774093, 60164204, 41874003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Below is the link to the electronic supplementary material.
Rights and permissions
About this article
Cite this article
Wang, Z., Liu, Z., Fu, G. et al. Observed and Calculated M2 Tidal Gravimetric Factors at 15 Stations in the Mainland of China. Pure Appl. Geophys. 178, 3069–3084 (2021). https://doi.org/10.1007/s00024-021-02777-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-021-02777-0