Seismic Instruments

, Volume 54, Issue 6, pp 650–661 | Cite as

The Atlantida 3.1_2014 Program for Earth Tide Prediction: New Version

  • E. A. SpiridonovEmail author
  • V. D. Yushkin
  • O. Yu. Vinogradova
  • L. V. Afanasyeva


The main distinctive features of ATLANTIDA3.1._2014, the first domestic program for the prediction of Earth tides, are discussed in comparison to similar programs of international authors, and some examples of the practical application of the program by different researchers are presented. The main functional features of the program are listed. Among them, the features for calculating amplitude delta factors of tidal waves for an oceanless Earth, as well as amplitude delta factors and phase shifts for an Earth with an ocean, tidal time series, and amplitudes and phases of the oceanic gravimetric effect, are especially distinguished. The theoretical developments included in the program are briefly described. The main differences of the latest version of the program are identified. The theoretical values of the amplitude delta factors for an inelastic self-gravitating rotating Earth, calculated with respect to the action of relative and Coriolis accelerations, as well as dissipation, are considered in detail. A total of 12 model variants are considered, which differ from each other by the inclusion or exclusion of separate factors affecting the result. The closeness of the results yielded by the program and the observations using the European superconducting gravimeters of the Global Geodynamic Project (GGP) is evaluated. It is shown that according to this criterion, our program surpasses the world’s most well-known counterparts. Tasks are listed that after their solution will expand the functional features of the program and clarify the results obtained so far.


ATLANTIDA3.1_2014 program for Earth tide prediction tidal amplitude delta factors tidal time series ocean loading effect theory of Earth tides Global Navigation Satellite System (GNSS) 



The authors are deeply grateful to Prof. Bernard Ducarme (International Center for Earth Tides (ICET), Catholic University of Leuven, Belgium) and Prof. Duncan Agnew (University of California, San Diego, USA), as well as to Dr. L. Petrov (Astrogeo Center, NASA, USA) and Dr. M. Efroimskii (United State Naval Observatory) for detailed discussion of the theoretical foundations established in the development of the ATLANTIDA3.1_2014 program and constructive comments.


  1. 1.
    Agnew, D.C., NLOADF: A program for computing ocean-tide loading, J. Geophys. Res.: Solid Earth, 1997, vol. 102, pp. 5109–5110.CrossRefGoogle Scholar
  2. 2.
    Agnew, D.C., SPOTL: Some Programs for Ocean-Tide Loading, no. 98-8 of SIO Reference Series, La Jolla, Calif.: Scripps Inst. Oceanogr., 1996.Google Scholar
  3. 3.
    Dehant, V., Tidal parameters for an inelastic Earth, Phys. Earth Planet. Inter., 1987, vol. 49, pp. 97–116.CrossRefGoogle Scholar
  4. 4.
    Dehant, V., Defraigne, P., and Wahr, J.M., Tides for a convective Earth, J. Geophys. Res.: Solid Earth, 1999, vol. 104, no. B1, pp. 1035–1058.CrossRefGoogle Scholar
  5. 5.
    Francis, O. and Mazzega, P., Global charts of ocean tide loading effects, J. Geophys. Res., [Solid Earth Planets], 1990, vol. 95, pp. 11 411–11 424.Google Scholar
  6. 6.
    Koneshov, V.N., Zheleznyak, L.K., Soloviev, V.N., and Mikhailov, P.S., Development of innovative methodological support for marine gravimetric surveys, Seism. Instrum., 2018, vol. 54, no. 6, pp. 642–649.Google Scholar
  7. 7.
    Mäkinen, J., Sermyagin, R.A., Oshchepkov, I.A., Basma-nov, A.V., Pozdnyakov, A.V., Yushkin, V.D., Stus, Yu.F., and Nosov, D.A., RFCAG2013: Russian–Finnish comparison of absolute gravimeters in 2013, J. Geod. Sci., 2016, vol. 6, no. 1, pp. 103–110. doi 10.1515/jogs-2016-0008Google Scholar
  8. 8.
    Mathews, P.M., Love numbers and gravimetric factor for diurnal tides, J. Geod. Soc. Jpn., 2001, vol. 47, no. 1, pp. 231–236.Google Scholar
  9. 9.
    Matsumoto, K., Sato, T., Takanezawa, T., and Ooe, M., GOTIC2: A program for computation of oceanic tidal loading effect, J. Geod. Soc. Jpn., 2001, vol. 47, no. 1, pp. 243–248. doi 10.11366/sokuchi1954.47.243Google Scholar
  10. 10.
    McCarthy, D.D., IERS Conventions (1992), IERS Technical Note 21, Paris: Int. Earth Rotation Serv., 1996.Google Scholar
  11. 11.
    Mikhailov, P.C., Improvement of marine gravimetric survey implementation techniques, Cand. Sci. (Tech.) Dissertation, Moscow: Inst. Fiz. Zemli Ross. Akad. Nauk, 2017.Google Scholar
  12. 12.
    Molodenskii, M.S., Elastic tides, free nutation, and some problems of the Earth’s structure, Tr. Geofiz. Inst. Akad. Nauk SSSR, 1953, no. 19, pp. 3–52.Google Scholar
  13. 13.
    Molodenskii, S.M., Prilivy, nutatsiya i vnutrennee stroenie Zemli (Tides, Nutation, and Internal structure of the Earth), Moscow: Inst. Fiz. Zemli Akad. Nauk SSSR, 1984.Google Scholar
  14. 14.
    Molodenskii, M.S. and Kramer, M.V., Love numbers for static earth tides of 2nd and 3rd orders, in Zemnye prilivy i nutatsiya Zemli (Tides in Solid Earth and Nutation of the Earth), Moscow: Akad. Nauk SSSR, 1961, p. 26.Google Scholar
  15. 15.
    Oshchepkov, I.A., Sermyagin, R.A., Spesivtsev, A.A., Yushkin, V.D., Pozdnyakov, A.V., Kovrov, A.A., and Yuzefovich, P.A., Gravity measurements in the Moscow gravity network, 4th IAG Symposium on Terrestrial Gravimetry: Static and Mobile Measurements, St. Petersburg, Russia, 2016. doi 10.5281/zenodo.5909610.5281/ zenodo.59096Google Scholar
  16. 16.
    Pertsev, B.P., On the influence of sea tides on tidal variations in gravity, Izv. Akad. Nauk SSSR. Fiz. Zemli, 1966, no. 10, pp. 25–29.Google Scholar
  17. 17.
    Pertsev, B.P., Estimation of sea tides on earth tides in the points far from oceans, in Zemnye prilivy i vnutrennee stroenie Zemli (Tides in Solid Earth and Inner Structure of the Earth), Moscow: Nauka, 1967, pp. 10–22.Google Scholar
  18. 18.
    Pertsev, B.P., Influence of sea tides in near zones on observations of solid earth tides, Izv. Akad. Nauk SSSR. Fiz. Zemli, 1976, no. 1, pp. 13–22.Google Scholar
  19. 19.
    Pertsev, B.P., Tidal corrections to gravity measurements, Izv., Phys. Solid Earth, 2007, vol. 43, no. 7, pp. 547–553.CrossRefGoogle Scholar
  20. 20.
    Pertsev, B.P. and Ivanova, M.V., Calculation of Love load numbers for the Earth model 508 by Gilbert and Dziewonski, in Izuchenie zemnykh prilivov (Studies of Earth Tides), Moscow: Nauka, 1980, pp. 42–47.Google Scholar
  21. 21.
    Pertsev, B.P. and Ivanova, M.V., Estimation of the influence of run-up water on the value of gravity and the height of earth surface in coastal areas, Izv. Akad. Nauk SSSR. Fiz. Zemli, 1981, no. 1, pp. 87–91.Google Scholar
  22. 22.
    Pertsev, B.P. and Ivanova, M.V., Estimation of accuracy of tidal corrections calculation, Izv. Ross. Akad. Nauk. Fiz. Zemli, 1994, no. 5, pp. 78–80.Google Scholar
  23. 23.
    Scherneck, H.G., A parameterized Earth tide observation model and ocean tide loading effects for precise geodetic measurements, Geophys. J. Int., 1991, vol. 106, pp. 677–695.CrossRefGoogle Scholar
  24. 24.
    Smith, M.L., The scalar equations of infinitesimal elastic gravitational motion for a rotating, slightly elliptical Earth, Geophys. J. R. Astron. Soc., 1974, vol. 37, pp. 491–526.CrossRefGoogle Scholar
  25. 25.
    Smith, M.L., Translational inner core oscillations of a rotating, slightly elliptical Earth, J. Geophys. Res., 1976, vol. 81, pp. 3055–3065.CrossRefGoogle Scholar
  26. 26.
    Smith, M.L., Wobble and nutation of the Earth, Geophys. J. R. Astron. Soc., 1977, vol. 50, pp. 103–140.CrossRefGoogle Scholar
  27. 27.
    Spiridonov, E.A., ATLANTIDA 3.1_2014 software for analysis of earth tides data, Nauka Tekhnol. Razrab., 2014, vol. 93, no. 3, pp. 3–48.Google Scholar
  28. 28.
    Spiridonov, E.A., ATLANTIDA 3.1_2014 software for calculating parameters of the earth tides, State Software Registry Certificate no. 2015619567, 2015.Google Scholar
  29. 29.
    Spiridonov, E.A., Results of comparison of predicted Earth tidal parameters and observational data, Seism. Instrum., 2016a, vol. 52, no. 1, pp. 60–69.CrossRefGoogle Scholar
  30. 30.
    Spiridonov, E.A., How dissipation and selection of the Earth model on the quality of the Earth tidal prediction, Seism. Instrum., 2016b, vol. 52, no. 3, pp. 224–232.CrossRefGoogle Scholar
  31. 31.
    Spiridonov, E.A., Corrections to the Love numbers for the relative and Coriolis accelerations and their latitude dependence, Geofiz. Protsessy Biosfera, 2016c, vol. 15, no. 1, pp. 73–81.Google Scholar
  32. 32.
    Spiridonov, E.A., Latitude dependence of amplitude factor δ for degree 2 tides, Russ. Geol. Geophys., 2016d, vol. 57, no. 4, pp. 629–636. doi 10.1016/j.rgg.2015.08.013CrossRefGoogle Scholar
  33. 33.
    Spiridonov, E.A., Amplitude factors δ and phase shifts of tidal waves for the models of the Earth with ocean, Geofiz. Protsessy Biosfera, 2017, vol. 16, no. 2, pp. 5–54. doi 10.21455/GPB2017.2-1Google Scholar
  34. 34.
    Spiridonov, E.A. and Vinogradova, O.Yu., Comparison of the model oceanic gravimetrical effect with the observations, Izv., Phys. Solid Earth, 2014, vol. 50, no. 1, pp. 118–126. doi 10.1134/S1069351314010078CrossRefGoogle Scholar
  35. 35.
    Spiridonov, E.A. and Vinogradova, O.Yu., The results of integrated modeling of the oceanic gravimetric effect, Seism. Instrum., 2018, vol. 54, no. 1, pp. 43–53. doi 10.3103/S0747923918010097CrossRefGoogle Scholar
  36. 36.
    Spiridonov, E.A., Yushkin, V.D., and Khrapenko, O.A., Tidal analysis and experimental oceanic load effect in Murmansk, Geod. Kartogr., 2014, no. 12, pp. 22–29.Google Scholar
  37. 37.
    Spiridonov, E., Vinogradova, O., Boyarskiy, E., and Afanasyeva, L., ATLANTIDA3.1_2014 for WINDOWS: A software for tidal prediction, Bull. Inf. Mar. Terr., 2015, vol. 149, pp. 12 063–12 081.Google Scholar
  38. 38.
    Valencio, A., Grebogi, C., and Baptista, M.S., Removing tides from gravity time-series: a comparison of classical methods applied to a global network of superconducting gravimeters. Accessed February 28, 2017.Google Scholar
  39. 39.
    Van Camp, M. and Vanterin, P., T-soft: Graphical and interactive software for the analysis of the time series and Earth tides, Comput. Geosci., 2005, vol. 31, pp. 631–640.CrossRefGoogle Scholar
  40. 40.
    Vinogradova, O.Yu., Oceanic tidal loads near the European coast calculated from Green’s function, Izv., Phys. Solid Earth, 2012, vol. 48, nos. 7–8, pp. 572–586.CrossRefGoogle Scholar
  41. 41.
    Vinogradova, O.Yu. and Spiridonov, E.A., Comparative analysis of oceanic corrections to gravity calculated from the PREM and IASP91 models, Izv., Phys. Solid Earth, 2012, vol. 48, no. 2, pp. 162–170.CrossRefGoogle Scholar
  42. 42.
    Vinogradova, O.Yu. and Spiridonov, E.A., Comparison of two methods for calculating tidal loads, Izv., Phys. Solid Earth, 2013a, vol. 49, no. 1, pp. 83–92. doi 10.1134/S1069351313010163CrossRefGoogle Scholar
  43. 43.
    Vinogradova, O.Yu. and Spiridonov, E.A., Some features of TOPEX/POSEIDON data application in gravimetry, in Reference Frames for Applications in Geosciences, vol. 138 of International Association of Geodesy Symposia, Altamimi, Z. and Collilieux, X., Eds., Berlin: Springer, 2013b, pp. 229–235. doi 10.1007/978-3-642-32998-2_3510.1007/978-3-642-32998-2_35Google Scholar
  44. 44.
    Wahr, J.M., The tidal motions of a rotating, elliptical, elastic and oceanless Earth, Ph.D. Thesis, Boulder, Univ. Color., 1979.Google Scholar
  45. 45.
    Wahr, J.M., Body tides on an elliptical, rotating, elastic and oceanless Earth, Geophys. J. R. Astron. Soc., 1981a, vol. 64, pp. 677–703.CrossRefGoogle Scholar
  46. 46.
    Wahr, J.M., A normal mode expansion for the forced response of a rotating Earth, Geophys. J. R. Astron. Soc., 1981b, vol. 64, pp. 651–675.CrossRefGoogle Scholar
  47. 47.
    Wahr, J.M. and Bergen, Z., The effects of mantle and an elasticity on nutations, earth tides, and tidal variations in rotation rate, Geophys. J., 1986, vol. 87, pp. 633–668.CrossRefGoogle Scholar
  48. 48.
    Wenzel, H.G., The Nanogal software: Earth tide data processing package Eterna3.30, Bull. Inf. Mar. Terr., 1996, vol. 124, pp. 9425–9439.Google Scholar
  49. 49.
    Zheleznyak, L.K., Koneshov, V.N., and Mikhailov, P.S., Experimental determination of the vertical gravity gradient below the sea level, Izv., Phys. Solid Earth, 2016, vol. 52, no. 6, pp. 866–868. doi 10.1134/S1069351316060124CrossRefGoogle Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • E. A. Spiridonov
    • 1
    Email author
  • V. D. Yushkin
    • 2
    • 3
  • O. Yu. Vinogradova
    • 1
  • L. V. Afanasyeva
    • 1
  1. 1.Schmidt Institute of Physics of the Earth, Russian Academy of SciencesMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia
  3. 3.Center of Geodesy, Cartography, and Space Data InfrastructureMoscowRussia

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