High-frequency analysis of Earth gravity field models based on terrestrial gravity and GPS/levelling data: a case study in Greece

References

Abramowitz M. and Stegun I. A., 1965, Handbook of Mathematical Functions, Dover, New York.Search in Google Scholar

Anagnostou E., 2007, National Report of Greece to EUREF 2007, EUREF Symposium Proceedings, 6-9 June 2007, London, UK.Search in Google Scholar

Andritsanos V.D., Vergos G.S., Grigoriadis V.N., Pagounis V. and Tziavos I.N. , 2014, Spectral characteristics of the Hellenic vertical network - Validation over Central and Northern Greece using GOCE/GRACE global geopotential models, Geophys. Res. Abstr., Vol. 16, EGU2014-1223.Search in Google Scholar

Arabelos D. and Tscherning C.C., 2010, A comparison of recent Earth gravitational models with emphasis on their contribution in refining the gravity and geoid at continental or regional scale, J. Geod, 84, 643–660. Barthelmes F. and Förste Ch., 2011, The ICGEM-format, ICGEM, GFZ Potsdam.10.1007/s00190-010-0397-zSearch in Google Scholar

Baur O., Bock H., Hock E., Jaggi A., Krauss S., Mayer-Gurr T., Reubelt T., Siemes C. and Zehentner N., 2014, Comparison of GOCE-GPS gravity fields derived by different approaches, J. Geod, 88, 10, 959- 973.10.1007/s00190-014-0736-6Search in Google Scholar

Beutler G., Jäggi A., Mervart L. and Meyer U., 2010, The celestial mechanics approach: theoretical foundations, J. Geod, 85, 10, 605- 624.10.1007/s00190-010-0401-7Search in Google Scholar

BoschW., 2000, On the Computation of Derivatives of Legendre Functions, Phys. Chem. Earth (A), 25, 9, 655-659.10.1016/S1464-1895(00)00101-0Search in Google Scholar

Bruinsma S., Forste C., Abrikosov O., Marty J.C., Rio M.H., Mulet S. and Bonvalot S., 2013, The new ESA satellite-only gravity field model via the direct approach, Geophys Res Lett, 40, 14, 3607- 3612.10.1002/grl.50716Search in Google Scholar

Dach R., Hugentobler U., Fridez P. and Meindl M., 2007, Bernese GPS Software Version 5.0. Usermanual, Astronomical Institute, Universtiy of Bern.Search in Google Scholar

Ditmar P, Kuznetsov V, van Eck van der Sluijs AA, Schrama E and Klees R, 2006, DEOS CHAMP-01C-70: a model of the Earth’s gravity field computed from accelerations of the CHAMP satellite, J. Geod, 79, 586–601.10.1007/s00190-005-0008-6Search in Google Scholar

Dow J.M., Neilan R.E. and Rizos C., 2009, The International GNSS Service in a Changing Landscape of Global Navigation Satellite Systems, J. Geod, 83, 191–198.10.1007/s00190-008-0300-3Search in Google Scholar

Claessens S.J., 2005, New Relations Among Associated Legendre Functions and Spherical Harmonics, J. Geod, 79, 6-7, 398-406.10.1007/s00190-005-0483-9Search in Google Scholar

Elsaka B., Raimondo J.C., Brieden P., Reubelt T., Kusche J., Flechtner F., Iran-Pour S. and Sneeuw N., 2014, Comparing seven candidate mission configurations for temporal gravity field retrieval through full-scale numerical simulation, J. Geod, 88, 1, 31-43.10.1007/s00190-013-0665-9Search in Google Scholar

ESA, 1999, Gravity Field and Steady-State Ocean Circulation Mission, ESA SP-1233(1), Report for mission selection of the four candidate earth explorer missions, ESA Publications Division, ESTEC, Noordwijk, The Netherlands.Search in Google Scholar

Featherstone W., 2001, Absolute and relative testing of gravimetric geoid models using Global Positioning System and orthometric height data, Comput. Geosci., 27, 807–814.10.1016/S0098-3004(00)00169-2Search in Google Scholar

Floberghagen R., Fehringer M., Lamarre D.,Muzi D., Frommknecht B., Steiger C., Pineiro J. and da Costa A., 2011, Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission, J. Geod, 85, 749–758.10.1007/s00190-011-0498-3Search in Google Scholar

Förste Ch., Schmidt R., Stubenvoll R., Flechtner F., Meyer Ul., König R., Neumayer H., Biancale R., Lemoine J.-M., Bruinsma S., Loyer S., Barthelmes F. and Esselborn S., 2008, The Geo- ForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGENGL04S1 and EIGEN-GL04C, J Geod, 82, 331-346.10.1007/s00190-007-0183-8Search in Google Scholar

Förste C., Bruinsma S., Marty J.C., Flechtner F., Abrikosov O., Dahle C., Lemoine J.M., Neumayer K.H., Biancale R., Barthelmes F. and König R., 2013, EIGEN-6C3 - the newest High Resolution Global Combined Gravity Field Model based on the 4th Release of the GOCE Direct Approach, Presented at the IAG Scientific Assembly, 1-6 September 2013, Potsdam, Germany.Search in Google Scholar

GFCT: GOCE Flight Control Team, 2014, GOCE End-of-Mission operations report, European Space Agency: GO-RP-ESC-FS-6268.Search in Google Scholar

Gianniou M., 2010, Investigating the Effects of Earthquakes Using HEPOS, IAG Symposia Series, 135, 661-668.10.1007/978-3-642-10634-7_87Search in Google Scholar

Grigoriadis VN, Kotsakis C, Tziavos IN, Vergos GS, 2014, Estimation of the geopotential value Wo for the local vertical datum of continental Greece using EGM08and GPS/leveling data, In:Marti U (ed) Gravity, Geoid and Height Systems, IAG Symposia, 141, 249-255.10.1007/978-3-319-10837-7_32Search in Google Scholar

Gruber T., Visser P.N.A.M., Ackermann Ch. and Hosse M., 2011, Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons, J. Geod, 85, 845–860.10.1007/s00190-011-0486-7Search in Google Scholar

Hashemi Farahani H., Ditmar P., Klees R., Teixeira da Encarnação J., Liu X., Zhao Q. and Guo J., 2013a, Validation of static gravity field models using GRACE K-band ranging and GOCE gradiometry data, Geophys. J. Int., 194, 2, 751-771.10.1093/gji/ggt149Search in Google Scholar

Hashemi Farahani H, Ditmar P, Klees R, Liu X, Zhao Q, and Guo J, 2013b, The static gravity field model DGM-1S from GRACE and GOCE data: computation, validation and an analysis of GOCE mission’s added value, J Geod, 87, 9, 843-867.10.1007/s00190-013-0650-3Search in Google Scholar

HeiskanenW.A. and Moritz H., 1967, Physical Geodesy,W.H. Freeman and Company, San Francisco.Search in Google Scholar

Hirt C., Gruber T. and Featherstone W.E., 2011, Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights, J Geod, 85, 10, 723- 740.10.1007/s00190-011-0482-ySearch in Google Scholar

Hobson E.W., 1931, The Theory of Spherical and Ellipsoidal Harmonics, Cambridge University Press.Search in Google Scholar

Holmes S.A. and Featherstone W.E., 2002, A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions, J Geod, 76, 279–299.10.1007/s00190-002-0216-2Search in Google Scholar

Holmes S.A., Pavlis N.K., 2008, HARMONIC_ SYNTH_ WGS84 (Version 06/03/2008); A Fortran program for very-high-degree harmonic synthesis, http://earth-info.nima.mil/GandG/wgs84/ gravitymod/egm2008/hsynth_WGS84.fSearch in Google Scholar

Jaggi A., Beutler G., Meyer U., Prange L., Dach R. and Mervart L., 2012, AIUB-GRACE02S: Status of GRACE Gravity Field Recovery using the Celestial Mechanics Approach, In: Geodesy for Planet Earth (Eds.: S. Kenyon, M.C. Pacino and U.Marti), IAG Symposia, 136, 161-169. Kotsakis C. and Katsambalos K., 2010, Quality Analysis of Global Geopotential Models at 1542 GPS/Levelling Benchmarks over the Hellenic Mainland, Surv. Rev., 42, 318, 327-344.10.1007/978-3-642-20338-1_20Search in Google Scholar

Kotsakis C., Katsambalos K. and Ampatzidis D., 2012, Estimation of the zero-height geopotential level WLVDo in a local vertical datum from inversion of co-located GPS, leveling and geoid heights: a case study in the Hellenic islands, J Geod, 86, 6, 423-439.10.1007/s00190-011-0530-7Search in Google Scholar

Lemoine F.G., Kenyon S.C., Factor J.K., Trimmer R.G., Pavlis N.K., Chinn D.S., Cox C.M., Klosko S.M., Luthcke S.B., Torrence M.H., Wang Y.M., Williamson R.G., Pavlis E.C., Rapp R.H. and Olson T.R. , 1998, The Development of the Joint NASA GSFC and the NIMA Geopotential Model EGM96, NASA Technical Paper NASA/TP1998206861, Goddard Space Flight Center, Greenbelt, USA.10.1007/978-3-662-03482-8_62Search in Google Scholar

Loomis B., Nerem R. and Luthcke S. , 2012, Simulation study of a follow-on gravity mission to GRACE, J Geod, 86, 319–335.10.1007/s00190-011-0521-8Search in Google Scholar

Mayer-Gürr T., 2006, Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE, Ph.D. Dissertation, University of Bonn, Germany.Search in Google Scholar

Mayer-Gürr T., 2007, ITG-Grace03s: The latest GRACE gravity field solution computed in Bonn, Presented at the Joint International GSTM and DFG SPP Symposium, 15–17 October, Potsdam, Germany.Search in Google Scholar

Mayer-Gürr T., Kurtenbach E. and Eicker A. , 2010, ITG-Grace2010 Gravity Field Model, http://www.igg.uni-bonn.de/apmg/index.php?id$=$itg-grace2010. Mayer- Gürr T. et al., 2012, The new combined satellite only model GOCO03s, Presented at GGHS2012, Venice, Italy.Search in Google Scholar

Migliaccio F., Reguzzoni M., Gatti A., Sanso F. and Herceg M., 2011, A GOCE-only global gravity field model by the space-wise approach, ESA Publication SP-696, Proceedings of the 4th InternationalGOCE User Workshop.Search in Google Scholar

Montenbruck O. and Gill E., 2000, Satellite Orbits; Models, Methods and Applications, Springer.10.1007/978-3-642-58351-3Search in Google Scholar

Morelli C. et al., 1974, The International Gravity Standardization Net 1971, IAG Special Publication No. 4, Paris, France.Search in Google Scholar

Moritz H., 2000, Geodetic Reference System 1980, J Geod, 74, 1, 128- 162, doi: 10.1007/s001900050278.10.1007/s001900050278Search in Google Scholar

Panet I., Flury J., Biancale R., Gruber T., Johannessen J., van den Broeke M. R., van Dam T., Gegout P., Hughes C. W., Ramillien G., Sasgen I., Seoane L. and Thomas M., 2013, Earth System Mass Transport Mission (e.motion): A Concept for Future Earth Gravity Field Measurements from Space, Surv. Geophys., 34, 2, 141-163.10.1007/s10712-012-9209-8Search in Google Scholar

Pail R., Goiginger H., Mayrhofer R., Schuh W.D., Brockmann J.M., Krasbutter I., Höck E. and Fecher T., 2010, GOCE gravity field model derived from orbit and gradiometry data applying the time-wise method, Proceedings of the ESA Living Planet Symposium, ESA Publication SP-686.Search in Google Scholar

Pail R., Bruinsma S., Migliaccio F., Forste C., Goiginger H., Schuh W.-D., Hock E., Reguzzoni M., Brockmann J.M., Abrikosov O., Veicherts M., Fecher T., Mayrhofer R., Krasbutter I., Sanso F. and Tscherning C.C., 2011, First GOCE gravity field models derived by three different approaches, J Geod, 85, 11, 819-843.10.1007/s00190-011-0467-xSearch in Google Scholar

Papanikolaou T.D., 2012, Dynamic satellite orbit modelling in the frame of space geodesy’s current missions (in Greek), Ph.D. Dissertation, Aristotle University of Thessaloniki, Greece.Search in Google Scholar

Papanikolaou T.D., 2013, Development of GRAVsynth software for spherical harmonic synthesis; User guide (in Greek), Department of Gravimetry, Hellenic Military Geographical Service, Athens, Greece.Search in Google Scholar

Papanikolaou T.D. and Papadopoulos N., 2013, Development of GRAVsynth software for spherical harmonic synthesis; Global gravity field models’ validation in the Hellenic region, Study Report (in Greek), Department of Gravimetry, Hellenic Military Geographical Service, Athens, Greece.Search in Google Scholar

Papanikolaou T.D. and Tsoulis D., 2014, Dynamic orbit parameterization and assessment in the frame of current GOCE gravity models, Phys. Earth Planet Inter., 236, 1-9.10.1016/j.pepi.2014.08.003Search in Google Scholar

Pavlis N. K., Holmes S. A., Kenyon S. C. and Factor J. K., 2012, The development and evaluation of the Earth Gravitational Model 2008 (EGM2008), J. Geophys. Res., 117, B04406, doi: 10.1029/2011JB008916.10.1029/2011JB008916Search in Google Scholar

Perosanz F., Marty J.C. and Balmino G., 1997, Dynamic orbit determination and gravity field model improvement from GPS, DORIS and Laser measurements on TOPEX/POSEIDON satellite, J Geod, 71:160-17010.1007/s001900050084Search in Google Scholar

Petit G. and Luzum B., 2010, IERS Conventions 2010, IERS Technical Note No.36, Verlag des Bundesamts für Kartographie und Geodäsie, Frankfurt am Main.Search in Google Scholar

Rapp R.H., 1997, Use of potential coeflcient models for geoid undulation determination using a spherical harmonic representation of the height anomaly/geoid undulations difference, J Geod, 71, 5, 282-299.10.1007/s001900050096Search in Google Scholar

Rexer M., Hirt C., Pail R. and Claessens S., 2014, Evaluation of the third- and fourth-generation GOCE Earth gravity field models with Australian terrestrial gravity data in spherical harmonics, J Geod, 88, 4, 319-333.10.1007/s00190-013-0680-xSearch in Google Scholar

Schall J., Eicker A. and Kusche J., 2014, The ITG-Goce02 gravity field model from GOCE orbit and gradiometer data based on the short arc approach, J Geod, 88, 4, 403-409.10.1007/s00190-014-0691-2Search in Google Scholar

Sheard B.S., Heinzel G., Danzmann K., Shaddock D.A., KlipsteinW.M. and FolknerW.M., 2012, Intersatellite laser ranging instrument for the GRACE follow-on mission, J Geod, 86, 1083–1095.10.1007/s00190-012-0566-3Search in Google Scholar

Šprlák M., Gerlach C. and Pettersen B., 2012, Validation of GOCE global gravity field models using terrestrial gravity data in Norway, J Geod. Sci., 2, 2, 134-143.10.2478/v10156-011-0030-ySearch in Google Scholar

Takos I., 1989, New adjustment of the national geodetic networks in Greece (in Greek), Bull. Hellenic Mil. Geogr. Serv., 136, 19-93.Search in Google Scholar

Tapley B.D., Bettadpur S.,Watkins M. and Reigber C., 2004, The gravity recovery and climate experiment: Mission overview and early results, Geophys. Res. Lett., 31, 9.10.1029/2004GL019920Search in Google Scholar

Tapley B., Ries J., Bettadpur S., Chambers D., Cheng M., Condi F., Gunter B., Kang Z., Nagel P., Pastor R., Pekker T., Poole S. and Wang F., 2005, GGM02 - An improved Earth gravity field model from GRACE. J Geod, 79, 467-478.10.1007/s00190-005-0480-zSearch in Google Scholar

Tapley B.D., Flechtner F., Bettadpur S.V. andWatkins M.M., 2013, The status and future prospect for GRACE after the first decade, Eos Trans., Fall Meet. Suppl., Abstract G22A-01, 2013. Tsoulis D. and Patlakis K., 2013, A spectral assessment review of current satellite-only and combined Earth gravity models, Rev. Geophys., 51, 2, 186-243.10.1002/rog.20012Search in Google Scholar

Tziavos IN, Vergos GS, Grigoriadis VN, Andritsanos VD, 2012, Adjustment of collocated GPS, geoid and orthometric height observations in Greece. Geoid or orthometric height improvement?, IAG Symposia Series, 136, 481-488.10.1007/978-3-642-20338-1_58Search in Google Scholar

Vergos GS, Grigoriadis VN, Tziavos IN and Kotsakis C, 2014, Evaluation of GOCE/GRACE Global Geopotential Models over Greece with collocated GPS/Levelling observations and local gravity data, IAG Symposia Series, 141, 85-92.10.1007/978-3-319-10837-7_11Search in Google Scholar

Voigt C. and Denker H., 2014, Validation of Second-Generation GOCE Gravity Field Models by Astrogeodetic Vertical Deflections in Germany, IAG Symposia Series, 139, 291-296.10.1007/978-3-642-37222-3_38Search in Google Scholar

Wilson P., 1996, An Introduction to the Working group of European Geo-scientists for the Establishment of Networks for Earth-science Research (WEGENER). J. Geodyn., 25, 3-4, 177-178.10.1016/S0264-3707(97)00031-8Search in Google Scholar

Wittwer T., Klees R., Seitz K. and Heck B., 2008, Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic, J Geod, 82, 223-229.10.1007/s00190-007-0172-ySearch in Google Scholar

YiW., Rummel R. and Gruber Th., 2013, Gravity field contribution analysis of GOCE gravitational gradient components, Stud. Geophys. Geod., 57, 2, 174-202.10.1007/s11200-011-1178-8Search in Google Scholar

Zerbini S. et al., 1996, Sea level in the Mediterranean: a first step towards separation of crustal movements and absolute sea-level variations. Glob. Planet. Change, 14, 1-48. 10.1016/0921-8181(96)00003-3Search in Google Scholar