Abstract
The aim of this study is to determine an accurate geoid model for Iran based on the Least Squares Collocation method in the framework of the Remove — Compute — Restore technique. In areas suffering from a lack of homogeneous and accurate gravity anomaly data, as is the case of Iran, the choice of the most compatible global gravity model has a significant impact on the estimated form of the geoid. Different combined and satellite-only global gravity models were therefore analyzed for Iran, and EIGEN6C4 was selected as the best one. The Shuttle Radar Topography Mission height model was used for the residual terrain correction. The covariance modeling, a crucial step in the Least Squares Collocation method, was based on two strategies. In the first, the study area was divided into four sub-areas, and then an individual empirical covariance was computed and a covariance model fitted to each of them. In the second, an empirical covariance was computed using all terrestrial gravity data, and a unique covariance model was fitted to it. Despite some border effects, the former strategy showed slightly better performance according to the resulting statistics, and therefore it was preferred for the estimation of the geoid model called IRG2018. To remove the offset of IRG2018 with respect to GNSS/Leveling-derived geoid heights, two alternative approaches were tested: subtracting a fitting polynomial surface or directly using the GNSS/Leveling data as an input to the IRG2018 computation process. Evaluation of the results, based on an independent control set of approximately half of available GNSS/Leveling points, showed an advantage of the latter approach, with an estimated accuracy of about 20 cm in terms of RMS.
Similar content being viewed by others
References
Amjadiparvar B., Sideris M.G., Rangelova E. and Ardalan A.A., 2011. Evaluation of GOCE-based global gravity field models in Iran. Abstract. American Geophysical Union, Fall Meeting 2011, Abstract G43A-0749.
Brockmann J.M., Zehentner N., Höck E., Pail R., Loth I., Mayer-Gürr T. and Schuh W.-D., 2014. EGM_TIM_RL05: An independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys. Res. Lett., 41, 8089–8099, DOI: https://doi.org/10.1002/2014gl061904.
Bruinsma S.L., Förste 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, 3607–3612, DOI: https://doi.org/10.1002/grl.50716.
Bucha B., Janák J., Papčo J. and Bezdĕk A., 2016. High-resolution regional gravity field modelling in a mountainous area from terrestrial gravity data. Geophys. J. Int., 207, 949–966, DOI: https://doi.org/10.1093/gji/ggw311.
Foroughi I., Afrasteh Y., Ramouz S. and Safari A., 2017. Local evaluation of Earth gravitational models, case study: Iran. Geod. Cartogr., 43, 1–13, DOI: https://doi.org/10.3846/20296991.2017.1299839.
Forsberg R., 1984. A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity field Modelling. Report 355. Department of Geodetic Science and Surveying, Ohio State University, Columbus, OH.
Förste C., Bruinsma S.L., Abrikosov O., Lemoine J.M., Marty J.C., Flechtner F., Balmino G., Barthelmes F. and Biancale R., 2014. EIGEN-6C4: The Latest Combined Global Gravity Field Model Including GOCE Data up to Degree and Order 2190 of GFZ Potsdam and GRGS Toulouse. GFZ Data Services, DOI: https://doi.org/10.5880/icgem.2015.1.
Gatti A. and Reguzzoni M., 2017. GOCE Gravity Field Model by Means of the Space-Wise Approach (Release R5). GFZ Data Services DOI: https://doi.org/10.5880/icgem.2017.005.
Hatam C.Y., 2010. Etablissement des nouveaux reseaux multi-observations geodesiques et gravimetriques et determination du geoide en Iran. PhD Thesis. Geophysics, University Montpellier 2, Montpellier, France (in French).
Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. W.H. Freeman San Francisco, CA.
Hirt C., 2011. Assessment of EGM2008 over Germany using accurate quasigeoid heights from vertical deflections, GCG05 and GPS/levelling. Zeitschrift für Geodäsie, Geoinformation und Landmanagement, 136(3), 138–149.
Hirt C. and Kuhn M., 2014. Band-limited topographic mass distribution generates full-spectrum gravity field: Gravity forward modeling in the spectral and spatial domains revisited. J. Geophys. Res.-Solid Earth, 119, 3646–3661, DOI: https://doi.org/10.1002/2013jb010900.
Kiamehr R., 2009. Evaluation of the new Earth gravitational model (EGM2008) in Iran. Abstract. Geophys. Res. Abs., 11, EGU2009–330.
Kiamehr R. and Sjöberg L.E., 2005. Effect of the SRTM global DEM on the determination of a high-resolution geoid model: a case study in Iran. J. Geodesy, 79, 540–551, DOI: https://doi.org/10.1007/s00190-005-0006-8.
Knudsen P., 1987. Estimation and modelling of the local empirical covariance function using gravity and satellite altimeter data. Bull. Geod., 61, 145–160.
Moritz H., 1980. Advanced Physical Geodesy. Herbert Wichmann Verlag Karlsruhe, Germany.
NASA JPL, 2013. NASA Shuttle Radar Topography Mission Global 1 Arc Second (Data Set). NASA LP DAAC DOI: 10.5067/measures/srtm/srtmgl1.003.
Pail R., Bruinsma S., Migliaccio F., Förste C., Goiginger H., Schuh W.-D, Höck E., Reguzzoni M., Brockmann J.M., Abrikosov O., Veicherts M., Fecher T., Mayrhofer R., Krasbutter I., Sansó F. and Tscherning, C.C., 2011. First GOCE gravity field models derived by three different approaches. J. Geodesy, 85, 819–843, DOI: https://doi.org/10.1007/s00190-011-0467-x.
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.-Solid Earth, 117, B04406, DOI: https://doi.org/10.1029/2011JB008916.
Reguzzoni M. and Tselfes N., 2008. Optimal multi-step collocation: application to the space-wise approach for GOCE data analysis. J. Geodesy, 83, 13–29, DOI: https://doi.org/10.1007/s00190-008-0225-x.
Rexer M., Hirt C., Bucha B. and Holmes S., 2017. Solution to the spectral filter problem of residual terrain modelling (RTM). J. Geodesy, 92, 675–690, DOI: https://doi.org/10.1007/s00190-017-1086-y.
Gruber T., Rummel R., Idhe J. Liebsch G., Rülke A., Schäfer U., Sideris M., Rangelova E., Woodworth P., Hughes C. and Gerlach C., 2014. Height System Unification with GOCE, Summary and Final Report. Doc. No. GO-HSU-PL-0021, Issue 1, Rev. 0. Institute of Astronomical and Physical Geodesy, Technical University Munich, Munich, Germany.
Saadat A., Safari A. and Needell D., 2018. IRG2016: RBF-based regional geoid model of Iran. Stud. Geophys. Geod., 62, 380–407, DOI: https://doi.org/10.1007/s11200-016-0679-x.
Sadiq M., Tscherning C.C. and Ahmad Z., 2009. An estimation of the height system bias parameter No using least squares collocation from observed gravity and GPS-levelling data. Stud. Geophys. Geod., 53, 375–388, DOI: https://doi.org/10.1007/s11200-009-0026-6.
Sansò F. and Sideris M.G., 2013. Geoid Determination — Theory and Methods. Lecture Notes in Earth System Sciences, 110, Springer-Verlag Berlin, Heidelberg, Germany, DOI: https://doi.org/10.1007/978-3-540-74700-0.
Shako R., Förste C., Abrikosov O., Bruinsma S., Marty J.C., Lemoine J.M., Flechtner F., Neumayer K. and Dahle C., 2013. EIGEN-6C: A high-resolution global gravity combination model including GOCE data. In: Flechtner F., Sneeuw N. and Schuh W.-D. (Eds), Observation of the System Earth from Space — CHAMP, GRACE, GOCE and Future Missions. 155–161, Springer-Verlag, Berlin, Heidelberg, Germany, DOI: https://doi.org/10.1007/978-3-642-32135-1_20.
Sjöberg L.E. and Bagherbandi M., 2012. Quasigeoid-to-geoid determination by EGM08. Earth Sci. Inform., 5, 87–91, DOI: https://doi.org/10.1007/s12145-012-0098-7.
Tscherning C.C., 2015. Least-squares collocation. In: Grafarend E. (Ed.), Encyclopedia of Geodesy. Springer, Cham, Switzerland, DOI: https://doi.org/10.1007/978-3-319-02370-0_51-1.
Tscherning C.C. and Rapp R., 1974. Closed Covariance Expressions for Gravity Anomalies, Geoid Undulations, and Deflections of the Vertical implied by Anomaly Degree Variance Models. Report No. 208 Department of Geodetic Science, The Ohio State University, Columbus, OH.
Tscherning C.C., Forsberg R. and Knudsen P., 1992. The GRAVSOFT package for geoid determination. Proceedings of the 1st Continental Workshop on the Geoid in Europe, Prague. Research Institute of Geodesy, Topography and Cartography, Prague, Czech Republic.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ramouz, S., Afrasteh, Y., Reguzzoni, M. et al. IRG2018: A regional geoid model in Iran using Least Squares Collocation. Stud Geophys Geod 63, 191–214 (2019). https://doi.org/10.1007/s11200-018-0116-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11200-018-0116-4