The Evaluation of Gravity Anomalies Based on Global Models by Land Gravity Data

Authors: M. Yilmaz, I. Yilmaz, M. Uysal

Abstract:

The Earth system generates different phenomena that are observable at the surface of the Earth such as mass deformations and displacements leading to plate tectonics, earthquakes, and volcanism. The dynamic processes associated with the interior, surface, and atmosphere of the Earth affect the three pillars of geodesy: shape of the Earth, its gravity field, and its rotation. Geodesy establishes a characteristic structure in order to define, monitor, and predict of the whole Earth system. The traditional and new instruments, observables, and techniques in geodesy are related to the gravity field. Therefore, the geodesy monitors the gravity field and its temporal variability in order to transform the geodetic observations made on the physical surface of the Earth into the geometrical surface in which positions are mathematically defined. In this paper, the main components of the gravity field modeling, (Free-air and Bouguer) gravity anomalies are calculated via recent global models (EGM2008, EIGEN6C4, and GECO) over a selected study area. The model-based gravity anomalies are compared with the corresponding terrestrial gravity data in terms of standard deviation (SD) and root mean square error (RMSE) for determining the best fit global model in the study area at a regional scale in Turkey. The least SD (13.63 mGal) and RMSE (15.71 mGal) were obtained by EGM2008 for the Free-air gravity anomaly residuals. For the Bouguer gravity anomaly residuals, EIGEN6C4 provides the least SD (8.05 mGal) and RMSE (8.12 mGal). The results indicated that EIGEN6C4 can be a useful tool for modeling the gravity field of the Earth over the study area.

Keywords: Free-air gravity anomaly, Bouguer gravity anomaly, global model, land gravity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.2021665

References:

[1] Helmert, F. R. Die Mathematischen und Physikalischen Theorieen der H¨oheren Geodäsie (Mathematical and Physical Theories of Higher Geodesy) (in German). Druck und Verlag von B.G. Teubner, Leipzig, Germany, (1880) 626 p.
[2] Plag, H-P., Altamimi, Z., Bettadpur, S., Beutler, G., Beyerle, G., Cazenave, A., Crossley, D., Donnellan, A., Forsberg, R., Gross, R., Hinderer, J., Komjathy, A., Ma, C., Mannucci, A. J., Noll, C., Nothnagel, A., Pavlis,, E. C., Pearlman, M., Poli, P., Schreiber, U., Senior, K., Woodworth, P. L., Zerbini, S., Zuffada, C. The goals, achievements, and tools of modern geodesy. In: Plag H-P, Pearlman M (Eds) Global Geodetic Observing System – Meeting the Requirements of a Global Society on a Changing Planet in 2020. Springer-Verlag, Berlin, Heidelberg, Germany, 2009, pp. 15-87.
[3] Dehant, V. International and national geodesy and its three pillars: (1) geometry and kinematics, (2) earth orientation and rotation, and (3) gravity field and its variability. In: Arijs E, Ducarme B (Eds) Earth Sciences Day of the CNBGG `Geodesy and Geophysics for the Third Millennium´. Belgian Academy of Sciences, 2005, pp. 27-35.
[4] Hildenbrand, T. G., Briesacher, A., Flanagan, G., Hinze, W. J., Hittelman, A. M., Keller, G. R., Kucks, R. P., Plouff, D., Roest, W., Seeley, J., Smith, D. A., Webring, M. Rationale and Operational Plan to Upgrade the U.S Gravity Database. USGS Open-File Report 02-463, 2002.
[5] Smith, D. The GRAV-D Project: Gravity for the Redefinition of the American Vertical Datum. A NOAA contribution to the Global Geodetic Observing System (GGOS) component of the Global Earth Observation System of Systems (GEOSS) Project Plan, 2007, http://www.ngs.noaa.gov/GRAV-D/pubs/GRAV- D_v2007_12_19.pdf (accessed 12 June 2018).
[6] Roman, D.R., Wang, Y.M., Saleh, J., Li, X. Geodesy, Geoids, & Vertical Datums: A Perspective from the U.S. National Geodetic Survey, Facing the Challenges - Building the Capacity. FIG Congress, 11-16 April 2010, Sydney, Australia, 2010.
[7] Li, X., Götze, H. J. Ellipsoid, geoid, gravity, geodesy, and geophysics, Geophysics (2001) 66 (6) 1660-1668.
[8] Barthelmes, F. Global models. In: Grafarend E (Ed) Encyclopedia of Geodesy. Springer International Publishing, Switzerland, 2014, pp.1-9, doi:10.1007/978-3-319-02370-0 43-1.
[9] Reigber, C., Lühr, H., Schwintzer, P. CHAMP mission status, Adv Space Res (2002) 30 (2) 129-134.
[10] Tapley, BD., Bettadpur, S., Watkins, M., Reigber, C. The gravity recovery and climate experiment: mission overview and early results, Geophys Res Lett (2004) 31 L09607.
[11] Floberghagen, R., Fehringer, M., Lamarre, D., Muzi, D., Frommknecht, B., Steiger, C. H., Pineiro, J., da Costa, A. Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission, J Geod (2011) 85 (11) 749-758.
[12] Godah, W., Szelachowska, M., Krynski, J. On the analysis of temporal geoid height variations obtained from GRACE-based GGMs over the area of Poland, Acta Geophys (2017) 65 713-725.
[13] Novák, P. Direct modeling of the gravitational field using harmonic series, Acta Geodyn Geomater (2010) 7 (1) 35-47.
[14] Bolkas, D., Fotopoulos, G., Braun, A. On the impact of airborne gravity data to fused gravity field models, J Geod (2016) 90 (6) 561-571.
[15] Pavlis, N. K., Holmes, S. A., Kenyon, S. C., Factor, J. K. An earth gravitational model to degree 2160: EGM2008. General Assembly of the European Geosciences Union, 13-18 April, Vienna, Austria, 2008.
[16] Förste, C., Bruinsma, S. L., Abrikosov, O., Lemoine, J-M., Marty, J. C., Flechtner, F., Balmino, G., Barthelmes, F., Biancale, R. 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, 2014, doi: 10.5880/ICGEM.2015.1.
[17] Gilardoni, M., Reguzzoni, M., Sampietro, D. GECO: a global gravity model by locally combining GOCE data and EGM2008, Stud Geophys Geod (2016) 60 (2), 228-247.
[18] Hill, P., Bankey, V., Langenheim, V. Introduction to Potential Fields: Gravity. USGS fact sheet, 1997, http://pubs.usgs.gov/fs/fs-0239-95/fs-0239-95.pdf (accessed 12 June 2018).
[19] Hackney, R. I., Featherstone, W. E. Geodetic versus geophysical perspectives of the ‘gravity anomaly’, Geophys J Int (2003) 154 (1) 35-43.
[20] Mishra, D. C. Gravity anomalies. In: Lastovicka J (Ed) Geophysics and Geochemistry - Volume 3. EOLSS publishers/UNESCO, 2009, pp. 111-136.
[21] Featherstone, W. E., Dentith, M. C. A geodetic approach to gravity data reduction for geophysics, Comput Geosci (1997) 23 (10) 1063-1070.
[22] Hofmann-Wellenhof, B., Moritz, H. Physical Geodesy, 2nd edition. Springer-Verlag, Vienna, Austria, 2006.
[23] Hackney, R. I. Gravity, data to anomalies. In: Gupta HK (Ed) Encyclopedia of Solid Earth Geophysics. Springer, Dordrecht, the Netherlands, 2011, pp. 524-533.
[24] Sjöberg, L. E., Bagherbandi, M. Gravity Inversion and Integration - Theory and Applications in Geodesy and Geophysics. Springer, 2017, doi: 10.1007/978-3-319-50298-4.
[25] Rummel, R., Balmino, G., Johannessen, J., Visser, P., Woodworth, P. Dedicated gravity field missions-principles and aims, J Geodyn (2002) 33 3-20.
[26] Barthelmes, F. Definition of Functionals of the Geopotential and Their Calculation from Spherical Harmonic Models: Theory and Formulas Used by the Calculation Service of the International Centre for Global Earth Models (ICGEM). Scientific Technical Report STR09/02, Revised Edition, January 2013, GeoForschungZentrum Potsdam, 2013, doi: 10.2312/GFZ.b103-0902-26, http://icgem.gfz-potsdam.de/str-0902-revised.pdf (accessed 12 June 2018).
[27] Yilmaz, M., Turgut, B., Gullu, M., Yilmaz, I. The evaluation of high-degree geopotential models for regional geoid determination in Turkey, AKU J Sci Eng (2017) 17 (1) 147-153.
[28] Pavlis, N. K., Holmes, S. A., Kenyon, S. C., Factor, J. K. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008), J Geophys Res (2012) 117 B04406, doi: 10.1029/2011JB008916.
[29] Morelli, C., Gantar, C., Honkasalo, T., McConnell, R. K., Tanner, J. G., Szabo, B., Uotila, U., Whalen, C. T. The International Gravity Standardization Net 1971 (IGSN71). International Association of Geodesy, Special Publication No. 4, 1974.
[30] Yilmaz, M., Gullu, M. A comparative study for the estimation of geodetic point velocity by artificial neural networks, J Earth Syst Sci (2014) 123 (4) 791-808.
[31] Karpik, A. P., Kanushin, V. F., Ganagina, I. G., Goldobin, D. N., Kosarev, N. S., Kosareva, A. M. Evaluation of recent Earth’s global gravity field models with terrestrial gravity data Contrib Geophys Geod (2016) 46 (1) 1-11.
[32] Barthelmes, F., Köhler, W. International Centre for Global Earth Models (ICGEM), The Geodesists Handbook 2016, J Geod (2016) 90 (10) 907-1205, doi: 10.1007/s00190-016-0948-z.
[33] Pavlis, N. K., Factor, J. K., Holmes, S. A. Terrain-related gravimetric quantities computed for the next EGM, Proceedings of the 1st International Symposium of the International Gravity Field Service, J Mapp (Special Issue) (2007) 18 318-323.