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Topographic Reductions in Gravity and Geoid Modeling

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Geoid Determination

Part of the book series: Lecture Notes in Earth System Sciences ((LNESS,volume 110))

Abstract

This chapter focuses on a review of the conventional methods widely used for the computation of the effects of topography and bathymetry in geoid and quasi-geoid modeling. Terrain and bathymetry models of high-resolution and accuracy are used in order to provide the high-frequency content of the gravity field spectrum through the available mass reduction methods (e.g., terrain corrections, simple and refined Bouguer effects, residual terrain model, isostatic reduction schemes). Several other reduction schemes (e.g., the Rudzki and Poincaré and Prey reductions), which are briefly discussed herein, can be possible alternatives of computation of mass effects in gravity field modeling, although they are not commonly used in geodetic applications. The high-frequency contribution of the topographic and bathymetric effects to gravity-field related quantities (e.g., gravity anomalies, gravity disturbances, geoid undulations, deflections of the vertical, gravity gradients) is primarily due to the strong correlation of the short-wavelength gravity features with topography and bathymetry.

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Notes

  1. 1.

    The GOCO02s global gravity field model is based on SLR, CHAMP, GRACE and GOCE data and its expansion is complete to degree and order 250.

References

  • Abd-Elmotaal H (1995) Attraction of the topographic masses. Bull Geod 69(4):304–307

    Article  Google Scholar 

  • Andersen OB, Knudsen P (2008) The DNSC08 global mean sea surface and bathymetry. Presented EGU-2008, Vienna, Apr 2008

    Google Scholar 

  • Bajracharya S (2003) Terrain effects on geoid determination. UCGE Report 20180, Department of Geomatics Engineering, University of Calgary, Calgary

    Google Scholar 

  • Bajracharya S, Sideris MG (2004) The Rudzki inversion gravimetric reduction scheme in geoid determination. J Geod 78:272–282

    Article  Google Scholar 

  • Barzaghi R, Tselfes N, Tziavos IN, Vergos GS (2009) Geoid and high resolution sea surface topography modelling in the Mediterranean from gravimetry, altimetry and GOCE data: evaluation by simulation. J Geod 83:751–772

    Article  Google Scholar 

  • Bendat JS, Piersol AG (2000) Random data analysis and measurement procedures, 3rd edn. Wiley, New York

    Google Scholar 

  • Biagi L, Sansò F (2001) TcLight: a new technique for fast RTC computation. In: Sideris MG (ed) Gravity, geoid and geodynamics 2000, IAG symposia, vol 123. Springer, Berlin/Heidelberg/ New York

    Google Scholar 

  • Denker H, Barriot J-P, Barzaghi R, Fairhead D, Forsberg R, Ihde J, Kenyeres A, Marti U, Sarrailh M, Tziavos IN (2009) The development of the European gravimetric geoid model EGG07. In: Sideris MG (ed) Proceedings of the international association of geodesy symposia “observing our changing Earth”, vol 133. Springer, Berlin/Heidelberg/New York, pp 177–185

    Chapter  Google Scholar 

  • Farr TG, Rosen PA, Caro E, Crippen R, Duren R, Hensley S, Kobrick M, Paller M, Rodriguez E, Roth L, Seal D, Shaffer S, Shimada J, Umland J (2007) The shuttle radar topography mission. Rev Geophys 45:RG2004. doi:10.1029/2005RG000183

  • Featherstone WE, Dentith MC (1997) A geodetic approach to gravity data reduction for geophysics. Comput Geosci 23(10):1063–1070

    Article  Google Scholar 

  • Featherstone WE, Kirby JF (2000) The reduction of aliasing in gravity anomalies and geoid heights using digital terrain data. Geophys J Int (141):204–212

    Article  Google Scholar 

  • Featherstone WE, Kirby JF, Hirt C, Filmer MS, Claessens SJ, Brown N, Hu G, Johnston GM (2011) The AUSGeoid2009 model of the Australian height datum. J Geod 85(3):133–150

    Article  Google Scholar 

  • Forsberg R (1984) A study of terrain corrections, density anomalies and geophysical inversion methods in gravity field modelling. Reports of the department of geodesy science and survey, vol 355. Ohio State University, Columbus

    Google Scholar 

  • Forsberg R (1985) Gravity field terrain effect computation by FFT. Bull Géod 59:342–360

    Article  Google Scholar 

  • Forsberg R (1993) Modelling the fine-structure of the geoid: methods, data requirements and some results. Surv Geophys 14(4–5):403–418

    Article  Google Scholar 

  • Forsberg R (2010) Terrain effects in geoid computations. In: Lecture notes, international school for the determination and use of the geoid, Saint Petersburg, 28 June–2 July 2010

    Google Scholar 

  • Forsberg R, Solheim D (1988) Performance of FFT methods in local gravity field modeling. In: Proceedings of the Chapman conference on progress in the determination of the Earth’s gravity field, Fort-Lauderdale, 13–16 Sept 1988, pp l00–103

    Google Scholar 

  • Forsberg R, Tscherning CC (1981) The use of height data in gravity field approximation by collocation. J Geophys Res 86(B9):7843–7854

    Article  Google Scholar 

  • Forsberg R, Tscherning CC (1997) Topographic effects in gravity field modelling for BVP. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimetre geoid. Lecture notes in Earth sciences, vol 65. Springer, Berlin/Heidelberg/New York, pp 241–272

    Google Scholar 

  • Goiginger H, Hoeck E, Rieser D, Mayer-Guerr T, Maier A, Krauss S, Pail R, Fecher T, Gruber T, Brockmann JM, Krasbutter I, Schuh W-D, Jaeggi A, Prange L, Hausleitner W, Baur O, Kusche J (2011) The combined satellite-only global gravity field model GOCO02S. Presented at the general assembly of the European geosciences union, Vienna, 4–8 Apr 2011

    Google Scholar 

  • Haagmans R, de Min E, Van Gelderen M (1993) Fast evaluation of convolution integrals on the sphere using 1D FFT, and a comparison with existing methods for Stokes’ integral. Man Geod 18:227–241

    Google Scholar 

  • Harrison JC, Dickinson M (1989) Fourier transform methods in local gravity field modelling. Bull Geod 63:149–166

    Article  Google Scholar 

  • Heck B (2003b) On Helmert’s methods of condensation. J Geod 77(3–4):155–170

    Article  Google Scholar 

  • Heck B, Seitz F (2007) A comparison of the tesseroid, prism and point mass approaches for mass reductions in gravity field modelling. J Geod 81(2):121–136

    Article  Google Scholar 

  • Heiskanen WA, Moritz H (1967) Physical geodesy. Freeman, San Francisco

    Google Scholar 

  • Hirt C, Featherstone WE, Marti U (2010) Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data. J Geod 84:557–567

    Article  Google Scholar 

  • Hofmann-Wellenhof B, Moritz H (2005) Physical geodesy. Springer, Vienna/New York

    Google Scholar 

  • Huang J, Vaniček P, Pagiatakis SD, Brink W (2001) Effect of topographical density on geoid in the Canadian Rocky Mountains. J Geod 74:805–815

    Article  Google Scholar 

  • Hwang C, Wang C-G, Hsiao Y-S (2003) Terrain correction computation using Gaussian quadrature. Comput Geosci 29:1259–1268

    Article  Google Scholar 

  • Jekeli C, Serpas JG (2003) Review and numerical assessment of the direct topographical reduction in geoid determination. J Geod 77:226–239

    Article  Google Scholar 

  • Jekeli C, Zhu L (2006) Comparisons of methods to model the gravitational gradients from topographic data bases. Geophys J Int 166:999–1014

    Article  Google Scholar 

  • Kirby JF, Featherstone WE (1999) Terrain correcting the Australian gravity observations using the national digital elevation model and the fast Fourier transform. Aust J Earth Sci 46:555–562

    Article  Google Scholar 

  • Kuhn M (2000) Geoidbestimmung unter Verwendung verschiedener Dichtehypothesen. Dissertation. DGK, Reihe C, Nr. 520

    Google Scholar 

  • Kuhn M (2003) Geoid determination with density hypotheses from isostatic models and geological information. J Geod 77:50–65

    Article  Google Scholar 

  • Kuhn M, Featherstone WE, Kirby JF (2009) Complete spherical Bouguer gravity anomalies over Australia. Aust J Earth Sci 56:213–223

    Article  Google Scholar 

  • Li YC (1993) Optimized spectral geoid determination. UCGE Report No. 20050. Department of Geomatics Engineering, The University of Calgary, Calgary

    Google Scholar 

  • Li YC, Sideris MG (1994) Improved gravimetric terrain corrections. Geophys J Int 119(3):740–752

    Article  Google Scholar 

  • Makhloof AA (2007) The use of topographic-isostatic mass information in geodetic application. Disseratation D98, Institute of Geodesy and Geoinformation, Bonn

    Google Scholar 

  • Martinec Z (1998) Boundary value problems for gravimetric determination of a precise geoid. Lecture notes in Earth sciences, vol 73. Springer, Heidelberg/Berlin

    Google Scholar 

  • Martinec Z, Vaniček P (1994) The indirect effect of topography in the Stokes-Helmert technique for a spherical approximation of the geoid. Man Geod 19:213–219

    Google Scholar 

  • Martinec Z, Vaniček P, Mainville A, Vèronneau M (1994) Evaluation of topographical effects in precise geoids computation from densely sampled heights. J Geod 70:746–754

    Google Scholar 

  • Molodensky MS, Ermeev VF, Yurkina MI (1962) Methods for the study of the gravitational field of the Earth. Translated from Russian (1960), Israel program for scientific translations, Jerusalem

    Google Scholar 

  • Moritz H (1980) Advanced physical geodesy, 2nd edn. Wichmann, Karlsruhe

    Google Scholar 

  • Nagy D (1966) The prism method for terrain corrections using digital computers. Pure Appl Geophys 63:31–39

    Article  Google Scholar 

  • Nagy D, Papp G, Benedek J (2000) The gravitational potential and its derivatives for the Prism. J Geod 74(7–8):552–560. Erratum in J Geod 76(8):475–475

    Google Scholar 

  • Novák P, Vaniček P, Martinec P, Vèronneau M (2001) Effects of the spherical terrain on gravity and the geoid. J Geod 75:491–504

    Article  Google Scholar 

  • Nowell DAG (1999) Gravity terrain corrections – an overview. J Appl Geophys 42:117–134

    Article  Google Scholar 

  • Omang ODC, Forsberg R (2000) How to handle topography in practical geoid determination: three examples. J Geod 74:458–466

    Article  Google Scholar 

  • Pagiatakis SD, Frazer D, McEwen K, Goodacre AK, Vèronneau M (1999) Topographic mass density and gravimetric geoid modelling. Boll di Geofis Teor ed Appl 40:189–194

    Google Scholar 

  • Parker RL (1995) Improved Fourier terrain correction, Part I. Geophysics 60:1007–1017

    Article  Google Scholar 

  • Parker RL (1996) Improved Fourier terrain correction, Part II. Geophysics 61:365–372

    Article  Google Scholar 

  • Pavlis NK, Factor JK, Holmes SA (2007a) Terrain-related gravimetric quantities computed for the next EGM. In: Gravity field of the Earth, proceedings of the 1st international symposium of the international gravity field service (IGFS), Istanbul. Harita Dergisi 18(Special issue):31–323

    Google Scholar 

  • Pavlis NK, Holmes SA, Kenyon, SC, Factor JK (2008) Earth gravitational model to degree 2160 EGM2008. Paper presented to the European geosciences union general assembly, Vienna, Apr 2008

    Google Scholar 

  • Peng M (1994) Topographic effects on gravity and gradiometry by the 3D FFT and FHT methods. M.Sc., Thesis, Department of Geomatics Engineering, The University of Calgary, Calgary

    Google Scholar 

  • Peng M, Li YC, Sideris MG (1995) First results on the computation of terrain corrections by the 3D-FFT method. Man Geod 20(6):475–488

    Google Scholar 

  • Sansò F, Venuti G, Tziavos IN, Vergos GS, Grigoriadis GN (2008) Geoid and sea surface topography from satellite and ground data in the Mediterranean region. A review and new proposals. Bull Geod Geomat 3:156–201

    Google Scholar 

  • Schwarz K-P (1984) Data types and their spectral properties. In: Schwarz K-P (ed) Proceedings of the international summer school on local gravity field approximation, Beijing, pp 1–66

    Google Scholar 

  • Schwarz K-P, Sideris MG, Forsberg R (1990) The use of FFT tecniques in physical geodesy. Geophys J Int 100:485–514

    Article  Google Scholar 

  • Sideris MG (1984) Computation of gravimetric terrain corrections using fast Fourier transform techniques. UCGE Report 20007, Department of Geomatics Engineering, The University of Calgary, Calgary

    Google Scholar 

  • Sideris MG (1985) A fast Fourier transform method of computing terrain corrections. Man Geod 10:(1)66–73

    Google Scholar 

  • Sideris MG (1987a) Spectral methods for the numerical solution of Molodensky’s problem. UCSE Report 20024, Department of Geomatics Engineering, The University of Calgary, Calgary

    Google Scholar 

  • Sideris MG (1990) Rigorous gravimetric terrain modeling using Molodensky’s operator. Man Geod 15:97–106

    Google Scholar 

  • Sideris MG (1994) Regional geoid determination. In: Vaniček P, Christou NT (eds) Geoid and its geophysical Interpretations. CRC Press, Boca Raton, pp 77–94

    Google Scholar 

  • Sideris MG (2010) Geoid determination by FFT techniques. In: Lecture notes, international school for the determination and use of the geoid, Saint Petersburg, 28 June –2 July 2010

    Google Scholar 

  • Sjöberg LE (2005) A discussion of the approximations made in the practical implementation of the remove-compute-restore technique in regional geoid modeling. J Geodyn 78:645–653

    Google Scholar 

  • Smith DA (2000) The gravitational attraction of any polygonally shaped vertical prism with inclined top and bottom faces. J Geod 74(5):414–420

    Article  Google Scholar 

  • Smith WHF, Sandwell DT (1997) Global seafloor topography from satellite altimetry and ship depth soundings. Science 277:1957–1962

    Google Scholar 

  • Strykowski G, Boschetti F, Papp G (2005) Estimation of the mass density contrasts and the 3D geometrical shape of the source bodies, in the Yilgarn area, Eastern Goldfields, Western Australia. J Geodyn 39:444–460

    Article  Google Scholar 

  • Sun W (2002) A formula for gravimetric terrain corrections using powers of topographic height. J Geodesy 76(8):399–406

    Article  Google Scholar 

  • Sünkel H (1986) Global topographic isostatic models. In: Sünkel H (ed) Mathematical and numerical techniques in physical geodesy. Lecture notes in Earth sciences, vol 7. Springer, Berlin/Heidelberg/New York

    Google Scholar 

  • Tenzer R, Vaniček P, Novák P (2003) Far-zone contributions to topographical effects in the Stokes-Helmert method of the geoid determination. Stud Geophys Geod 47:467–480

    Article  Google Scholar 

  • Torge W (1989) Gravimetry. Walter de Gruyter, Berlin/New York

    Google Scholar 

  • Torge W (2001) Geodesy, 3rd edn. de Gruyter, Berlin/New York

    Google Scholar 

  • Tscherning CC (1991) The use of optimal estimation for gross-error detection in databases of spatially correlated data. Bull Inf 68:79–89

    Google Scholar 

  • Tscherning CC (2010) Geoid determination by 3D least squares collocqation. In: Lecture notes, international school for the determination and use of the geoid, Saint Petersburg, 28 June–2 July 2010

    Google Scholar 

  • Tscherning CC, Forsberg R, Knudsen P (1992) The GRAVSOFT package for geoid determination. In: Holota P, Vermeer M (eds) 1st continental workshop on the geoid in Europe, Prague, pp 327–334

    Google Scholar 

  • Tsoulis D (1999) Analytical and numerical methods in gravity field modelling of ideal and real masses. Dissertation, DGK, Reihe C, Nr. 510, Munchen

    Google Scholar 

  • Tsoulis D, Grigoriadis VN, Tziavos IN (2007) The utilization of global digital crustal databases in regional applications of forward gravity field modeling. In: Forsberg R, Kilio̧ǧlu A (eds) 1st international symposium of the international gravity field service “gravity field of the Earth”. General Command of Mapping 18(Special issue):348–353

    Google Scholar 

  • Tziavos IN (1992) Alternative numerical techniques for the efficient computation of terrain corrections and geoid undulations. In: 1st continental workshop on the geoid in Europe – “Towards a precise pan European reference geoid for the nineties”, Prague

    Google Scholar 

  • Tziavos IN (1993) Numerical considerations of FFT methods in gravity field modelling, Wissenschaftliche Arbeiten der Facbrichtung Vennessungswesen der Universitiit Hannover Nr. 188, Hannover

    Google Scholar 

  • Tziavos IN, Featherstone WE (2001) First results of using digital density data in gravimetric geoid computation in Australia. In: Sideris MG (ed) Proceedings of international association of geodesy symposia “gravity, geoid and geodynamics 2000”, vol 123. Springer, Berlin/Heidelberg, pp 335–340

    Google Scholar 

  • Tziavos IN, Sideris MG, Forsberg R, Schwarz K-P (1988) The effect of the terrain on airborne gravity and gradiometry. J Geophys Res 93(B8):9173–9186

    Article  Google Scholar 

  • Tziavos IN, Sideris MG, Schwarz K-P (1992) A study of the contribution of various gravimetric data types on the estimation of gravity field parameters in the mountains. J Geophys Res 97(B6):8843–8852

    Article  Google Scholar 

  • Tziavos IN, Sideris MG, Sünkel H (1996) The effect of surface density variation on terrain modeling – A case study in Austria. In: Tziavos IN, Vermeer M (eds) Techniques for local geoid determination, Report No. 96(2). Finish Geodetic Institute, Masala, pp 99–110

    Google Scholar 

  • Tziavos IN, Andritsanos VD (1998) Recent advances in terrain correction computations. In: Vermeer M, Adam J (eds) Proceedings of the 2nd continental workshop on the geoid in Europe, Budapest, 10–14 March 1998, pp 169–176

    Google Scholar 

  • Tziavos IN, Vergos GS, Grigoriadis VN (2010) Investigation of topographic reductions and aliasing effects on gravity and the geoid over Greece based on various digital terrain models. Surv Geophys 31:23–67

    Article  Google Scholar 

  • Vaniček P, Novák, Martinec Z (2001) Geoid, topography, and the Bouguer plate or shell. J Geod 75:210–215

    Article  Google Scholar 

  • Vaniček P, Tenzer R,, Sjöberg LE, Martinec Z, Featherstone WE (2004) New views of the spherical Bouguer gravity anomaly. Geophys J Int 159:460–472

    Article  Google Scholar 

  • Vergos GS, Tziavos IN, Andritsanos VD (2005a) On the determination of marine geoid models by least squares collocation and spectral methods using heterogeneous data. In: Sansò F (ed) Proceedings of international association of geodesy symposia “a window on the future of geodesy”, vol 128. Springer, Berlin/Heidelberg, pp 332–337

    Chapter  Google Scholar 

  • Vergos GS, Tziavos IN, Andritsanos VD (2005b) Gravity database generation and geoid model estimation using heterogeneous data. In: Jekeli C, Bastos L, Fernandes J (eds) Proceedings of international association of geodesy symposia “gravity geoid and space missions”, vol 129. Springer, Berling/Heidelberg, pp 155–160

    Chapter  Google Scholar 

  • Vermeer M, Forsberg R (1992) Filtered terrain effects: a frequency domain approach to terrain effect evaluation. Man Geod (17):215–226

    Google Scholar 

  • Wang YM, Rapp RH (1990) Terrain effects on geoid undulation computations. Man Geod 15:23–29

    Google Scholar 

  • Wichiencharoen C (1982) The indirect effects on the computation of geoids undulations. Reports of the department of geodesy science and survey, vol 336. Ohio State University, Columbus

    Google Scholar 

  • Wild-Pfeiffer F (2008) A comparison of different mass elements for use in gravity gradiometry. J Geod 83: 637–653

    Article  Google Scholar 

  • Yamaguchi Y, Kahle AB, Tsu H, Kawakami T, Pniel M (1998) Overview of advanced spaceborne thermal emission and reflection radiometer (ASTER). IEEE Tans Geosci Remote Sens 36(4):1062–1071

    Article  Google Scholar 

  • Zhu L, Jekeli C (2009) Gravity gradient modeling using gravity and DEM. J Geod 83:557–567

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Geodesy and Surveying, Aristotle University of Thessaloniki, Thessaloniki, Greece

    Ilias N. Tziavos

  2. Geomatics Engineering, University of Calgary, Calgary, Canada

    Michael G. Sideris

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  1. Ilias N. Tziavos
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  2. Michael G. Sideris
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Correspondence to Ilias N. Tziavos .

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  1. Fac. Ingneria di Como, Politecnico Milano, via Valleggio 11, Como, 22100, Italy

    Fernando Sansò

  2. Fac. Engineering, Dept. Geomatics Engineering, University of Calgary, University Drive NW., 2500, Calgary, T2N 1N4, Alberta, Canada

    Michael G. Sideris

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Tziavos, I.N., Sideris, M.G. (2013). Topographic Reductions in Gravity and Geoid Modeling. In: Sansò, F., Sideris, M. (eds) Geoid Determination. Lecture Notes in Earth System Sciences, vol 110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74700-0_8

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