Contribution of mass density heterogeneities to the quasigeoid-to-geoid separation

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• 作者：Robert Tenzer ; Christian Hirt ; Pavel Novák ; Martin Pitoňák…
• 关键词：Density ; Geoid ; to ; quasigeoid separation ; Gravity ; Spherical harmonics ; Topography
• 刊名：Journal of Geodesy
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：90
• 期：1
• 页码：65-80
• 全文大小：5,960 KB
• 参考文献：Allister NA, Featherstone WE (2001) Estimation of Helmert orthometric heights using digital barcode levelling, observed gravity and topographic mass-density data over part of Darling Scarp, Western Australia. Geom Res Aust 75:25–52
  Andersen OB (2010) The DTU10 gravity field and Mean sea surface, (2010) second international symposium of the gravity field of the Earth (IGFS2). Fairbanks, Alaska
  Ågren J (2004) The analytical continuation bias in geoid determination using potential coefficients and terrestrial gravity data. J Geod 78:314–332CrossRef
  Bagherbandi M, Tenzer R (2013) Geoid-to-quasigeoid separation computed using the GRACE/GOCE global geopotential model GOCO02S—a case study of Himalayas, Tibet and central Siberia. Terr Atmos Ocean Sci 24(1):59–68CrossRef
  Bamber JL, Griggs JA, Hurkmans RTWL, Dowdeswell JA, Gogineni SP, Howat I, Mouginot J, Paden J, Palmer S, Rignot E, Steinhage D (2013) A new bed elevation dataset for Greenland. Cryosphere 7:499–510CrossRef
  Becker JJ, Sandwell DT, Smith WHF, Braud J, Binder B, Depner J, Fabre D, Factor J, Ingalls S, Kim S-H, Ladner R, Marks K, Nelson S, Pharaoh A, Trimmer R, Von Rosenberg J, Wallace G, Weatherall P (2009) Global bathymetry and elevation data at 30 arc seconds resolution: \({\rm SRTM30}\_{\rm PLUS}\) . Mar Geod 32(4):355–371CrossRef
  Bruns H (1878) Die Figur der Erde. Publ Preuss Geod Inst, Berlin
  Cutnell JD, Kenneth WJ (1995) Physics, 3rd edn. Wiley, New York
  Flury J, Rummel R (2009) On the geoid-quasigeoid separation in mountain areas. J Geod 83:829–847CrossRef
  Förste C, Bruinsma SL, Abrikosov O, Lemoine J-M, Schaller T, Götze H-J, Ebbing J, Marty J-C, Flechtner F, Balmino G, 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; presented at the 5th GOCE user workshop. Paris, pp 25–28
  Fretwell P, Pritchard HD, Vaughan DG, Bamber JL, Barrand NE, Bell R, Bianchi C, Bingham RG, Blankenship DD, Casassa G, Catania G, Callens D, Conway H, Cook AJ, Corr HFJ, Damaske D, Damm V, Ferraccioli F, Forsberg R, Fujita S, Gim Y, Gogineni P, Griggs JA, Hindmarsh RCA, Holmlund P, Holt JW, Jacobel RW, Jenkins A, Jokat W, Jordan T, King EC, Kohler J, Krabill W, Riger-Kusk M, Langley KA, Leitchenkov G, Leuschen C, Luyendyk BP, Matsuoka K, Mouginot J, Nitsche FO, Nogi Y, Nost OA, Popov SV, Rignot E, Rippin DM, Rivera A, Roberts J, Ross N, Siegert MJ, Smith AM, Steinhage D, Studinger M, Sun B, Tinto BK, Welch BC, Wilson D, Young DA, Xiangbin C, Zirizzotti A (2013) Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. Cryosphere 7:375–393CrossRef
  Heiskanen WH, Moritz H (1967) Physical geodesy. WH Freeman and Co, San Francisco
  Helmert FR (1884) Die mathematischen und physikalischen Theorien der höheren Geodäsie, vol 2. Teubner, Leipzig
  Helmert FR (1890) Die Schwerkraft im Hochgebirge, insbesondere in den Tyroler Alpen. Veröff Königl Preuss Geod Inst, No 1, Berlin
  Hinze WJ (2003) Bouguer reduction density, why 2.67? Geophysics 68(5):1559–1560CrossRef
  Hirt C (2012) Efficient and accurate high-degree spherical harmonic synthesis of gravity field functionals at the earth’s surface using the gradient approach. J Geod 86(9):729–744CrossRef
  Hirt C, Kuhn M (2012) Evaluation of high-degree series expansions of the topographic potential to higher-order powers. J Geophys Res 117:B12407CrossRef
  Hirt C, Rexer M (2015) Earth2014: 1 arc-min shape, topography, bedrock and ice-sheet models—available as gridded data and degree-10,800 spherical harmonics. Int J Appl Earth Obs Geoinf 39:103–112. doi:10.​1016/​j.​jag.​2015.​03.​001
  Hofmann-Wellenhof B, Moritz H (2005) Physical geodesy, 2nd edn. Springer, Berlin
  Jarvis A, Reuter HI, Nelson A, Guevara E (2008) Hole-filled SRTM for the globe Version 4, available from the CGIAR-SXI SRTM 90m database. http://​srtm.​csi.​cgiar.​org
  Laske G, Masters G, Ma Z, Pasyanos M (2013) Update on CRUST1.0—a 1-degree global model of earth’s crust. Geophys Res Abst 15. Abstract EGU2013-2658
  Ledersteger K (1968) Astronomische und Physikalische Geodäsie (Erdmessung). In: Jordan W, Eggert E, Kneissl M (eds) Handbuch der Vermessungskunde, vol V. Metzler, Stuttgart
  Mader K (1954) Die orthometrische Schwerekorrektion des Präzisions-Nivellements in den Hohen Tauern. Österreichische Zeitschrift für Vermessungswesen, Sonderheft 15
  Marti U (2005) Comparison of high precision geoid models in Switzerland. In: Tregonig P, Rizos C (eds) Dynamic planet. Springer, Berlin
  Martinec Z (1998) Boundary value problems for gravimetric determination of a precise geoid. Lecture notes in earth sciences, Vol 73. Springer, Berlin
  Martinec Z, Vaníček P, Mainville A, Veronneau M (1995) The effect of lake water on geoidal height. Manuscr Geod 20:193–203
  Molodensky MS (1945) Fundamental problems of geodetic gravimetry (in Russian). TRUDY Ts NIIGAIK, 42, Geodezizdat, Moscow
  Molodensky MS (1948) External gravity field and the shape of the Earth surface. Izv CCCP, Moscow (in Russian)
  Molodensky MS, Yeremeev VF, Yurkina MI (1960) Methods for study of the external gravitational field and figure of the earth. TRUDY Ts NIIGAiK, Vol. 131, Geodezizdat, Moscow. English translation: Israel program for scientific translation, Jerusalem 1962
  Moritz H (2000) Geodetic reference system 1980. J Geod 74:128–162CrossRef
  Niethammer T (1932) Nivellement und Schwere als Mittel zur Berechnung wahrer Meereshöhen. Schweizerische Geodätische Kommission
  Niethammer T (1939) Das astronomische Nivellement im Meridian des St Gotthard, Part II, Die berechneten Geoiderhebungen und der Verlauf des Geoidschnittes. Astronomisch-Geodätische Arbeiten in der Schweiz, Vol 20, Swiss Geodetic Commission
  Santos MC, Vaníček P, Featherstone WE, Kingdon R, Ellmann A, Martin B-A, Kuhn M, Tenzer R (2006) The relation between rigorous and Helmert’s definitions of orthometric heights. J Geod 80:691–704
  Sjöberg LE (1995) On the quasigeoid to geoid separation. Manuscr Geod 20(3):182–192
  Sjöberg LE (2006) A refined conversion from normal height to orthometric height. Stud Geophys Geod 50:595–606CrossRef
  Sjöberg LE (2007) The topographical bias by analytical continuation in physical geodesy. J Geod 81:345–350CrossRef
  Sjöberg LE (2008) Answers to the comments by M Vermeer on LE Sjöberg (2007). The topographic bias by analytical continuation in physical geodesy. J Geod 81:345–350. J Geod 82(7):451–452
  Sjöberg LE (2010) A strict formula for geoid-to-quasigeoid separation. J Geod 84:699–702
  Sjöberg LE (2012) The geoid-to-quasigeoid difference using an arbitrary gravity reduction model. Stud Geophys Geod 56:929–933CrossRef
  Sjöberg LE, Bagherbandi M (2012) Quasigeoid-to-geoid determination by EGM08. Earth Sci Inform 5:87–91CrossRef
  Sünkel H, Bartelme N, Fuchs H, Hanafy M, Schuh WD, Wieser M (1987) The gravity field in Austria. In: Austrian geodetic commission (ed) The gravity field in Austria. Geodätische Arbeiten Österreichs für die Intenationale Erdmessung, Neue Folge, Vol IV, pp 47–75
  Tenzer R, Vaníček P (2003) Correction to Helmert’s orthometric height due to actual lateral variation of topographical density. Braz J Cartogr Rev Brasil Cartogr 55(02):44–47
  Tenzer R (2004) Discussion of mean gravity along the plumbline. Stud Geoph Geod 48:309–330CrossRef
  Tenzer R, Vaníček P, Santos M, Featherstone WE, Kuhn M (2005) The rigorous determination of orthometric heights. J Geod 79(1–3):82–92CrossRef
  Tenzer R, Moore P, Novák P, Kuhn M, Vaníček P (2006) Explicit formula for the geoid-to-quasigeoid separation. Stud Geoph Geod 50:607–618CrossRef
  Tenzer R, Abdalla A, Vajda P, Hamayun, (2010) The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast. Contrib Geophys Geod 40(3):207–223
  Tenzer R, Sirguey P, Rattenbury M, Nicolson J (2011) A digital bedrock density map of New Zealand. Comput Geosci 37(8):1181–1191CrossRef
  Tenzer R, Novák P, Vajda P, Gladkikh V, Hamayun (2012a) Spectral harmonic analysis and synthesis of earth’s crust gravity field. Comput Geosci 16(1):193–207
  Tenzer R, Gladkikh V, Vajda P, Novák P (2012b) Spatial and spectral analysis of refined gravity data for modelling the crust-mantle interface and mantle-lithosphere structure. Surv Geophys 33(5):817–839CrossRef
  Tenzer R, Hirt Ch, Claessens S, Novák P (2015a) Spatial and spectral representations of the geoid-to-quasigeoid correction. Surv Geophys. doi:10.​1007/​s10712-015-9337-z
  Tenzer R, Chen W, Tsoulis D, Bagherbandi M, Sjöberg LE, Novák P, Jin S (2015b) Analysis of the refined CRUST1.0 crustal model and its gravity field. Surv Geophys 36(1):139–165CrossRef
  Tziavos IN, Featherstone WE (2001) First results of using digital density data in gravimetric geoid computation in Australia. In: Sideris MG (ed) Gravity, geoid and geodynamics 2000. Springer, Berlin, pp 335–340CrossRef
  van den Broeke M (2008) Depth and density of the Antarctic firn layer. Arct Antarct Alp Res 40(2):432–438CrossRef
  Vaníček P, Kleusberg A, Martinec Z, Sun W, Ong P, Najafi M, Vajda P, Harrie L, Tomášek P, Horst B (1995) Compilation of a precise regional geoid. Final report on research done for the geodetic survey division, Fredericton
  Vaníček P, Tenzer R, Sjöberg LE, Martinec Z, Featherstone WE (2005) New views of the spherical Bouguer gravity anomaly. Geophys J Int 159:460–472CrossRef
  Vermeer M (2008) Comment on Sjöberg (2006) The topographic bias by analytical continuation in physical geodesy. J Geod 81(5):345–350. J Geod 82:445–450
  Wirth B (1990) Höhensysteme, Schwerepotentiale und Niveauflächen. Geodätisch-Geophysikalische Arbeiten in der Schweiz, Vol 42, Swiss Geodetic Commission
  
• 作者单位：Robert Tenzer (1) (2)
  Christian Hirt (3) (4)
  Pavel Novák (1)
  Martin Pitoňák (1)
  Michal Šprlák (1)
  
  1. NTIS - New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Plzeň, Czech Republic
  2. The Key Laboratory of Geospace Environment and Geodesy, School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, 430079, China
  3. Western Australian Geodesy Group, Department of Spatial Sciences, The Institute for Geoscience Research, Curtin University, Perth, Australia
  4. Institute for Advanced Study, Institute for Astronomical and Physical Geodesy, TU Munich, Germany
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geophysics and Geodesy
  Mathematical Applications in Geosciences
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1394

文摘

The geoid-to-quasigeoid separation is often computed only approximately as a function of the simple planar Bouguer gravity anomaly and the height of the computation point while disregarding the contributions of terrain geometry and anomalous topographic density as well as the sub-geoid masses. In this study we demonstrate that these contributions are significant and, therefore, should be taken into consideration when investigating the relation between the normal and orthometric heights particularly in the mountainous, polar and geologically complex regions. These contributions are evaluated by applying the spectral expressions for gravimetric forward modelling and using the EIGEN-6C4 gravity model, the Earth2014 datasets of terrain, ice thickness and inland bathymetry and the CRUST1.0 sediment and (consolidated) crustal density data. Since the global crustal density models currently available (e.g. CRUST1.0) have a limited accuracy and resolution, the comparison of individual density contributions is—for consistency—realized with a limited spectral resolution up to a spherical harmonic degree 360 (or 180). The results reveal that the topographic contribution globally varies between \(-\)0.33 and 0.57 m, with maxima in Himalaya and Tibet. The contribution of ice considerably modifies the geoid-to-quasigeoid separation over large parts of Antarctica and Greenland, where it reaches \(\sim \)0.2 m. The contributions of sediments and bedrock are less pronounced, with the values typically varying only within a few centimetres. These results, however, have still possibly large uncertainties due to the lack of information on the actual sediment and bedrock density. The contribution of lakes is mostly negligible; its maxima over the Laurentian Great Lakes and the Baikal Lake reach only several millimetres. The contribution of the sub-geoid masses is significant. It is everywhere negative and reaches extreme values of \(-\)4.43 m. According to our estimates, the geoid-to-quasigeoid separation globally varies within \(-\)4.19 and 0.26 m while the corresponding values computed according to a classical definition are only negative and reach extreme values of \(-\)3.5 m. A comparison of these results reveals that inaccuracies caused by disregarding the terrain geometry and mass density heterogeneities distributed within the topography and below the geoid surface can reach \(\pm \)2 m or more in the mountainous regions. Keywords Density Geoid-to-quasigeoid separation Gravity Spherical harmonics Topography