Advertisement

Surveys in Geophysics

, Volume 40, Issue 1, pp 107–132 | Cite as

How to Calculate Bouguer Gravity Data in Planetary Studies

  • Robert TenzerEmail author
  • Ismael Foroughi
  • Christian Hirt
  • Pavel Novák
  • Martin Pitoňák
Article
  • 247 Downloads

Abstract

In terrestrial studies, Bouguer gravity data is routinely computed by adopting various numerical schemes, starting from the most basic concept of approximating the actual topography by an infinite Bouguer plate, through adding a planar terrain correction to account for a local/regional terrain geometry, to more advanced schemes that involve the computation of the topographic gravity correction by taking into consideration a gravitational contribution of the whole topography while adopting a spherical (or ellipsoidal) approximation. Moreover, the topographic density information has significantly improved the gravity forward modeling and interpretations, especially in polar regions (by accounting for a density contrast of polar glaciers) and in regions characterized by a complex geological structure. Whereas in geodetic studies (such as a gravimetric geoid modeling) only the gravitational contribution of topographic masses above the geoid is computed and subsequently removed from observed (free-air) gravity data, geophysical studies focusing on interpreting the Earth’s inner structure usually require the application of additional stripping gravity corrections that account for known anomalous density structures in order to reveal an unknown (and sought) density structure or density interface. In planetary studies, numerical schemes applied to compile Bouguer gravity maps might differ from terrestrial studies due to two reasons. While in terrestrial studies the topography is defined by physical heights above the geoid surface (i.e., the geoid-referenced topography), in planetary studies the topography is commonly described by geometric heights above the geometric reference surface (i.e., the geometric-referenced topography). Moreover, large parts of a planetary surface have negative heights. This obviously has implications on the computation of the topographic gravity correction and consequently Bouguer gravity data because in this case the application of this correction not only removes the gravitational contribution of a topographic mass surplus, but also compensates for a topographic mass deficit. In this study, we examine numerically possible options of computing the topographic gravity correction and consequently the Bouguer gravity data in planetary applications. In agreement with a theoretical definition of the Bouguer gravity correction, the Bouguer gravity maps compiled based on adopting the geoid-referenced topography are the most relevant. In this case, the application of the topographic gravity correction removes only the gravitational contribution of the topography. Alternative options based on using geometric heights, on the other hand, subtract an additional gravitational signal, spatially closely correlated with the geoidal undulations, that is often attributed to deep mantle density heterogeneities, mantle plumes or other phenomena that are not directly related to a topographic density distribution.

Keywords

Bouguer gravity Correction Moon Telluric planets Topography 

Notes

Acknowledgements

This research is conducted under the HK science Project 1-ZE8F: Remote-sensing data for studding the Earth’s and planetary inner structure. Prof. Pavel Novák and Dr. Martin Pitoňák are supported by the Project 18-06943S of the Czech Science Foundation.

References

  1. Airy GB (1855) On the computations of the effect of the attraction of the mountain masses as disturbing the apparent astronomical latitude of stations in geodetic surveys. Trans R Soc Lond 145(B):101–104Google Scholar
  2. Archinal BA, A’Hearn MF, Conrad A, Consolmagno GJ, Courtin R, Fukushima T, Hestroffer D, Hilton JL, Krasinsky GA, Neumann G, Oberst J, Seidelmann PK, Stooke P, Tholen DJ, Thomas PC, Williams IP (2011) Report of the IAU/IAG Working Group on cartographic coordinates and rotational elements. Celest Mech Dyn Astron 109(2):101–135CrossRefGoogle Scholar
  3. Ardalan AA, Karimi R (2014) Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon. Celest Mech Dyn Astron 118:75–88CrossRefGoogle Scholar
  4. Balmino G, Vales N, Bonvalot S, Briais A (2012) Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. J Geod 86(7):499–520CrossRefGoogle Scholar
  5. 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 7:499–510CrossRefGoogle Scholar
  6. Barker MK, Mazarico E, Neumann GA, Zuber MT, Haruyama J, Smith DE (2016) A new lunar digital elevation model from the Lunar Orbiter Laser Altimeter and SELENE Terrain Camera. Icarus 2723(15):346–355CrossRefGoogle Scholar
  7. Basilevsky AT, Head JW (2002) Venus: timing and rates of geologic activity. Geology 30(11):1015–1018CrossRefGoogle Scholar
  8. 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: SRTM30_PLUS. Mar Geod 32(4):355–371CrossRefGoogle Scholar
  9. Becker KJ, Robinson MS, Becker TL, Weller LA, Edmundson KL, Neumann GA, Perry ME, Sean C (2016) First global digital elevation model of Mercury. In: 47th Lunar and Planetary Science Conference, LPS 47, Abstract 2959Google Scholar
  10. Bjerhammar A (1963) A note on gravity reduction to a spherical surface. Tellus 15(3):319–320CrossRefGoogle Scholar
  11. Claessens SJ, Hirt C (2013) Ellipsoidal topographic potential—new solutions for spectral forward gravity modelling of topography with respect to a reference ellipsoid. J Geophys Res Solid Earth 118(11):5991–6002CrossRefGoogle Scholar
  12. Erwan M, Genova A, Goossens S, Lemoine FG, Neumann GA, Zuber MT, Smith DE, Solomon SC (2014) The gravity field, orientation, and ephemeris of Mercury from MESSENGER observations after three years in orbit. J Geophys Res Planets 119(12):2417–2436CrossRefGoogle Scholar
  13. Förste C, Bruinsma SL, Abrikosov O, Lemoine JM, Marty JC, Flechtner F, Balmino G, Barthelmes F, 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 Tapley BD, Bettadpur S, Watkins MGoogle Scholar
  14. 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 7:375–393CrossRefGoogle Scholar
  15. Goossens S, Sabaka TJ, Genova A, Mazarico E, Nicholas JB, Neumann GA (2017) Evidence for a low bulk crustal density for Mars from gravity and topography. Geophys Res Lett 44(15):7686–7694CrossRefGoogle Scholar
  16. Hammer S (1939) Terrain corrections for gravimeter stations. Geophysics 4:184–194CrossRefGoogle Scholar
  17. Hayford JF, Bowie W (1912) The effect of topography and isostatic compensation upon the intensity of gravity. US Coast Geod Surv 10, Special Publication, 132 ppGoogle Scholar
  18. Heiskanen WH, Moritz H (1967) Physical geodesy. WH Freeman and Co, San FranciscoGoogle Scholar
  19. Hinze WJ (2003) Bouguer reduction density, why 2.67? Geophysics 68(5):1559CrossRefGoogle Scholar
  20. Hirt C, Rexer M (2015) Earth 2014: 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 Geoinform 39:103–112CrossRefGoogle Scholar
  21. Hirt C, Reußner E, Rexer M, Kuhn M (2016) Topographic gravity modelling for global Bouguer maps to degree 2,160: validation of spectral and spatial domain forward modelling techniques at the 10 microgal level. J Geophys Res Solid Earth 121(9):6846–6862CrossRefGoogle Scholar
  22. Huang Q, Wieczorek MA (2012) Density and porosity of the lunar crust from gravity and topography. J Geophys Res Planets 117:E05003CrossRefGoogle Scholar
  23. Ivanov MA, Head JW (2015) The history of tectonism on Venus: a stratigraphic analysis. Planet Space Sci 113–114:10–32CrossRefGoogle Scholar
  24. Jarvis A, Reuter HI, Nelson A, Guevara E (2008) Hole-filled SRTM for the globe Version 4, available from the CGIAR-SXI SRTM 90 m database. http://srtm.csi.cgiar.org. Accessed 17 May 2018
  25. Johnson CL, Phillips RJ (2005) Evolution of the Tharsis region of Mars: insights from magnetic field observations. Earth Planet Sci Lett 230:241–254CrossRefGoogle Scholar
  26. Karimi R, Ardalan AA, Farahani SV (2016) Reference surface of the planet Mercury from MESSENGER. Icarus 264:239–245CrossRefGoogle Scholar
  27. Konopliv AS, Banerdt WB, Sjogren WL (1999) Venus gravity: 180th degree and order model. Icarus 139:3–18CrossRefGoogle Scholar
  28. Konopliv AS, Park RS, Folkner WM (2016) An improved JPL Mars gravity field and orientation from Mars orbiter and lander tracking data. Icarus 274:253–260CrossRefGoogle Scholar
  29. Laske G, Masters G, Ma Z, Pasyanos M (2013) Update on CRUST1.0—a 1-degree global model of earth’s crust. Geophys Res Abstr 15. Abstract EGU2013-2658Google Scholar
  30. Lemoine FG, Goossens S, Sabaka TJ, Nicholas JB, Mazarico E, Rowlands DD, Loomis BD, Chinn DS, Neumann GA, Smith DE, Zuber MT (2014) GRGM900C: a degree 900 lunar gravity model from GRAIL primary and extended mission data. Geophys Res Lett 41(10):3382–3389CrossRefGoogle Scholar
  31. McKenzie D (1994) The relationship between topography and gravity on Earth and Venus. Icarus 112(1):55–88CrossRefGoogle Scholar
  32. McNamee JB, Borderies NJ, Sjogren WL (1993) Venus: global gravity and topography. J Geophys Res Planets 98(E5):9113–9128CrossRefGoogle Scholar
  33. Melosh HJ, Freed AM, Johnson BC, Blair DM, Andrews-Hanna JC, Neumann GA, Phillips RJ, Smith DE, Solomon SC, Wieczorek MA, Zuber MT (2013) The origin of Lunar mascon basins. Science 340(6140):1552–1555CrossRefGoogle Scholar
  34. Neumann GA, Zuber MT, Wieczorek MA, McGovern PJ, Lemoine FG, Smith DE (2004) Crustal structure of Mars from gravity and topography. J Geophys Res 109:E08002CrossRefGoogle Scholar
  35. Nimmo F (2002) Admittance estimates of mean crustal thickness and density at the Martian hemispheric dichotomy. J Geophys Res 107(E11):5117CrossRefGoogle Scholar
  36. Nimmo F, Stevenson DJ (2001) Estimates of Martian crustal thickness from viscous relaxation of topography. J Geophys Res 106:5085–5098CrossRefGoogle Scholar
  37. Novák P, Vaníček P, Martinec Z, Véronneau M (2001) The effect of distant terrain on gravity and the geoid. J Geod 75(9–10):491–504Google Scholar
  38. Padovan S, Wieczorek MA, Margot J-L, Solomon SC (2014) Thickness of the crust of Mercury from geoid-to-topography ratios. EPSC Abstracts 9. EPSC2014-738, European Planetary Science Congress 2014Google Scholar
  39. Phillips RJ, Hansen VL (1994) Tectonic and magmatic evolution of Venus. Annu Rev Earth Planet Sci 22(1):597–656CrossRefGoogle Scholar
  40. Phillips RJ, Lambeck K (1980) Gravity fields of the terrestrial planets: long-wavelength anomalies and tectonics. Rev Geophys 18(1):27–76CrossRefGoogle Scholar
  41. Phillips RJ, Saunders RS (1975) The isostatic state of Martian topography. J Geophys Res 80:2893–2898CrossRefGoogle Scholar
  42. Pizzetti P (1911) Sopra il calcolo teorico delle deviazioni del geoide dall` ellissoide. Atti R Accad Sci Torino 46:331Google Scholar
  43. Rummel R (2005) Gravity and topography of Moon and planets. Earth Moon Planets 94:103–111CrossRefGoogle Scholar
  44. Sebera J, Haagmans R, Floberghagen R, Ebbing J (2018) Gravity spectra from the density distribution of Earth’s uppermost 435 km. Sur Geophys 9(2):227–244CrossRefGoogle Scholar
  45. Sjöberg LE (1997) The topographic bias by analytical continuation in physical geodesy. J Geod 81:345–350CrossRefGoogle Scholar
  46. Sjöberg LE (2013) On the isotactic gravity anomaly and disturbance and their applications to Vening Meinesz-Moritz gravimetric inverse problem. Geophys J Int 193(3):1277–1282CrossRefGoogle Scholar
  47. Smith DE, Zuber MT (1996) The shape of Mars and the topographic signature of the hemispheric dichotomy. Science 271:184–188CrossRefGoogle Scholar
  48. Smith DE, Zuber MT, Solomon SC, Phillips RJ, Head JW, Garvin JB, Banerdt WB, Muhleman DO, Pettengill GH, Neumann GA, Lemoine FG, Abshire JB, Aharonson OC, Brown D, Hauck SA, Ivanov AB, McGovern PJ, Zwally HJ, Duxbury TC (1999) The global topography of Mars and implications for surface evolution. Science 284:1495–1503CrossRefGoogle Scholar
  49. Smith DE, Zuber MT, Phillips RJ et al (2012) Gravity field and internal structure of Mercury from MESSENGER. Science 336:214–217CrossRefGoogle Scholar
  50. Somigliana C (1929) Teoria Generale del Campo Gravitazionale dell’Ellisoide di Rotazione. Memoire della Società Astronomica Italiana, IV, MilanoGoogle Scholar
  51. Stofan ER, Smrekar SE (2005) Large topographic rises, coronae, large flow fields, and large volcanoes on Venus: evidence for mantle plumes? Geol Soc Am Spec Papers 388:841–861Google Scholar
  52. Tenzer R, Bagherbandi M (2012) Reformulation of the Vening-Meinesz Moritz inverse problem of isostasy for isostatic gravity disturbances. Int J Geosci 3(5):918–929CrossRefGoogle Scholar
  53. Tenzer R, Vaníček P, Santos M, Featherstone WE, Kuhn M (2005) The rigorous determination of orthometric heights. J Geod 79(1–3):82–92CrossRefGoogle Scholar
  54. Tenzer R, Moore P, Novák P, Kuhn M, Vaníček P (2006) Explicit formula for the geoid-to-quasigeoid separation. Stud Geophys Geodaet 50:607–618CrossRefGoogle Scholar
  55. Tenzer R, Novák P, Gladkikh V (2011) On the accuracy of the bathymetry-generated gravitational field quantities for a depth-dependent seawater density distribution. Stud Geophys Geodaet 55(4):609–626CrossRefGoogle Scholar
  56. Tenzer R, Novák P, Gladkikh V (2012a) The bathymetric stripping corrections to gravity field quantities for a depth-dependent model of the seawater density. Mar Geod 35:198–220CrossRefGoogle Scholar
  57. Tenzer R, Novák P, Vajda P, Gladkikh V, Hamayun (2012b) Spectral harmonic analysis and synthesis of Earth’s crust gravity field. Comput Geosci 16(1):193–207CrossRefGoogle Scholar
  58. Tenzer R, Chen W, Tsoulis D, Bagherbandi M, Sjöberg LE, Novák P, Jin S (2015a) Analysis of the refined CRUST1.0 crustal model and its gravity field. Surv Geophys 36(1):139–165CrossRefGoogle Scholar
  59. Tenzer R, Eshagh M, Jin S (2015b) Martian sub-crustal stress from gravity and topographic models. Earth Planet Sci Lett 425:84–92CrossRefGoogle Scholar
  60. Tenzer R, Foroughi I, Pitoňák M, Šprlák M (2017) Effect of the Earth’s inner structure on the gravity in definitions of height systems. Geophys J Int 209(1):297–316Google Scholar
  61. Tenzer R, Foroughi I, Sjöberg LE, Bagherbandi M, Hirt Ch, Pitoňák M (2018) Definition of physical height systems for telluric planets and moons. Surv Geophys 39(1):23–56CrossRefGoogle Scholar
  62. Vajda P, Vaníček P, Novák P, Tenzer R, Ellmann A (2007) Secondary indirect effects in gravity anomaly data inversion or interpretation. J Geophys Res Solid Earth 112:B06411CrossRefGoogle Scholar
  63. Vajda P, Ellmann A, Meurers B, Vanícek P, Novák P, Tenzer R (2008a) Global ellipsoid-referenced topographic, bathymetric and stripping corrections to gravity disturbance. Stud Geophys Geodaet 52:19–34CrossRefGoogle Scholar
  64. Vajda P, Ellmann A, Meurers B, Vanícek P, Novák P, Tenzer R (2008b) Gravity disturbances in regions of negative heights: a reference quasi-ellipsoid approach. Stud Geophys Geodaet 52:35–52CrossRefGoogle Scholar
  65. Vaníček P, Tenzer R, Sjöberg LE, Martinec Z, Featherstone WE (2005) New views of the spherical Bouguer gravity anomaly. Geophys J Int 159:460–472CrossRefGoogle Scholar
  66. Wieczorek MA (2007) The gravity and topography of the terrestrial planets. In: Schubert G (ed) Treatise on Geophysics 10. Elsevier, Oxford, pp 165–206CrossRefGoogle Scholar
  67. Wieczorek MA (2015) Gravity and topography of the terrestrial planets. Treatise Geophys 10:153–193CrossRefGoogle Scholar
  68. Wieczorek MA, Zuber MT (2004) The thickness of the Martian crust: improved constraints from geoid-to-topography ratios. J Geophys Res 109(E1):E01009CrossRefGoogle Scholar
  69. Wieczorek MA, Neumann GA, Nimmo F, Kiefer WS, Taylor GJ, Melosh HJ, Phillips RJ, Solomon SC, Andrews-Hanna JC, Asmar SW, Konopliv AS, Lemoine FG, Smith DE, Watkins MM, Williams JG, Zuber MT (2013) The crust of the Moon as seen by GRAIL. Science 339:671–675CrossRefGoogle Scholar
  70. Zuber MT (2001) The crust and mantle of Mars. Nature 412(12):220–227CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  • Robert Tenzer
    • 1
    Email author
  • Ismael Foroughi
    • 2
  • Christian Hirt
    • 3
  • Pavel Novák
    • 4
  • Martin Pitoňák
    • 4
  1. 1.Department of Land Surveying and Geo-InformaticsHong Kong Polytechnic UniversityKowloonHong Kong
  2. 2.Department of Geodesy and GeomaticsUniversity of New BrunswickFrederictonCanada
  3. 3.Institute for Astronomical and Physical Geodesy and Institute for Advanced Study, TUMunichGermany
  4. 4.New Technologies for the Information Society (NTIS), Faculty of Applied SciencesUniversity of West BohemiaPlzeňCzech Republic

Personalised recommendations