Abstract
The Earth topographic masses are compensated by an isostatic adjustment. According to the isostatic hypothesis a mountain is compensated by mass deficiency beneath it, where the crust is floating on the viscous mantle. For study of the impact of the compensating mass on the topographic mass a crustal thickness (Moho boundary) model is needed. A new gravimetric-isostatic model to estimate the Moho depth, Vening Meinesz-Moritz model, and two well-known Moho models (CRUST2.0 and Airy-Heiskanen) are used in this study. All topographic masses cannot be compensated by simple isostatic assumption then other compensation mechanism should be considered. In fact small topographic masses can be supported by elasticity of the larger masses and deeper Earth’s layers. We discuss this issue applying spatial and spectral analyses in this study. Here we are going to investigate influence of the crustal thickness and its density in compensating the topographic potential. This study shows that the compensating potential is larger than the topographic potential in low-frequencies vs. in high-frequencies which are smaller. The study also illustrates that the Vening Meinesz-Moritz model compensates the topographic potential better than other models, which is more suitable for interpolation of the gravity field in comparison with two other models. In this study, two methods are presented to determine the percentage of the compensation of the topographic potential by the isostatic model. Numerical studies show that about 75% and 57% of the topographic potentials are compensated by the potential beneath it in Iran and Tibet. In addition, correlation analysis shows that there is linear relation between the topographic above the sea level and underlying topographic masses in the low-frequencies in the crustal models. Our investigation shows that about 580±7.4 metre (in average) of the topographic heights are not compensated by variable the crustal root and density.
Similar content being viewed by others
References
Airy G B 1855: Trans. Roy. Soc. London, Ser. B, 145, 101–104.
Bagherbandi M 2011: An Isostatic Earth Crustal Model and Its Applications. PhD Thesis, KTH Royal Institute of Technology, Stockholm, Sweden
Bagherbandi M, Sjöberg L 2011: Stud. Geophys. Geod., 55, 641–666.
Balmino G, Lambeck K, Kaula W 1973: J. Geophys. Res., 78, 478–521.
Bassin C, Laske G, Masters T G 2000: EOS Trans AGU, 81, F897.
Bjerhammer A, Stocki S, Svensson L 1980: A geodetic determination of viscosity. Report, KTH Royal Institute of Technology, Stockholm, Sweden
Dziewonski A M, Anderson D L 1981: Phys. Earth Planet. Inter., 25, 297–356.
Fowler C M R 2001: The Solid Earth. An Introduction to Global Geophysics. 2nd Edition, Royal Holloway, University of London
Göttl F, Rummel R 2009: Pure Applied Geophysics, Vol. 166, 1247–1260.
Haagmans R 2000: J. Geod., 74, 503–511.
Heiskanen W A, Moritz H 1967: Physical geodesy. W H Freeman and Co., San Francisco and London
Heiskanen W A, Vening Meinesz F A 1958: The Earth and its Gravity Field. McGraw-Hill Book Company, Inc.
Hurtig E, Cermak V, Haenel R, Zui V eds 1992: Geothermal Atlas of Europe. 1st edition, Hermann Haack Verlagsgesellschaft, Gotha
Kaban M K, Schwintzer P, Tikhotsky S A 1999: Geophys. J. Int., 136, 519–536.
Kaban M K, Schwintzer P, Artemieva I M, Mooney W D 2003: Earth Planet Sci. Lett., 209, 53–69.
Kaban M K, Schwintzer P, Reigber Ch 2004: J. Geod., 78, 368–385.
Kuhn M 2003: J. Geod., 77, 50–65.
Kuhn M, Featherstone W E 2005: In: A Window on the Future of Geodesy. F Sansò ed., Springer, Berlin, Heidelberg, New York, 350–355.
Lambeck K 1976: J. Geophys. Res., 81, 6333–6340.
Martinec Z 1993: Surveys Geophys., 14, 525–535.
Martinec Z 1994: Geoph. J. Inter., 117, 545–554.
Martinec Z 1998: Boundary-value problems for gravimetric determination of a precise geoid. Lecture notes in Earth Sciences, No. 73, Springer
Moritz H 1990: The figure of the Earth. H Wichmann, Karlsruhe
Mooney W D, Laske G, Masters T G 1998: J. Geophys. Res., 103, 727–747.
Parker R L 1972: Geophys. J. R. Astr. Soc, 31, 447–455.
Pavlis N K, Rapp R H 1990: Geophys. J. Inter., 100, 369–378.
Pavlis N, Factor K, Holmes Simon A 2007: Terrain-Related Gravimetric Quantities Computed for the Next EGM. Presented at the 1st International symposium of the International gravity service 2006, Istanbul, Turkey
Pavlis N, Holmes S A, Kenyon S C, Factor J K 2008: An Earth Gravitational model to degree 2160: EGM08. Presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria
Pratt J H 1855: Trans. Roy. Soc. London, Ser. B, Vol. 145, 53–100.
Rapp R H 1982: Bull. Geod., 56, 84–94.
Reed G B 1973: Application of kinematical geodesy for determining the shorts wavelength component of the gravity field by satellite gradiometry. Ohio state University, Dept. of Geod. Science, Rep. No. 201, Columbus, Ohio
Rummel R H, Rapp H, Sünkel H, Tscherning C C 1988: Comparison of global topographic/isostatic models to the Earth’s observed gravity field. Dept. of Geodetic Science and Suveying, Report No. 388, The Ohio State University, Columbus, Ohio
Sansò F, Barzaghi R, Tscherning C C 1986: Geophys. J. R. Astr. Soc., 87, 123–141.
Sjöberg L E 1998a: J. Geod., 72, 654–662.
Sjöberg L E 1998b: J. Geodyn., 26, 137–147.
Sjöberg L E 2009: Geophys. J. Int., 179, 1527–1536.
Sjöberg L E, Bagherbandi M 2011: Acta Geoph., 59, 502–525.
Su W J, Woodward R L, Dziewonski A M 1994: J. Geoph. Res., 99, 6945–6980.
Sünkel H 1985: An isostatic earth model. In: Dept. of Geodetic Science and Surveying Report No. 367, The Ohio State University, Columbus, Ohio
Sünkel H ed. 1986: In: Mathematical and Numerical Techniques in Physical Geodesy. Springer, Berlin, 417–462.
Tenzer R, Hamayun K, Vajda P 2009: J. Geoph. Res., 11, B05408.
Tsoulis D 2001: J. Geod., 74, 637–643.
Tsoulis D 2004: J. Geod., 78, 7–11.
Tsoulis D, Stary B 2005: J. Geod., 78, 418–424.
Vening Meinesz F A 1931: Bull. Geod., 29, 33–51.
Watts A B 2001: Isostasy and Flexure of the Lithosphere. Cambridge University Press, Cambridge, New York, Melbourne
Xu P, Rummel R 1994: Geophys. J. Int., 117, 472–486.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bagherbandi, M. Impact of compensating mass on the topographic mass — A study using isostatic and non-isostatic Earth crustal models. Acta Geod. Geoph. Hung 47, 29–51 (2012). https://doi.org/10.1556/AGeod.47.2012.1.3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1556/AGeod.47.2012.1.3