Advertisement

Studia Geophysica et Geodaetica

, Volume 58, Issue 2, pp 227–248 | Cite as

Moho depth uncertainties in the Vening-Meinesz Moritz inverse problem of isostasy

  • Mohammad BagherbandiEmail author
  • Robert Tenzer
  • Lars E. Sjöberg
Article

Abstract

We formulate an error propagation model based on solving the Vening Meinesz-Moritz (VMM) inverse problem of isostasy. The system of observation equations in the VMM model defines the relation between the isostatic gravity data and the Moho depth by means of a second-order Fredholm integral equation of the first kind. The corresponding error model (derived in a spectral domain) functionally relates the Moho depth errors with the commission errors of used gravity and topographic/bathymetric models. The error model also incorporates the non-isostatic bias which describes the disagreement, mainly of systematic nature, between the isostatic and seismic models. The error analysis is conducted at the study area of the Tibetan Plateau and Himalayas with the world largest crustal thickness. The Moho depth uncertainties due to errors of the currently available global gravity and topographic models are estimated to be typically up to 1–2 km, provided that the GOCE gravity gradient observables improved the medium-wavelength gravity spectra. The errors due to disregarding sedimentary basins can locally exceed ∼2 km. The largest errors (which cause a systematic bias between isostatic and seismic models) are attributed to unmodeled mantle heterogeneities (including the core-mantle boundary) and other geophysical processes. These errors are mostly less than 2 km under significant orogens (Himalayas, Ural), but can reach up to ∼10 km under the oceanic crust.

Keywords

crust gravity isostasy mantle Moho interface 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Airy G.B., 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. London B, 145.Google Scholar
  2. Allègre C.J., Courtillot V., Tapponier P., Hirn A., Mattauer M., Coulon C., Jaeger J.J., Achache J., Schärer U., Marcoux J., Burg J.P., Girardeau J., Armijo R., Garie C., Göpel C., Li T., Xiao X., Chang C. and Li G., 1984. Structure and evolution of the Himalaya-Tibet orogenic belt. Nature, 307, 17–22.CrossRefGoogle Scholar
  3. Bagherbandi M., 2012. A comparison of three gravity inversion methods for crustal thickness modelling in Tibet plateau. J. Asian Earth Sci., 43, 89–97, DOI: 10.1016/j.jseaes.2011.08.013.CrossRefGoogle Scholar
  4. Bagherbandi M. and Sjöberg L.E., 2012. Non-isostatic effects on crustal thickness: a study using CRUST2.0 in Fennoscandia. Phys. Earth Planet. Inter., 200–201, 37–44.CrossRefGoogle Scholar
  5. Bagherbandi M., Tenzer R., Sjöberg L.E. and Novák P., 2013. Improved global crustal thickness modeling based on the VMM isostatic model and non-isostatic gravity correction. J. Geodyn., 66, 25–37.CrossRefGoogle Scholar
  6. Bassin C., Laske G. and Masters T.G., 2000. The current limits of resolution for surface wave tomography in North America. EOS Trans AGU, 81, F897.Google Scholar
  7. Braitenberg C., Zadro M., Fang J., Wang Y. and Hsu H.T., 2000a. Gravity inversion in Quinghai-Tibet plateau. Phys. Chem. Earth, 25, 381–386.CrossRefGoogle Scholar
  8. Braitenberg C., Zadro M., Fang J., Wang Y. and Hsu H.T., 2000b. The gravity and isostatic Moho undulations in Qinghai-Tibet plateau. J. Geodyn., 30, 489–505.CrossRefGoogle Scholar
  9. Braitenberg C., Wienecke S. and Wang Y., 2006. Basement structures from satellite-derived gravity field: south China Sea ridge. J. Geophys. Res., 111, B05407.Google Scholar
  10. Caporali A., 1995. Gravity anomalies and the flexure of the lithosphere in the Karakoram, Pakistan. J. Geophys. Res., 100, 15075–15085.CrossRefGoogle Scholar
  11. Caporali A., 1998. Gravimetric constraints on the rheology of the Indian and Tarim plates in the Karakoram continent collision zone. J. Asian Earth Sci., 16, 313–321.CrossRefGoogle Scholar
  12. Caporali A., 2000. Buckling of the lithosphere in western Himalaya; constraints from gravity and topography data. J. Geophys. Res., 105, 3103–3113.CrossRefGoogle Scholar
  13. Čadek O. and Martinec Z., 1991. Spherical harmonic expansion of the earth’s crustal thickness up to degree and order 30. Stud. Geophys. Geod., 35, 151–165.CrossRefGoogle Scholar
  14. Dziewonski A.M. and Anderson D.L., 1981. Preliminary Reference Earth Model. Phys. Earth Planet. Inter., 25, 297–356.CrossRefGoogle Scholar
  15. Gao R., Lu Z., Li Q., Guan Y., Zhang J., He R. and Huang L., 2005. Geophysical survey and geodynamic study of crust and upper mantle in the Qinghai-Tibet Plateau. Episode, 28, 263–273.Google Scholar
  16. Gladkikh V. and Tenzer R., 2011. A mathematical model of the global ocean saltwater density distribution. Pure Appl. Geophys., 169, 249–257.CrossRefGoogle Scholar
  17. Grad M., Tiira T. and ESC Working Group, 2009. The Moho depth map of the European Plate. Geophys. J. Int., 176, 279–292.CrossRefGoogle Scholar
  18. Hayford J.F., 1909. The Figure of the Earth and Isostasy from Measurements in the United States. U.S. Coast and Geodetic Survey, Govt. Print. Off., Washington, D.C.Google Scholar
  19. Hayford J.F. and Bowie W., 1912. The Effect of Topography and Isostatic Compensation upon the Intensity of Gravity. U.S. Coast and Geodetic Survey, Govt. Print. Off., Washington, D.C.Google Scholar
  20. Heiskanen W.A. and Vening Meinesz F.A., 1958. Earth and its Gravity Field. McGraw-Hill Book Company Inc., New York, NY.Google Scholar
  21. Heiskanen W.A. and Moritz H., 1967. Physical Geodesy. Freeman W.H., New York, N.Y.Google Scholar
  22. Hirn A., Lepine J.C., Jobert T.G., Sapin M., Wittlinger G., Xu Z.X., Gao E.Y., Wang X.J., Teng J.W., Xiong S.B., Pandey M.R. and Talte J.M., 1984. Crust structure and variability of the Himalayan border of Tibet. Nature, 307, 23–25.CrossRefGoogle Scholar
  23. Kaban M.K., Schwintzer P. and Tikhotsky S.A., 1999. Global isostatic gravity model of the Earth. Geophys. J. Int., 136, 519–536.CrossRefGoogle Scholar
  24. Kaban M.K., Schwintzer P., Artemieva I.M. and Mooney W.D., 2003. Density of the continental roots: compositional and thermal contributions. Earth Planet. Sci. Lett., 209, 53–69.CrossRefGoogle Scholar
  25. Kaban M.K., Schwintzer P. and Reigber Ch., 2004. A new isostatic model of the lithosphere and gravity field. J. Geodesy, 78, 368–385.CrossRefGoogle Scholar
  26. Kind R., Ni J., Zhao W., Wu J., Yuan X., Zhao L., Sandvol E., Reeses C., Nabelek J. and Hearn T., 1996. Evidence from earthquake data for a partially molten crustal layer in Southern Tibet. Science, 274, 1692–1694.CrossRefGoogle Scholar
  27. Kind R., Yuan X., Saul J., Nelson D., Sobolev S.V., Mechie J., Zhao W., Kosarev G., Ni J., Achauer U. and Jiang M., 2002. Seismic images of crust and upper mantle beneath Tibet: evidence for Eurasian plate subduction. Science, 298, 1219–1221.CrossRefGoogle Scholar
  28. Lyon-Caen H. and Molnar P., 1983. Constraints on the structure of the Himalaya from an analysis of gravity anomalies and a flexural model of the lithosphere. J. Geophys. Res., 88, 8171–8191.CrossRefGoogle Scholar
  29. Lyon-Caen H. and Molnar P., 1984. Gravity anomalies and the structure of western Tibet and the southern Tarim basin. Geophys. Res. Lett., 11, 1251–1254.CrossRefGoogle Scholar
  30. Mayer-Guerr T., Rieser D., Höck E., Brockmann J.M., Schuh W.-D., Krasbutter I., Kusche J., Maier A., Krauss S., Hausleitner W., Baur O., Jäggi A., Meyer U., Prange L., Pail R., Fecher T. and Gruber T., 2012. The new combined satellite only model GOCO03s. http://icgem.gfz-potsdam.de/ICGEM/modelstab.html.Google Scholar
  31. Moritz H., 1980. Advanced Physical Geodesy. Abacus Press, Tunbridge Wells, U.K.Google Scholar
  32. Moritz H., 1990. The Figure of the Earth. Wichmann H., Karlsruhe, Germany.Google Scholar
  33. Nelson K.D., Zhao W., Brown L.D., Kuo J., Che J., Liu X., Klemperer S.L., Makovsky Y., Meissner R., Mechie J., Kind R., Wenzel F., Ni J. and Nabelek J., 1996. Partially molten middle crust beneath southern Tibet Synthesis of Project INDEPTH results. Science, 274, 1684–1688.CrossRefGoogle Scholar
  34. Pavlis N.K., Factor J.K. and Holmes S.A., 2007. Terrain-related gravimetric quantities computed for the next EGM. In: Kiliçoglu A. and Forsberg R. (Eds.), Gravity Field of the Earth. Proceedings of the 1st International Symposium of the International Gravity Field Service (IGFS). Harita Dergisi, Special Issue No. 18, General Command of Mapping, Ankara, Turkey.Google Scholar
  35. Pavlis N.K., Holmes S.A., Kenyon S.C. and Factor J.K., 2012. The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J. Geophys. Res., 117, B04406.Google Scholar
  36. Pratt J.H., 1855. On the attraction of the Himalaya Mountains and of the elevated regions beyond upon the plumb-line in India. Trans. R. Soc. London B, 145.Google Scholar
  37. Rai S.S., Priestley K., Gaur V.K., Mitra S., Singh M.P. and Searle M., 2006. Configuration of the Indian Moho beneath the NW Himalaya and Ladakh. Geophys. Res. Lett., 33, L15308.CrossRefGoogle Scholar
  38. Rodriguez E., Morris C.S., Belz J.E., Chapin E.C., Martin J.M., Daffer W. and Hensley S., 2005. An Assessment of the SRTM Topographic Products. Technical Report D31639, Jet Propulsion Laboratory, Pasadena, California, 143 pp.Google Scholar
  39. Sampietro D., Reguzzoni M. and Braitenberg C., 2014. The GOCE estimated Moho beneath the Tibetan Plateau and Himalaya. In: Rizos C. and Willis P. (Eds.), Earth on the Edge: Science for a Sustainable Planet. International Association of Geodesy Symposia 139, Springer-Verlag, Berlin, Germany.Google Scholar
  40. Schulte-Pelkum V., Monsalve G., Sheehan A., Pandey M.R., Sapkota S. and Bilham R., 2005. Imaging the Indian subcontinent beneath the Himalaya. Nature, 435, 1222–1225.CrossRefGoogle Scholar
  41. Shin Y.H., Xu H., Braitenberg C., Fang J. and Wang Y., 2007. Moho undulations beneath Tibet from GRACE-integrated gravity data. Geophys. J. Inter., 170, 971–985.CrossRefGoogle Scholar
  42. Shin Y.H., Shum C.-K., Braitenberg C., Lee S.M., Xu H., Choi K.S., Baek J.H. and Park J.U., 2009. Three dimensional fold structure of the Tibetan Moho from GRACE gravity data. Geophys. Res. Lett., 36, L01302.Google Scholar
  43. Sjöberg L.E., 2009. Solving Vening Meinesz-Moritz inverse problem in isostasy. Geophys. J. Int., 179, 1527–1536.CrossRefGoogle Scholar
  44. Sjöberg L.E. and Bagherbandi M., 2011. A method of estimating the Moho density contrast with a tentative application by EGM2008 and CRUST2.0. Acta Geophysica, 59, 502–525.CrossRefGoogle Scholar
  45. Teng J.W., Yin Z.X., Xu Z.X., Wang X.T. and Lu D.Y., 1983. Structure of the crust and upper mantle pattern and velocity distributional characteristics in the Northern Himalayan mountain region. Acta Geophysica Sincia, 26, 525–540.Google Scholar
  46. Tenzer R. and Bagherbandi M., 2012. Reformulation of the Vening-Meinesz Moritz inverse problem of isostasy for isostatic gravity disturbances. Int. J. Geosci., 3(5), 918–929; DOI: 10.4236/ijg.2012.325094.CrossRefGoogle Scholar
  47. Tenzer R., Hamayun and Vajda P., 2009. Global maps of the CRUST2.0 crustal components stripped gravity disturbances. J. Geophys. Res., 114, B05408.Google Scholar
  48. Tenzer R., Abdalla A., Vajda P., Hamayun, 2010. The spherical harmonic representation of the gravitational field quantities generated by the ice density contrast, Contributions to Geophysics and Geodesy, 40,3, 207–223.CrossRefGoogle Scholar
  49. Tenzer R., Novák P. and Gladkikh V., 2011. On the accuracy of the bathymetry-generated gravitational field quantities for a depth-dependent seawater density distribution. Stud. Geophys. Geod., 55, 609–626.CrossRefGoogle Scholar
  50. Tenzer R., Gladkikh V., Vajda P. and Novák P., 2012a. Spatial and spectral analysis of refined gravity data for modelling the crust-mantle interface and mantle-lithosphere structure. Surv. Geophys., 33, 817–839.CrossRefGoogle Scholar
  51. Tenzer R., Novák P. and Gladkikh V., 2012b. The bathymetric stripping corrections to gravity field quantities for a depth-dependant model of the seawater density. Marine Geodesy, 35, 198–220.CrossRefGoogle Scholar
  52. Tenzer R., Novák P., Vajda P., Gladkikh V. and Hamayun, 2012c. Spectral harmonic analysis and synthesis of Earth’s crust gravity field. Comput. Geosci., 16, 193–207.CrossRefGoogle Scholar
  53. Tenzer R., Bagherbandi M., Hwang Ch. and Chang E.T.Y., 2014. Moho interface modeling beneath Himalayas, Tibet and central Siberia using GOCO02S and DTM2006.0. Terr. Atmos. Ocean. Sci., (in print).Google Scholar
  54. Tseng T.L., Chen W.P. and Nowack R.L., 2009. Northward thinning of Tibetan crust revealed by virtual seismic profiles. Geophys. Res. Lett., 36, L24304, DOI: 10.1029/2009GL040457.CrossRefGoogle Scholar
  55. Vening Meinesz F.A., 1931. Une nouvelle méthode pour la réduction isostatique régionale de l’intensité de la pesanteur. Bulletin Géodésique, 29, 33–51 (in French).CrossRefGoogle Scholar
  56. Watts A.B., 2001. Isostasy and Flexure of the Lithosphere. Cambridge University Press, Cambridge, U.K., 458 pp.Google Scholar
  57. Wienecke S., Braitenberg C. and Götze H.-J., 2007. A new analytical solution estimating the flexural rigidity in the Central Andes. Geophys. J. Int., 169, 789–794.CrossRefGoogle Scholar
  58. Wittlinger G., Vergne J., Tapponnier P., Farra V., Poupinet G., Jiang M., Su H., Herquel G. and Paul A., 2004. Teleseismic imaging of subducting lithosphere and Moho offsets beneath western Tibet. Earth Planet. Sci. Lett., 221, 117–130.CrossRefGoogle Scholar
  59. Wu G., Xiao X. and Li T., 1991. Yadong to Golmud Transect Qinghai-Tibet Plateau, China. Global Geoscience Transects Series 3, AGU, Washington, D.C.Google Scholar
  60. Xiong S.B., Teng J.W. and Yin Z.X., 1985: Research on the fine crustal structure of the northern Qilian-Hexi Corridor by deep seismic reflection. Chinese J. Geophys., 38, 29–35.Google Scholar
  61. Xu Z.Q., Jiang M., Yang J.S., Xue G.Q., Su H.P., Li H.B., Cui J.W., Wu C.L. and Liang F.H., 2004. Mantle structure of Qinghai-Tibet plateau: Mantle plume, mantle shear zone and delamination of lithospheric slab. Earth Sci. Front., 11, 329–343.Google Scholar
  62. Zeng R.S., Ding Z.F. and Wu Q.J., 1994. A review of the lithospheric structure in Tibetan plateau and constraints for dynamics. Acta Geophys. Sinica, 37, 99–116.Google Scholar
  63. Zeng R.S., Teng J.W., Li Y.K., Klemperer S. and Yang L.Q., 2002. Crustal velocity structure and eastward escaping of crustal material in the southern Tibet. Science in China, 32, 793–798.Google Scholar
  64. Zhang Z.J., Li Y.K., Wang G.J., Teng J.W., Klemperer S., Li J.W., Gan J.Y. and Chen Y., 2001. E-W Crustal structure under the northern Tibet revealed by wide-angle seismic profiles. Science in China D, 31, 881–888.Google Scholar
  65. Zhao W.-J., Nelson K.D. and Project INDEPTH Team, 1993. Deep seismic reflection evidence for continental underthrusting beneath southern Tibet. Nature, 366, 557–559.CrossRefGoogle Scholar

Copyright information

© Institute of Geophysics of the ASCR, v.v.i 2014

Authors and Affiliations

  • Mohammad Bagherbandi
    • 1
    • 2
    Email author
  • Robert Tenzer
    • 3
  • Lars E. Sjöberg
    • 2
  1. 1.Department of Industrial DevelopmentIT and Land Management University of GävleGävleSweden
  2. 2.Division of Geodesy and GeoinformaticsRoyal Institute of Technology (KTH)StockholmSweden
  3. 3.School of Geodesy and GeomaticsWuhan UniversityWuhanChina

Personalised recommendations