Co-seismic Gravity Changes Computed for a Spherical Earth Model Applicable to GRACE Data

  • W. SunEmail author
  • G. Fu
  • Sh. Okubo
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 135)


Dislocation theories were developed conventionally for a deformed earth surface because most traditional gravity measurements are performed on the terrain surface. However, through development of space geodetic techniques such as the satellite gravity missions, co-seismic gravity changes can be detected from space. In this case, the conventional dislocation theory cannot be applied directly to the observed data because the data do not include surface crustal deformation (the free air gravity change). Correspondingly, the contribution by the vertical displacement part must be removed from the traditional theory. This study presents the corresponding expressions applicable to space observations. In addition, a smoothing technique is necessary to damp the high-frequency contribution so that the theory can be applied reasonably. As examples, the Sumatra earthquakes (2004, 2007) are considered and discussed.


Bouguer Gravity Gravity Change Dislocation Theory Sumatra Earthquake Spherical Harmonic Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported financially by a JSPS Grant-in-Aid for Scientific Research (C16540377). The authors thank Dr. C. K. Shum and Mr. L. Wang very much for sharing their computing code of the Gaussian filter.


  1. Ammon, C.J., J. Chen, and H. Thio, et al. (2005). Rupture process of the 2004 Sumatra-Andaman earthquake, Science, 308, 1133–1139.CrossRefGoogle Scholar
  2. Banerjee, P., F.F. Pollitz, and Burgmann (2005). The size and duration of the Sumatra-Andaman earthquake from far-field static offsets, Science, 308, 1769–1772.CrossRefGoogle Scholar
  3. Ben-Menahem, A. and S.J. Singh (1968). Eigenvector expansions of Green’s dyads with applications to geophysical theory, Geophys. J. R. Astron. Soc., 16, 417–452.CrossRefGoogle Scholar
  4. Chen, J. (2007). Preliminary result of the September 12, 2007 Sumatra earthquake,
  5. Dziewonski, A.M. and D.L. Anderson (1981). Preliminary reference earth model, Phys. Earth Planet. Inter., 25, 297–356.CrossRefGoogle Scholar
  6. Fu, G. and W. Sun (2008). Surface co-seismic gravity changes caused by dislocations in a 3-D heterogeneous earth, Geophys. J. Int., 172(2), 479–503.CrossRefGoogle Scholar
  7. Gross, R.S. and B.F. Chao (2001). The gravitational signature of earthquakes, in Gravity, Geoid, and Geodynamics 2000, 205–210, IAG Symposia 123, Springer-Verlag, New York.Google Scholar
  8. Han, S.-C., C.K. Shum, M. Bevis, C. Ji, and C-Y. Kuo (2006). Crustal dilatation observed by GRACE after the 2004 Sumatra-Andaman earthquake, Science, 313, 658–662.CrossRefGoogle Scholar
  9. Maruyama, T. (1964). Static elastic dislocations in an infinite and semi-infinite medium, Bull. Earthquake Res. Inst. Univ. Tokyo, 42, 289–368.Google Scholar
  10. Okada, Y. (1985). Surface deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., 75, 1135–1154.Google Scholar
  11. Okubo, S. (1992). Potential gravity changes due to shear and tensile faults, J. Geophys. Res., 97, 7137–7144.CrossRefGoogle Scholar
  12. Piersanti, A., G. Spada, R. Sabadini, and M. Bonafede (1995). Global post-seismic deformation, Geophys. J. Int., 120, 544–566.CrossRefGoogle Scholar
  13. Pollitz, F.F. (1992). Postseismic relaxation theory on the spherical Earth, Bull. Seismol. Soc. Am., 82, 422–453.Google Scholar
  14. Rundle, J.B. (1982). Viscoelastic gravitational deformation by a rectangular thrust fault in a layered Earth, J. Geophys. Res., 87, 7787–7796.CrossRefGoogle Scholar
  15. Sabadini, R., A. Piersanti, and G. Spada (1995). Toroidal-poloidal partitioning of global Post-seismic deformation, Geophys. Res. Lett., 21, 985–988.CrossRefGoogle Scholar
  16. Smylie, D.S. and L. Mansinha (1971). The elasticity theory of dislocation in real Earth models and changes in the rotation of the earth, Geophys. J. R. Astron. Soc., 23, 329–354.CrossRefGoogle Scholar
  17. Sun, W. and S. Okubo (1993). Surface potential and gravity changes due to internal dislocations in a spherical Earth – I. Theory for a point dislocation, Geophys. J. Int., 114, 569–592.CrossRefGoogle Scholar
  18. Sun, W. and S. Okubo (2002). Effects of the earth’s spherical curvature and radial heterogeneity in dislocation studies, Geophys. R.L., 29(12), 46 (1–4).Google Scholar
  19. Sun, W. and S. Okubo (2004). Co-seismic deformations detectable by satellite gravity missions, J. Geophys. Res., 109, B4, B04405.Google Scholar
  20. Steketee, J.A. (1958). On Volterra’s dislocations in a semi-infinite elastic medium, Can. J. Phys., 36, 192–205.CrossRefGoogle Scholar
  21. Tanaka, T., J. Okuno, and S. Okubo (2006). A new method for the computation of global viscoelastic post-seismic deformation in a realistic earth model (I), Geophys. J. Int., 164, 273.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Earthquake Research Institute, The University of TokyoTokyoJapan

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