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Truncated co-seismic geoid and gravity changes in the domain of spherical harmonic degree
Earth, Planets and Spacevolume 56, pages881–892 (2004)
A concept of truncated geoid and gravity changes is proposed in this study and corresponding truncated expressions are presented for investigating co-seismic deformations. Numerical investigations are carried out to observe whether or not co-seismic geoid and gravity changes are detectable by gravity satellite missions. Results of an individual harmonic degree or a summation to interested degrees are compared with the expected errors of the gravity missions, assuming a seismic source equivalent to the fault size of the Alaska earthquake (1964, m w = 9.2). Corresponding co-seismic deformations indicate that both the gravity and geoid changes are about two orders larger than the precision of GRACE. Based on these results, the minimum magnitudes of earthquakes detectable by GRACE are derived. The conclusion is that co-seismic deformations for an earthquake with a seismic magnitude above m = 7.5 (for the tensile sources) and m = 9.0 (for the shear sources) are expected to be detected by GRACE. Finally, a case study is made on the 2002 Alaska earthquake (m = 7.9). Results show that the co-seismic geoid and gravity changes are at or below the error level of GRACE, and are difficult to detect.
Chao, B. F., Geodesy is not just for static measurements any more, Eos, Transactions, American Geophysical Union, 84, 145–156, 2003.
Dziewonski, A. M. and D. L. Anderson, Preliminary Reference Earth Model, Phys. Earth Planet. Inter., 25, 297–356, 1981.
ESA, Gravity field and steady-state ocean circulation mission, Reports for mission selection: The four candidates earth explorer core missions, SP-1233 (1), 1999.
Gilbert, F. and A. M. Dziewonski, An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra, Phil. Trans. R. Soc. London, A 278, 187–269, 1975.
Gross, R. S. and B. F. Chao, The gravitational signature of earthquakes, in Gravity, Geoid, and Geodynamics 2000, edited by M. G. Sideris, pp. 205–210, IAG Symposia Vol. 123, Springer-Verlag, New York, 2001.
National Research Council, NAS, Satellite Gravity and the Geosphere, edited J. O. Dickey, Washington, D.C., 1997.
Pollitz, F. F., Gravitational-viscoelastic postseismic relaxation on a layered spherical Earth, J. Geophys. Res., 102, 17921–17941, 1997.
Savage, J. C. and L. M. Hastie, Surface deformation associated with dip-slip faulting, J. Geophys. Res., 71, 4897–4904, 1966.
Sun, W. and S. Okubo, 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, 1993.
Sun, W. and S. Okubo, Surface potential and gravity changes due to internal dislocations in a spherical earth—II. Application to a finite fault, Geophys. J. Int., 132, 79–88, 1998.
Sun, W. and S. Okubo, Co-seismic Deformations Detectable by Satellite Gravity Missions—a Case Study of Alaska (1964, 2002) and Hokkaido (2003) Earthquakes in Spectral Domain, J. Geophys. R., 109(B4), B04405, doi:10.1029/2003JB002554, 2004.
Sun, W., S. Okubo, and P. Vanicek, Global displacement caused by dislocations in a realistic earth model, J. Geophys. Res., 101, 8561–8577, 1996.
Wang, H., Surface vertical displacements, potential perturbations and gravity changes of viscoelastic earth model induced by internal point dislocations, Geophys J. Int., 137, 429–440, 1999.
Watkins, M. M., W. M. Folkner, B. F. Chao, and B. D. Tapley, The NASA EX-5 Mission: A laser interferometer follow-on to GRACE, IAG Symp. GGG2000, Banff, July, 2000.