Response of the Earth’s Crust due to Topographic Loads Derived by Inverse Isostasy
Let us propose that the density anomaly is proportional to the earth’s radius vector in such a way that it is linearly related to the topography by a convolution of the topography and an isotropic kernel function. Hence, one can derive that the attraction of the compensating masses is also a convolution of the topography and an isotropic isostatic response function. Such an isostatic response function of the earth’s crust can be determined by deconvolution. The paper gives the necessary derivation of such a deconvolution by means of global spherical harmonics. A practical determination of the isotropic isostatic response of the earth’s crust needs the harmonic analysis of both the topography and the attraction of the compensating masses. To avoid the assumption of an isostatic model, the principle of inverse isostasy, by which we aim to have zero isostatic anomalies, has been employed. The harmonic analysis of the Bouguer anomalies is thus a combination of the harmonic analysis of the topographic potential and the already existed global (free-air) reference models. Two global reference models have been used. They are EGM96 and GPM98CR models complete to degree and order 360 and 540, respectively. The needed harmonic analysis of the topography has been carried out using TUG87 and TBASE digital height models after smoothing to 20′ and 30′ resolutions. The results show that the isostatic response of the earth’s crust derived by inverse isostasy behaves in the same sense as those given by the exact solution of the Vening Meinesz isostatic model.
Keywordsisostasy inverse problems response function density anomaly.
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- Abd-Elmotaal, H. (1993) Vening Meinesz Moho Depths: Traditional, Exact and Approximated, man uscripta geodaetica, 18, 171–181.Google Scholar
- Abd-Elmotaal, H. (2001) Enhanced Approach for Harmonic Analysis on the Ellipsoid, Scientific Bulletin, Ain Shams University, Faculty of Engineering, 36 (3), 53–65.Google Scholar
- Colombo, 0 (1981) Numerical Methods for Harmonic Analysis on the Sphere, Department of Geodetic Science, The Ohio State University, Columbus, Ohio, 310 Google Scholar
- Hein, G.W., Eissfeller, B., Ertel, M., Hehl, K., Jacoby, W. and Czerwek, D. (1989) On Gravity Prediction Using Density and Seismic Data, Preprint, Institute of Astronomical and Physical geodesy, University FAF Munich.Google Scholar
- Heiskanen, W.A. and Moritz, H. (1967) Physical Geodesy, Freeman, San Francisco.Google Scholar
- Lewis, B.T.R. and Dorman, L.M. (1970) Experimental Isostasy: 2. An Isostatic Model for the USA Derived from Gravity and Topographic Data, Journal of Geophysical Research, 75, 33673386.Google Scholar
- Moritz, H. (1990) The Figure of the Earth: Theoretical Geodesy and the Earth’s Interior, Wichmann, Karlsruhe.Google Scholar
- Sünkel, H. (1985) An Isostatic Earth Model, Department of Geodetic Science, The Ohio State University, Columbus, Ohio, 367.Google Scholar