Isostatic response of the earth's crust derived by inverse isostasy

Abstract

Postulate that the density anomaly is proportional to the earth's radius vector so that it is linearly related to the topography by a convolution of the topography and an isotropic kernel function. Accordingly, one can prove 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 can be determined by deconvolution. The paper gives the derivation of such a deconvolution by means of spherical harmonics. A practical determination of the isotropic isostatic response function needs the harmonic analysis of both the topography and the attraction of the compensating masses. Applying the principle of inverse isostasy, by which we aim to achieve zero isostatic anomalies, then the attraction of the compensating masses equals the Bouguer anomalies with an opposite sign. The harmonic analysis of the Bouguer anomalies is thus a combination of the harmonic analysis of the topographic potential and the already existed global reference models. A practical application has been carried out using EGM96 and GPM98CR geopotential earth models as well as TUG87 and TBASE digital height models. The results show that the estimated isotropic isostatic response functions behave similarly as that given by the exact bending curve of the earth's crust represented by the Kelvin function kei x. This shows that the isostatic response of the earth's crust computed by direct isostasy using the most realistic isostatic model (modified Vening Meinesz isostatic model with Kelvin function kei x as the exact bending curve) matches the isostatic response of the earth's crust derived by inverse isostasy.