Global isotropic isostatic response function in terms of zonal spherical harmonics

Assume that the density anomaly is linearly related to the topography by a convolution of the topography and an isotropic kernel function. Hence, it can be shown that the attraction of the compensating masses is also a convolution of the topography and an isotropic isostatic response function, which 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 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. The needed harmonic analysis of the topography has been carried out using different global digital height models. 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.