Classical Theory of Isostasy
Author Name : Rajesh Kumar
ABSTRACT: The isostatic reduction is made using the isostatic response function (the response of the earth's gravity field to a point load) derived for an assumed mechanism of compensation, as, for example, in the hypotheses of Pratt, Airy. A method is given here for the computation of this function directly from observational data, eliminating the need for assuming a compensation mechanism. If the earth is linear in its response to the crustal loading of the topography, the response of the earth's gravity field to this loading can be represented as the two-dimensional convolution of the topography with the earth's isostatic response function. Actually, the topography is more likely to be the result of changes in density at depth than the cause, but the mathematical treatment is the same in both cases. Through transformation into the frequency domain, the convolution becomes multiplication, and one is led directly to the result that the isostatic response function is equal to the inverse transform of the quotient of the transforms of the Bouguer gravity anomaly and the topography. If one assumes local compensation, one can invert the isostatic response function to find the changes in density with depth that result in the uplift of the topography.