In classical isostatic computations, 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.
DISCUSSION OF THE I:)ROBLEiVI
Isostasy is the process by which the elevation of the earth's surface is adjusted in response to density changes at depth or to surface loads in order to bring about uniformity of pressure at some depth, when an area of some size is considered. Isostasy is studied by several groups of people, for reasons both mundane and sublime. The mundane reasons generally involve the need to know the departures from symmetry of the density distribution within the earth, since these affect the earth's shape and gravity field, the transmission of seismic waves within the earth, and the horizontal and vertical movements of the earth's surface. The sublime reasons usually center around the desire to understand the development of the earth. In the past, studies have generally been carried out by hypothesizing a model describing the 'x Contribution No. 232,