Experimental isostasy: 1. Theory of the determination of the Earth's isostatic response to a concentrated load

Abstract

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.

Thermal and mechanical development of the East African Rift System

“…The primary advantage of the coherence technique we use over more conventional admittance techniques is that estimates of the effective elastic plate thickness obtained using the coherence technique are not biased towards low values of flexural rigidity in the presence of subsurface loading, unlike those obtained using admittance techniques (e.g., Dorman and Lewis, 1970;McKenzie and Bowin, 1976). The coherence technique is also less biased toward regions with high topography, such as the uplifted flanks of the East African rift valleys (Forsyth, 1985).…”

“…Therefore, the gravity field at short wavelengths largely is due to different processes than the dynamic processes supporting the long wavelength topography. At wavelengths where the gravity and topography signals are coherent, we use the ratio of the transformed gravity, G(k), to the transformed topography, H(k), the admittance, to estimate the depth of compensation for the broad East African plateau (e.g., Dorman and Lewis, 1970). In order to include a region large enough to examine the long wavelength aspects of the gravity field beneath the 1300 km wide East African plateau, we have computed the admittance in a sub-region encompassing the uplifted East African plateau, excluding cratonic regions outside the uplift (BIG; Figure 5).…”

Local Covariance Functions and Density Distributions.

“…This relationship, which says that the degree-variances and the power spectrum are more or less the same, have been given e.g. by Dorman and Lewis (1970), in a form slightly different than the one given below.…”

Gravity, Geoid, Isostasy and Moho Depth in the Ross Sea, Antarctica

“…Assuming that the isostatic response of the lithosphere is isotropic, following the approach suggested by Dorman and Lewis (1970) we have computed the isostatic admittance as :…”