Experimental isostasy: 2. An isostatic model for the U.S.A. derived from gravity and topographic data

Abstract

By using a fast Fourier transform algorithm, the two‐dimensional transform of the Bouguer anomaly (with terrain correction) BA (kx, ky), free‐air anomaly FA ( kx, Ky), and topography H (kx, ky) on a 32‐km grid has been obtained, being based on some 80,000 actual gravity observations and on the Bouguer anomaly map of the U.S.A. The azimuthally symmetric, real function R (k) = 〈Re (BA (kx, ky)/H(kx, ky))〉, averaged over azimuth so as to minimize the geological ‘noise,’ gives the transfer function of the earth to a concentrated load. Assuming local compensation, the experimentally obtained R (k) has been inverted to give the change in density with depth (to about 400 km, a rough limit imposed by the long wavelength resolution of the data) causing the isostatic compensation. The compensation appears to be in the mantle and not related to parameters less than 30–40 km deep. Some features of this isostatic model compare favorably with recent seismic results. R (k) has also been used to obtain the gravity field from the compensation and hence to construct an isostatic anomaly map by multiplying H (kx, ky) by R (k), subtracting this from BA (kx, ky), and taking the inverse transform. The assumption inherent in these calculations, that any nonlinear relationships between the gravity field of the compensation and the topography are small, has been tested by computing the coherency between the isostatic anomaly and the (topography)n and is found to be justified. Another function R′ (k) = Re 〈(FA(kx, ky) / H(kx, ky))〉 is used to predict the gravity field due to both the topography and the compensation.

Isostatic response of the Laccadive Ridge from admittance analysis of gravity and bathymetry data

“…The admittance is based completely on the observed relationship between gravity and bathymetry and is not tied to any isostatic model. However, Dorman and Lewis (1970), Lewis and Dorman (1970), McKenzie and Bowin (1976), Walcott (1976), Watts (1978), Banks et al (1977) and Louden (1981) showed that admittance could be easily compared with admittance calculated for various isostatic models based on different hypotheses of compensation.…”

Strength of Faults on Mars from MOLA Topography

“…In this method, the admittance (Lewis andDorman 1970, McKenzie andBowin 1976) is calculated using the line-of-sight accelerations of the Mars Global Surveyor (MGS) in its orbit, as a proxy for the gravity field, and the MOLA topography. The admittance spectrum for VM could be modeled by a best-fit elastic thickness of around 50 km, the short-wavelength admittance estimates being consistent with a crustal density of around 2.4 Mg m −3 .…”

Isostatic Compensation and Conduit Structures of Western Pacific Seamounts: Results of Three-Dimensional Gravity Modeling

“…The main assumption is that the wavelength of any subsurface a.nomalous distribution of mass must be much shorter or much longer than the dimensions of the bathymetric feature being studied. Lewis and Dorman (1970) pointed out that this method is successful only for topography with wavelengths much shorter than those of gravity anomalies produced by regional isostatic compensation. This technique is not valid for a seamount ifit has a local gravity "root" or a large magma chamber (Le Pichon and TaI wani, 1964).…”