Geoid anomalies over cooling lithosphere: source for a third kernel of upper mantle thermal parameters and thus an inversion

Abstract

Summary. The geoid anomaly over an isostatic mass redistribution on an infinite flat earth is simply 27πC/g times the differential mass moment. On a spheroidal earth the limiting value can never quite be reached because the external effect of a spherical shell of mass dipole is identically zero, so distant portions of the spherical surface subtract from the effect of the region under the point of observation. The width of the integrating kernel varies with the depth of the mass distribution, but the observable fraction of the limiting geoid slope can be estimated, at least for ocean basins of moderate extent, where it should reach about 90 per cent. For very small (< 1 cm yr−1) or very large (> 3 cm yr−1) ocean basins, the observable geoid slope is smaller. A consideration of published geoid data, together with gravity anomalies in the same area, compared to the theoretical free geoid gravity anomalies (= gravity observed on the geoid) leads, with great caution, to a crude estimate of the thermally produced slope of 0.14 ± 0.02 m Myr−1. Given a value of the thermal geoid signal, it is possible to conduct an inversion for the upper mantle thermal parameters if two, the density and specific heat, are assumed to be known. The parameter ‘kernels’ for the heat flow, topographic decay and geoid give three equations to solve for expansion coefficient α, diffusivity κ and initial temperature TI. The results are different from common modelling assumptions: 3.1 × 10−5°C−1±17 per cent; 0.0065 cm2 s−l±45 per cent; and 1660°C ±29 per cent. Manipulation of the equations in the case of general temperature‐variable parameters leads to partial explanations: α appears multiplied by k0.7/k0 (conductivity at 0.7 of T1; at surface temperature), while k is weighted toward the lower values in the low‐to‐medium temperature range. An estimate of T1, using the shape of the temperature variations of k and k in the most reliable available data for olivine, remains at about 1660°C ±30 per cent. In spite of the large error band, the higher initial temperature is plausible because decompression of upwelling material produces enough partial melting to generate the oceanic crust. The latent heat of melting must be supplied from somewhere, and the only other possible source is a large amount of mechanical work applied to the system in the divergent flow. Copyright © 1982, Wiley Blackwell. All rights reserved