Global isostatic geoid anomalies for plate and boundary layer models of the lithosphere

Abstract

Isostatic geoid anomalies are usually interpreted using a flat-earth, one-dimensional idealization. Isostatic anomalies on the spherical, self-gravitating earth differ from this idealization because: (1) degree one terms in the spherical harmonic expansion vanish; (2) each term in the spherical harmonic expansion is multiplied by (l + 2)/(l + 0.5) relative to the flat-earth case; (3) mass in cones rather than straight-sided columns is constant; and (4) further deformation of the earth is induced by the gravitational attraction of the deformation caused by the isostatic potential anomaly. When the effect of each of these is quantified, the second, third, and fourth nearly cancel, leaving the degree one, “over the horizon” effect providing the most important difference. Calculations of model isostatic geoid anomalies for the spherical analogues (developed here) of the plate and boundary layer thermal models show that this effect can bias estimates of geoid slopes by over 20%, although the effect is usually less than 5%. The geoid anomalies for these two models are quite different over old ocean basins, but they are unlikely to be distinguishable on the basis of global geoid observations owing to the presence of other larger perturbations in the geoid. Stripping the effects of plate aging and a hypothetical uniform, 35 km thick, isostatically-compensated continental crust from the observed geoid emphasizes that the largest-amplitude geoid anomaly is the geoid low of almost 120 m over West Antarctica. This anomaly is a factor of two greater in amplitude than the low of 60 m over Sri Lanka.