I have derived an analytical expression for the on-axis free-air gravity anomaly over a cone or frustum of a cone. Using this expression I have developed an algorithm to estimate the degree of compensation of a seamount from its bathymetry and on-axis gravity anomaly. The algorithm allows rapid estimation of the degree of compensation and thus is useful for large data sets. It makes no mechanical assumptions about the lithosphere. Using this algorithm, I have determined the degree of isostatic compensation and uncertainty for 152 seamounts from their bathymetry and maximum gravity anomalies.

For twelve well-dated seamounts, a compensation vs. age of loading curve was constructed. Although there are only a few data points, the data are roughly consistent with the square root of time relationship which is predicted by cooling plate models, however, other similar curves fit the data equally well. For any assumed functional form, there is a consistent trend from high compensation at a low age of loading to low compensation at a high age of loading. This trend implies that seamounts erupted onto old, thick oceanic lithosphere should have low degrees of compensation, and seamounts erupted onto young, thin lithosphere should have high degrees of compensation.

Using data from 77 well-constrained seamounts, we have constructed isostatic compensation maps for several seamount groups in the Central and Western Pacific. Important regional groupings in the compensation values are readily visible. The regional groupings suggest that the seamounts in each group had similar tectonic origins. The Hawaiian - Emperor chain, the Caroline Islands and the Magellan seamounts are uncompensated, suggesting a mid- plate hotspot origin. The Musicians seamounts, Mid-Pacific Mountains and Marshall Islands are highly compensated, suggesting a near ridge-crest origin, although the Marshall Islands display some complexities.