A three-dimensional approach to estimating elastic thickness is presented which uses dense satellite altimetry and sparse ship bathymetry. This technique is applied to the Louisville Ridge system to study the tectonic history of the region. The inversion is performed as both a first-order approximation and a nonlinear relationship between gravity and topography based on Parker's <1973> equation. While the higher-order effect on the gravity anomaly is nearly zero for most of the region, the magnitude is significant over the summits of the ridge. Nevertheless, the inclusion of the nonlinear terms has only a minor influence on the elastic thickness estimate within each region, lowering the value by ~1-2 km compared with the linear result. The incorrect assumption of two dimensionality for circular features exhibits a marked effect on the gravitational anomaly, resulting in false sidelobe structure of nearly 20 mGal for large seamounts. Our elastic thickness estimates are compared with the contradictory values obtained in previous studies by Cazenave and Dominh <1984> and Watts et al. <1988>. We find an increasing elastic thickness along the chain from southeast to northwest, with a discontinuity along the Wishbone scarp. The jump in elastic thickness values northwest of the scarp appears to be an indication of an age discontinuity caused by an extinct spreading center north of the ridge. ¿ 2000 American Geophysical Union