A general method for the local downward continuation at ground level of geopotentials measured by low-orbiting satellites at different altitudes is proposed. Such a continuation is the inverse solution of the external Dirichlet problem. The stability of the solution with respect to the altitude and the distribution of data points is discussed. Principal component analysis is shown to perform well and leads to a stable solution. The method proposed has the advantage of being directly applicable to measured data points which are not evenly spaced and at different altitude. As an illustration, it is applied to Magsat data over southeast Asia. Two independent maps of the vertical component of the anomaly field at a constant altitude near ground level are derived for dawn (descending orbits) and dusk (ascending orbits) data separately. The two maps reveal similar anomalies and confirm the correlation of the Magsat-derived anomaly field with the mosaic structure of the continental crust in southeast Asia. Stable continental blocks are associated with positive anomalies, and intervening collision belts correspond to well-defined negative anomalies. A very prominent low is observed above the Himalaya and extends over the Tibet plateau, confirming an anomalous crustal and thermal structure of the plateau. ¿ American Geophysical Union 1987