We apply the method of Projection Onto Convex Sets (POCS) to the problem of solving geophysical inverse problems. The advantage of this iterative method is its flexability in handling non-linear equality and inequality constraints, including constraints on the spectrum of unknown functions. We give examples of using POCS to interpolate topographic profiles, topographic maps, and the physical properties of the earth between well logs. ¿ American Geophysical Union 1991