Analytic continuation of isolated gravitational anomalies in the three-dimensional case

The present work proposes a method for carrying out analytic continuation of isolated gravitational anomalies in the region outside of a given sphere, within which the sources of the anomalies are located, for the case when the surface of the earth has an arbitrary shape. It is assumed that the values of the first and second derivatives of the anomalous field are known at the earth's surface. The method makes use of a technique for the analytic continuation of a harmonic function into the region outside the given sphere, when the values of this function and its normal derivative are defined over some closed surface containing the given sphere. Kelvin's theorem is also invoked.-