An equivalent source algorithm is described for continuing either one or two dimensional potential fields between arbitrary surfaces. In the two dimensional case, the dipole surface is approximated as a set of plane faces with constant moments over each face. In the one-dimensional case, the plane faces of the dipole surface reduce to straight line segments. Model and field examples of aeromagnetic data show the method to be effective and accurate even when the terrain has strong topographic relief and is composed of highly magnetic volcanic rocks.--Modified journal abstract.

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