DETERMINATION OF THE EXTERNAL GEOMAGNETIC FIELD FROM INTENSITY MEASUREMENTS

Suppose a closed, bounded region M contains all the sources (currents and magnets) of the geomagnetic field B, and M', the rest of space, is connected(any two points in M' can be joined by a smooth curve). Suppose that the total intensity of B is known in some open region contained entirely inside; M'. Then the vector field B is uniquely determined up to sign in all of M'. The result is less trivial it seems, being false in two dimensions. Since the method of proof involves analytic continuation, computations based on it will probably be numerically unstable.