On the non-uniqueness of main geomagnetic field determined by surface intensity measurements: the Backus problem

Abstract

SUMMARY We revisit the problem of non-uniqueness of harmonic magnetic field models in a region outside a sphere containing the field sources, when only intensity values on the sphere surface are known. Using the angular momentum algebra and the Clebsch-Gordan coefficients, we are able to treat different aspects of this non-uniqueness following a unified line of reasoning. In this new framework, we first recover two Backus results, namely the proof of uniqueness in the case of a field generated by a finite number of harmonics and the recurrence relation that defines the well-known Backus series. This formalism allows us to extend previous studies in two ways: firstly, we show how to produce an harmonic series orthogonal on the sphere to some other arbitrary harmonic series; secondly, we outline a new method for computing magnetic field models starting from scalar intensity values alone.