On the Backus Effect—I

Recovering the internal geomagnetic vector field B on and outside the Earth's surface S from the knowledge of only its direction or its intensity ||B|| on S , and assessing the uniqueness of geomagnetic models computed in this way, have been long-standing questions of interest. In the present paper we address the second problem. Backus (1968, 1970) demonstrated uniqueness in some particular cases, but also produced a theoretical counter-example for which uniqueness could not be guaranteed. Using the same line of reasoning as Backus (1968), we show that adding the knowledge of the location of the dip equator on S to the knowledge of ||B|| everywhere on S guarantees the uniqueness of the solution, to within a global sign, provided that the dip equator is made of one or possibly several closed curves on S , across which the normal component of the field changes sign (this component not being zero anywhere else).