Abstract:
Some distributions of magnetization give rise to magnetic fields that vanish everywhere above the surface, rendering these distributions of magnetization completely invisible. They are the annihilators of the magnetic inverse problem. Known examples are the infinite sheet with constant magnetization and the spherical shell of constant susceptibility magnetized by an arbitrary internal field. Here, we show that remarkably more interesting annihilators exist for the Earth's dipole-dominated inducing field. Indeed, any susceptibility profile along the magnetic equator can be extended north/south into an annihilator. Consequently, the induced magnetization along the magnetic equator is entirely undetermined by the visible magnetic field. In contrast to the Backus effect, this ambiguity persists even if the full magnetic vector field is known.
