Mars has a magnetic field originating in its strongly magnetised crust that holds clues to the planet’s interior. We apply vector spherical harmonic decomposition to simple candidate magnetic structures to separate the parts responsible for the anomalies from those that remain invisible. A uniform magnetic layer produces no anomalies: spatial variations are essential although secondary magnetisation does produce a weak field that might reflect the primordial dynamo field. A hemispheric layer produces anomalies confined to the equator rather than the observed hemispheric difference. A uniformly magnetised crust with variable thickness determined from gravity and topography produces a crustal field with large anomalies at the major impact crater sites that are not observed. These anomalies are not present if the magnetic layer lies deeper than the crater floor. We conclude that decomposing magnetisations in this way is a useful tool in the interpretation of Martian magnetic anomalies.