Mars has a magnetic field originating in its strongly magnetised crust that holds clues to the planet’s interior. The relation between magnetic anomalies and the underlying crustal magnetisation is complex because of magnetic structures that produce no observable field. We use a recently-developed method to isolate these “invisible’ structures to explore explanations for the observations. The strong magnetisation suggested by ground observations from InSight can be obtained simply by adding a suitable invisible magnetisation to that required to explain the data. A thin Northern Hemisphere and thick Southern Hemisphere crust produces magnetic anomalies confined around the equator, not the Southern Hemisphere. Variations in crustal thickness produce differences with the satellite field, most notably strong anomalies associated with the impact craters that are not in the data. Magnetisation may be confined to depths greater than that of the craters, or anomalies from shallower material are not observable at satellite altitude.