There is a problem with Alex's argument about Hellas destroying a pre-existing magnetic signal, while in other areas it was preserved.

The problem is that gravity data tells us that at the time Hellas formed, the solid "skin" of Mars - the Lithosphere was around 10 km deep. With time, as Mars cooled, it thickened until today it is 300-400 km thick.

(This cooling is more a reduction in the rate of radioactive heating than a loss of primordial heat)

We can measure the depth of origin of the magnetic sources in two ways:

1) Quite large craters are found at the surface over them. One would expect such craters to destroy the local part of the magnetic field, just as proposed for Hellas. Many of these craters are clearly younger than Hellas.

The depth to which the magnetic field should have been destroyed is 20-50 km

2) We can actually measure the source depth by inversion of the magnetic field at altitude and using mathematical techniques of "downward continuation". This results in source depths ~ 50 km.

Now, the vital observation is that the temperature at which magnetisation is destroyed by heat - the Curie Point - is similar to the temperature at which the Lithosphere softens and stops acting as a skin. So we can see that the magnetic sources must post-date Hellas by quite a bit.

The implication seems to be that the Lithosphere thickened with time in all areas, but only became magnetic in some areas.

This is puzzling, and I have yet to see a good answer that integrates the thermal results from both gravity and magnetics.