Magnetic Field Inversion – the cost of freedom

We created a funnel-shaped magnetic body from magnetite powder dispersed in plaster and used a travelling 3-component fluxgate magnetometer to map the magnetic field at a low elevation above it. This provided a dataset with signal and noise characteristics similar to those of a field survey, but for a source much better known than any buried geological body. We then used this survey data and the known source details to evaluate recovery of that information from inversions with different degrees of freedom and constraint. This provides guidance in evaluation of inversion results from field data for which the source characteristics are unknown. We found that because of small imperfections in the data and model, the inversion result closest to the truth, although fitting the data quite acceptably, is not the model with the smallest data misfit. Chasing further reduction in data misfit in some cases leads to inversion results which better fit the data but which diverge from the known magnetization. Furthermore, inversions to fit the noise-free field forward computed from a digital version of the model do not recover that exact model, with increasing deviation (but smaller data misfits) as increasing complexity is added to the inversion models.