A study of spectral methods of estimating the depth to the bottom of magnetic sources from near-surface magnetic anomaly data

Based on a critical evaluation of several different spectral magnetic depth determination techniques on areally large synthetic layered and random magnetization models, we recommend the following considerations in the usage of the methods as necessary prerequisites to successful bottom depth determinations: (1) using windows with sufficient width to ascertain that the response of the deepest magnetic layer is captured and by verifying the spectra and computing the depth estimates with the largest possible windows (>300-500 km); (2) avoiding filtering to remove arbitrary regional fields, accomplished by compiling magnetic anomalies derived from modern spherical harmonic degree 13 Earth's main field models [e.g. recent International Geomagnetic Reference Field models (IGRF) or Comprehensive models (CM)]; (3) ascertaining the near-circularity of the autocorrelation function to avoid analysing biased spectra containing strong anomaly trends; and (4) avoid determining the slopes from the exponential, low wavenumber part of the spectra in the cases of layered magnetization. We also describe the details of the new spectral peak forward modelling method and discuss the conditions under which the method can lead to useful results. We found that, despite all these precautions, in some cases, the results can still be erroneous and, therefore, we recommend a critical evaluation of the results by modelling heat flow and taking into account seismic information on the crustal and lithospheric thicknesses and seismic velocities wherever possible. In the southcentral US, east of the Rockies, where the surface heat flow ranges between 40 and 65 mW m^-2, we obtained the magnetic bottom depth of 40 ± 10 km using the approach of the forward modelling of the spectral peak. This range is similar to the seismically derived crustal thickness of 45-50 km, suggesting, therefore, that the entire crust may be magnetic in this region. Because of the uncertainties in the various heat flow contributing parameters, such as the variations in thermal conductivity, radiogenic heat and hydraulic regime, we could not constrain the lithospheric thickness beyond an estimate ranging approximately from 100 to 200 km.