Inherent power-law behavior of magnetic field power spectra from a Spector and Grant ensemble

The Spector and Grant method, which has been in use for 25 years, relates average depths to source to rate of decay of the magnetic power spectra. This method, which assumes a uniform distribution of parameters for an en semble of magnetized blocks, leads to a depth-dependent exponential rate of decay. We show that also inherent in this model is a power-law rate of decay that is independent of depth. For most cases, except for extreme depths and small block sizes, the observed power spectrum should be corrected for a power law decay rate of beta similar to 3. If the depth distribution of the magnetic blocks is Gaussian, then the observed power spectrum should be corrected for both a depth independent power law and exponential decay. This power-law decay is very similar to the scaling behavior, supposed as a fractal character, of observed magnetic fields in North America. As a general rule, when beta similar to 3, further information is needed to discriminate between a fractal or Spector and Grant model. However, it is becoming quite clear that magnetic power spectra should be corrected for a power law decay before applying the Spector and Grant method for depth determination.