Theory

Both methods estimate the depth and thickness of a buried magnetic source from the slope of the radially averaged spectrum of the magnetic anomaly. They differ in the model fitted to that spectrum and in how the fit is turned into a Curie depth with an uncertainty.

• The Bouligand fractal model
  • The analytic spectrum
  • The inverse problem
  • Uncertainties
  • References
• The Tanaka centroid method
  • The two bands
  • What PyCurious adds
  • Choosing the bands
  • Fractal magnetisation
  • References

Conventions

A few conventions run through the whole package and are easy to get wrong:

• Wavenumbers are in rad/km, everywhere. radial_spectrum() returns k in rad/km, and the Tanaka fitting bands are given in the same units.

• The DFT fundamental is \(dk = 2\pi/(N\,dx)\), not \(2\pi/((N-1)\,dx)\); using \(N-1\) understates every depth by a factor \((N-1)/N\).

• Depths are positive downwards. The optimisers return depths, not the negative gradients the fits produce.

• The power argument selects which spectrum you get. radial_spectrum() raises \(|\mathrm{FFT}|\) to power before averaging. Since \(\Phi = |\mathrm{FFT}|^2\), Bouligand fits the log power spectrum (power=2.0, the default) while Tanaka fits the log amplitude spectrum (power=1.0).