Fractal magnetization of continental crust

Abstract

Many geophysical variables exhibit fractal or at least scaling behaviour, notably in having power spectra proportional to some power of frequency. Power spectra of magnetic susceptibility logs from boreholes are proportional to spatial frequency f −2 for wavelengths from 0.1 to 100 m. If the power spectrum of the susceptibility or magnetization of the crust is known then the power spectrum of the magnetic field at the surface can be calculated. We show that if magnetization is scaling with a single scaling exponent then the observed f −3 power spectra of aeromagnetic data implies a three‐dimensional f −4 susceptibility distribution for length scales of 1 to 1000 km. One way to reconcile the two results is to introduce anisotropy in the form of a f −4 variation for the horizontal direction and f −2 for the vertical.