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Fractal magnetization of continental crust
Author(s) -
Pilkington M.,
Todoeschuck J. P.
Publication year - 1993
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/92gl03009
Subject(s) - magnetization , scaling , fractal , anisotropy , geophysics , geology , crust , spectral line , exponent , physics , magnetic field , spectral density , magnetic susceptibility , condensed matter physics , geometry , optics , mathematics , mathematical analysis , statistics , linguistics , philosophy , quantum mechanics , astronomy
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.