On the roles of magnetization and topography in the scaling behaviour of magnetic‐anomaly fields

SUMMARY There is lack of agreement on the underlying cause of widely observed power‐law scaling behaviour of magnetic‐anomaly fields. Some workers ascribe this behaviour to intrinsic 3‐D fractal distributions of magnetization in the crust of the Earth; others point to a power‐law exponent β∼ 3 , expected for a random ensemble of statistically independent magnetized prisms: the classic Spector & Grant model (SG model). We apply a perturbation approach to the Parker model to derive expressions for the power spectra of magnetic‐anomaly fields in the presence of laterally varying magnetization and/or topography at the top of magnetic basement. Under appropriate assumptions, our modified Parker model reduces to either an SG model or a 2‐D fractal model. In the case of fractal magnetization without topography, the power‐law slope of the magnetic‐anomaly field (after depth correction) is equal to the power‐law slope for the magnetization distribution. In the case of fractal basement topography alone, the power‐law slope is reduced by 2. Where both the magnetization and topography are fractal, the effects of magnetization tend to dominate the power‐law behaviour of the associated magnetic‐anomaly field. Two real‐data examples from the Canadian Shield exhibit power‐law exponents of 2.02 ± 0.02 and 1.42 ± 0.01 , within a wavelength band of 2 to 100 km. These slopes are significantly different from previously cited values of ∼3, casting doubt on the general applicability of the β∼ 3 slope that is inherent to SG models at high wavenumber.