Statistical Treatment of Crustal Magnetization

Abstract

We present a general statistical theory for relating magnetic fields to the magnetization of their source region, when the geometry of the source is spherical and the magnetization is a realization of a stationary, isotropic random process. For the case of Gaussian statistics, considered here, the second‐order statistics are sufficient to determine the process uniquely. Observed high‐degree coefficients from a spherical‐harmonic expansion of the field appear to be consistent with this model. We find simple models of crustal magnetization that are compatible with observational constraints, namely the values of the magnetic power spectra believed to be derived from the crust, and the total crustal power. Any statistical model of the crust can be used to ‘pre‐whiten’ observations prior to modelling the core field in a way described previously by Jackson. Copyright © 1994, Wiley Blackwell. All rights reserved