STRATIFIED MULTIFRACTAL MAGNETIZATION AND SURFACE GEOMAGNETIC FIELDS-II. MULTIFRACTAL ANALYSIS AND SIMULATIONS

Abstract

In Paper I, we showed how anisotropic scaling spectral (second-order) models of the magnetization (M) were realistic at both high- and intermediate-wavenumber regimes of the surface magnetic field (B). However, in order to produce full stochastic M and surface B models, we need assumptions about statistical moments other than second order. The usual approach is to assume quasi-Gaussian statistics so that all the statistical moments are scaling according to a single exponent. The corresponding fields are monofractal. All structures-both weak and strong-have the same unique fractal dimension, there are no strong anomalies and there are no intermittent transitions from one strata or region to another; such assumptions are quite unrealistic. Using seven surface B surveys, we show that the data are, on the contrary, multifractal, and we characterize their multifractal parameters in both the high- and intermediate-wavenumber regimes with the help of universal multifractal exponents. Using anisotropic (stratified) multifractal models, we deduce the M statistics and produce M and surface B simulations with all statistical exponents quite near to those of the observed surface B field; they are also visually realistic, showing anomalies at all scales. Finally, we analyse the horizontal anisotropy of the surface B fields and use this to infer the M statistics. This enables us to produce anisotropic 3-D M, B models with more realistic texture and morphology of structures. We conclude that both multifractality and scaling anisotropy are indispensable for realistic geophysical models.