Stratified multifractal magnetization and surface geomagnetic fields - II.Multifractal analysis and simulations

In Paper I, we showed how anisotropic scaling spectral (second-order) model s of the magnetization (M) were realistic at both high- and intermediate-wa venumber regimes of the surface magnetic field (B). However, in order to pr oduce full stochastic M and surface B models, we need assumptions about sta tistical moments other than second order. The usual approach is to assume q uasi-Gaussian statistics so that all the statistical moments are scaling ac cording to a single exponent. The corresponding fields are mono-fractal. Al l structures-both weak and strong-have the same unique fractal dimension, t here are no strong anomalies and there are no intermittent transitions from one strata or region to another; such assumptions are quite unrealistic. U sing seven surface B surveys, we show that the data are, on the contrary, m ultifractal, and we characterize their multifractal parameters in both the high- and intermediate-wavenumber regimes with the help of universal multif ractal exponents. Using anisotropic (stratified) multifractal models, we de duce the M statistics and produce M and surface B simulations with all stat istical 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 i nfer the M statistics. This enables us to produce anisotropic 3-D M, B mode ls with more realistic texture and morphology of structures. We conclude th at both multifractality and scaling anisotropy are indispensable for realis tic geophysical models.