Accounting for crustal magnetization in models of the core magnetic field

Abstract

Remanent and induced magnetization occurs in crustal materials when they are below their Curie temperature, and we consider the problem of determining the magnetic field originating in the earth's core in the presence of such magnetization. Simple physical models of induced magnetization which have been proposed and which lead to deterministic effects account for only a small proportion of the high-degree internal field found using Magsat data, and thus a stochastic description appears more useful. We investigate the effect of remanent magnetization in the crust on satellite measurements of the core magnetic field by posing the question: if the crustal magnetization is correlated only on the shortest possible length-scale, and different components are uncorrelated everywhere, what is the correlation lengthscale at a radius above the earth's surface? Using an idea due to Parker (1988), we model the crust as a zero-mean, stationary, Gaussian random process. We show that the matrix of second-order statistics is proportional to the Gram matrix, which depends only on the inner-products of the appropriate Green's functions, and that at a typical satellite altitude of 400km the data are correlated out to an angular separation of approximately 15". Accurate and efficient means of calculating the matrix elements are given. This theory leads to a more conservative form for the correlation in the data than that previously given by Langel, Estes & Sabaka (1989), whilst not being incommensurate with the imprecisely known high-degree power spectrum. Previous studies examining the core field have treated satellite data as independent, and have given different orthogonal components equal weight. Both these assumptions are incorrect, and we show that the variance of measurements of the radial component of magnetic field due to the crust is expected to be approximately twice that in horizontal components. However, the size of the crustal effect is small compared to the random noise in the data, and may not lead to radically different results from those already published.

A statistical spatial power spectrum of the Earth's lithospheric magnetic field

“…In particular, the spectral form discussed in this paper is more energetic at the low SH degrees than the ones previously published (Jackson 1990(Jackson , 1994Voorhies 1998;Voorhies et al 2002). This suggests that the main field modelling error caused by the crustal field could have been so far underestimated (see Baerenzung et al 2014, for a recent consideration of the crustal field error).…”

“…Such statistical hypotheses can be defined for the susceptibility κ(r) in the spatial domain. This is a line traditionally followed in geomagnetism, where processes involving spatially uncorrelated or slightly correlated sources have been often considered (for instance Jackson 1990Jackson , 1994Voorhies 1998). One major difficulty with this approach is to define a priori a realistic correlation function for the sources when our knowledge of the source magnetization is incomplete and in general indirect.…”

“…Various statistical forms for the spatial power spectrum expressed in SH have been devised relying on first order physical principles. Jackson (1990Jackson ( , 1994 proposes two statistical spectra based on the assumption that the crustal magnetization is spatially randomly distributed, that it lies within a thin shell, and that it is characterized by a typical lateral correlation length. He then uses these expressions to constrain the waveband where the core and the crustal fields overlap (Jackson 1996).…”

Spectral analysis of vector magnetic field profiles

“…Making the potential spectrum white is clearly artificial; instead, we attribute the disorder to the sources: under the plane z =0 we place a half space of random magnetization, the model of Parker and Daniell [1979], with a three-dimensional magnetization autoco-variance tensor that is a delta function times the unit tensor. This model has been studied by Jackson [1990], who gives an expression (his equation (18) …”

Electric Fields Derived from the Earth's Magnetic Field and Their Application to Fluid Motion in the Outer Core

“…MEYER et al, 1983) or possibly statistically (e.g. JACKSON, 1990) and remove the corresponding magnetic field. Nevertheless, we are still faced with the problem that when we consider the induced electric field intensity, 0A/at, which should be essentially unaffected by crustal magnetization, the amplitude spectrum of the spherical harmonic expansion is an increasing function of degree, n, at the core-mantle boundary.…”