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 400 km 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.
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