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Korte, M, Constable CG, Parker RL.  2002.  Revised magnetic power spectrum of the oceanic crust. Journal of Geophysical Research-Solid Earth. 107   10.1029/2001jb001389   AbstractWebsite

[1] The magnetic field originating within the Earth can be divided into core and crustal components, which can be characterized by the geomagnetic power spectrum. While the core spectrum is determined quite well by satellite studies, models of the shorter wavelength crustal spectrum disagree considerably. We reexamine aeromagnetic data used by O'Brien et al. [1999] to obtain a new, improved estimate of the crustal geomagnetic power spectrum. O'Brien et al. 's model somewhat failed to give a satisfactory connection between the longer-wavelength satellite studies and a reliable crustal model. We show that this was caused by an inadequate processing step that aimed to remove external variations from the data. We moreover attempt to bound the long-wavelength part of the spectrum using constraints of monotonicity in the correlation of the magnetization. However, this proves to be a weak constraint. Reversing the process, though, we are able to evaluate the correlation function using the reliable part of our geomagnetic spectrum. Thus we can obtain a sensible estimate for the long-wavelength part of the spectrum that is not well constrained by the data. Our new model shows better agreement with earlier satellite studies and can be considered reliable in the spherical harmonic degree range l = 30 to 1200.

RygaardHjalsted, C, Constable CG, Parker RL.  1997.  The influence of correlated crustal signals in modelling the main geomagnetic field. Geophysical Journal International. 130:717-726.   10.1111/j.1365-246X.1997.tb01866.x   AbstractWebsite

Algorithms used in geomagnetic main-field modelling have for the most part treated the noise in the field measurements as if it were white. A major component of the noise consists of the field due to magnetization in the crust and it has been realized for some time that such signals are highly correlated at satellite altitude. Hence approximation by white noise, while of undoubted utility, is of unknown validity. Langel, Estes & Sabaka (1989) were the first to evaluate the influence of correlations in the crustal magnetic field on main-field models. In this paper we study two plausible statistical models for the crustal magnetization described by Jackson (1994), in which the magnetization is a realization of a stationary, isotropic, random process. At a typical satellite altitude the associated fields exhibit significant correlation over ranges as great as 15 degrees or more, which introduces off-diagonal elements into the covariance matrix, elements that have usually been neglected in modelling procedures. Dealing with a full covariance matrix for a large data set would present a formidable computational challenge, brit fortunately most of the entries in the covariance matrix are so small that they can be replaced by zeros. The resultant matrix comprises only about 3 per cent non-zero entries and thus we can take advantage of efficient sparse matrix techniques to solve the numerical system. We construct several main-field models based on vertical-component data from a selected 5 degrees by 5 degrees data set derived from the Magsat mission. Models with and without off-diagonal terms are compared. For one of the two Jackson crustal models, k(3), we find significant changes in the main-field coefficients, with maximum discrepancies near degree 11 of about 27 per cent. The second crustal spectrum gives rise to much smaller effects for the data set used here, because the correlation lengths are typically shorter than the data spacing. k(4) also significantly underpredicts the observed magnetic spectrum around degree 15. We conclude that there is no difficulty in computing main-field models that include off-diagonal terms in the covariance matrix when sparse matrix techniques are employed; we find that there may be important effects in the computed models, particularly if we wish to make full use of dense data sets. Until a definitive crustal field spectrum has been determined, the precise size of the effect remains uncertain. Obtaining such a statistical model should be a high priority in preparation for the analysis of future low-noise satellite data.

Obrien, MS, Constable CG, Parker RL.  1997.  Frozen-flux modelling for epochs 1915 and 1980. Geophysical Journal International. 128:434-450.   10.1111/j.1365-246X.1997.tb01566.x   AbstractWebsite

The frozen-flux hypothesis for the Earth's liquid core assumes that convective terms dominate diffusive terms in the induction equation governing the behaviour of the magnetic field at the surface of the core. While highly plausible on the basis of estimates of physical parameters, the hypothesis has been questioned in recent work by Bloxham, Gubbins & Jackson (1989) who find it to be inconsistent with their field models for most of the century. To study this question we improve the method of Constable, Parker & Stark (1993), which tests the consistency of magnetic observations with the hypothesis by constructing simple, flux-conserving core-field models fitting the data at pairs of epochs. We introduce a new approach that fixes the patch configurations at each of the two epochs before inversion, so that each configuration is consistent with its respective data set but possesses the same patch topology. We expand upon the inversion algorithm, using quadratic programming to maintain the proper flux sign within patches; the modelling calculations are also extended to include data types that depend non-linearly on the model. Every test of a hypothesis depends on the characterization of the observational uncertainties; we undertake a thorough review of this question. For main-field models, the primary source of uncertainty comes from the crustal field. We base our analysis on one of Jackson's (1994) statistical models of the crustal magnetization, adjusted to bring it into better conformity with our data set. The noise model permits us to take into account the correlations between the measurements and requires that a different weighting be given to horizontal and vertical components. It also indicates that the observations should be fit more closely than has been the practice heretofore. We apply the revised method to Magsat data from 1980 and survey and observatory data from 1915.5, two data sets believed to be particularly difficult to reconcile with the frozen-flux hypothesis. We compute a pair of simple, flux-conserving models that fit the averaged data from each epoch. We therefore conclude that present knowledge of the geomagnetic fields of 1980 and 1915.5 is consistent with the frozen-flux hypothesis.