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O'Brien, MS, Parker RL, Constable CG.  1999.  Magnetic power spectrum of the ocean crust on large scales. Journal of Geophysical Research-Solid Earth. 104:29189-29201.   10.1029/1999jb900302   AbstractWebsite

The geomagnetic power spectrum R-l is the squared magnetic field in each spherical harmonic degree averaged over a spherical surface. Satellite measurements have given reliable estimates of the spectrum for the part that originates in the core, but above I = 15, where the geomagnetic field arises primarily from crustal magnetization, there is considerable disagreement between various estimates derived from observation. Furthermore, several theoretical models for the spectrum disagree with each other and the data. We have examined observations from a different source, 5000-km-long Project Magnet aeromagnetic survey lines; we make new estimates of the spectrum which overlap with the wavelength interval accessible to the satellites. The usual way the spectrum is derived from observation is to construct a large spherical harmonic decomposition first, then square, weight, and add the Gauss coefficients in each degree, but this method cannot be applied to isolated flight lines. Instead, we apply a statistical technique based on an idea of McLeod and Coleman which relates the geomagnetic spectrum to the power and cross spectra of magnetic field components measured on the survey lines. Power spectra from the 17 aeromagnetic surveys, all of which were conducted over the oceans, are averaged together to improve geographic coverage and reduce variance, and the average spectra are then inverted for the geomagnetic spectrum R-l. Like most of the theoretical models, our spectrum exhibits a maximum, but at a wavelength of 100 km, about a factor of 2 smaller than the closest theoretical prediction. Our spectrum agrees quite well with the most recent estimates based on satellite observations in the range 20 less than or equal to l less than or equal to 50, but above l=50, our values increase slowly, while all the satellite data suggest a sharply rising curve. In this wavelength range we believe our measurements are more trustworthy. Further work is planned to confirm the accuracy of our spectrum when continental survey paths are included.

O'Brien, MS, Parker RL.  1993.  Regularized geomagnetic field modelling using monopoles. Geophysical Journal International. 118:566-578.   10.1111/j.1365-246X.1994.tb03985.x   AbstractWebsite

There are many techniques for modelling the geomagnetic field, any one of which may be suitable for a particular application depending on its associated modelling goals. Each method combines a choice of functions and an approach to fitting data so that, in general, it is best suited to a particular type of field modelling, e.g. core versus crustal, regional versus global, downward continuation versus interpolation. Those few approaches such as spherical cap harmonic analysis (Haines 1985a) that possess any true flexibility in this respect suffer from mathematical and computational complexity. In addition, regularization is still a somewhat overlooked issue. Regularization is essential for downward continuing geomagnetic data because shorter wavelength field components and their errors blow up in this process. Approaches such as harmonic spline modelling (Shure, Parker and Backus 1982) which include regularization do so while significantly complicating the task of inversion. We present a new regularized modelling scheme which employs magnetic monopoles as representing functions. We apply regularizing norms of the type introduced by Shure et al. (1982). Owing to the mathematical simplicity of the monopoles, the expressions for the norms are themselves very simple and flexible, and the monopole models very easy to compute. Moreover, the conceptual simplicity of this representation allows for easy modification to accommodate most geomagnetic modelling problems. We apply the technique to problems on three different length scales, each application having distinctly different modelling goals: globally we model the radial core field at the core-mantle boundary (CMB) from satellite data; on a large regional scale we model the radial crustal field at the earth's surface from satellite data; on a small regional scale we model the radial crustal field at the earth's surface from surface data. For each of these varied applications we are able to generate monopole models which produce smooth, plausible fields that fit the data.

O'Brien, 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.

Oldenburg, DW, Whittall KP, Parker RL.  1984.  Inversion of ocean bottom magnetotelluric data revisited. Journal of Geophysical Research. 89:1829-1833.   10.1029/JB089iB03p01829   AbstractWebsite

Three ocean bottom magnetotelluric data sets from sites on the Pacific plate are reinterpreted. The initial analysis found a correlation between the lithospheric age and the depth to a conductive zone beneath each site. That work also suggested that the resistivity increased below the conductor. This analysis, which includes new methods for constructing one-dimensional conductivity models, shows that the postulated increase in resistivity is not demanded by the data. It also reveals an unexpectedly large nonuniqueness inherent in the interpretation of these data. The previously reported trends with lithospheric age still exist, but they are not as strong as initially believed. Finally, it is shown rigorously that the different age sites are distinct in that no one-dimensional model can account for all three data sets.