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Bowers, NE, Cande SC, Gee JS, Hildebrand JA, Parker RL.  2001.  Fluctuations of the paleomagnetic field during chron C5 as recorded in near-bottom marine magnetic anomaly data. Journal of Geophysical Research-Solid Earth. 106:26379-26396.   10.1029/2001jb000278   AbstractWebsite

Near-bottom magnetic data contain information on paleomagnetic field fluctuations during chron C5 as observed in both the North and South Pacific. The North Pacific data include 12 survey lines collected with a spatial separation of up to 120 kin, and the South Pacific data consist of a single long line collected on the west flank of the East Pacific Rise (EPR) at 19 degreesS. The North Pacific magnetic profiles reveal a pattern of linear, short-wavelength (2 to 5 km) anomalies (tiny wiggles) that are highly correlated over the shortest (3.8 km) to longest (120 km) separations in the survey. Magnetic inversions incorporating basement topography show that these anomalies are not caused by the small topographic relief. The character of the near-bottom magnetic profile from anomaly 5 on the west flank of the EPR, formed at a spreading rate more than twice that of the North Pacific, displays a remark-able similarity to the individual and stacked lines from the North Pacific survey area, Over distances corresponding to 1 m.y., 19 lows in the magnetic anomaly profile can be correlated between the North and South Pacific lines. Modeling the lows as due to short polarity events suggests that they may be caused by rapid swings of the magnetic field between normal and reversed polarities with little or no time in the reversed state. Owing to the implausibly high number of reversals required to account for these anomalies and the lack of any time in the reversed state, we conclude that the near-bottom signal is primarily a record of pateointensity fluctuations during chron C5. Spectral analysis of the North Pacific near bottom lines shows that the signal is equivalent to a paleointensity curve with a temporal resolution of 40 to 60 kyr, while measurements of the smallest separations of correlatable dips in the field suggest a temporal resolution of 36 kyr.

Prieto, GA, Parker RL, Vernon FL.  2009.  A Fortran 90 library for multitaper spectrum analysis. Computers & Geosciences. 35:1701-1710.   10.1016/j.cageo.2008.06.007   AbstractWebsite

The spectral analysis of geological and geophysical data has been a fundamental tool in understanding Earth's processes. We present a Fortran 90 library for multitaper spectrum estimation, a state-of-the-art method that has been shown to outperform the standard methods. The library goes beyond power spectrum estimation and extracts for the user more information including confidence intervals, diagnostics for single frequency periodicities, and coherence and transfer functions for multivariate problems. In addition, the sine multitaper method can also be implemented. The library presented here provides the tools needed in multiple fields of the Earth sciences for the analysis of data as evident from various examples. (C) 2008 Elsevier Ltd. All rights reserved.

Backus, G, Parker RL, Constable C.  1996.  Foundations of Geomagnetism. :xiv,369p.., Cambridge England ; New York: Cambridge University Press AbstractWebsite

The main magnetic field of the Earth is a complex phenomenon. To understand its origins in the fluid of the Earth's core, and how it changes in time requires a variety of mathematical and physical tools. This book presents the foundations of geomagnetism, in detail and developed from first principles. The book is based on George Backus' courses for graduate students at the University of California, San Diego. The material is mathematically rigorous, but is logically developed and has consistent notation, making it accessible to a broad range of readers. The book starts with an overview of the phenomena of interest in geomagnetism, and then goes on to deal with the phenomena in detail, building the necessary techniques in a thorough and consistent manner. Students and researchers will find this book to be an invaluable resource in the appreciation of the mathematical and physical foundations of geomagnetism.

Parker, RL, Wheelock B.  2012.  Fourier domain calculation of terrain effects in marine MT. Geophysical Journal International. 189:240-250.   10.1111/j.1365-246X.2011.05350.x   AbstractWebsite

Magnetotelluric surveys on the seafloor have become an important part of marine geophysics in recent years. The distorting effects of topographic relief on the electromagnetic fields can be far-reaching, but local terrain is also important. Thus, computational techniques that can treat a large area containing fine-scale topography could find widespread application. We describe a new solution to the problem based on a well-established theory of electromagnetic induction in thin sheets. The procedure requires taking the Fourier transform of the integral equations derived by Dawson and Weaver in 1979, and by McKirdy, Weaver and Dawson in 1985. The equations in the transformed electric field are solved iteratively by a new technique. We prove the new iterative procedure is always convergent, whereas the original scheme diverges when the grid spacing of the discretization is small. We also give a means of correcting for distant features that need not be specified in as great detail. Preliminary tests confirm the new process is very efficient and that topographic data sets of several million points will be handled with ease.

Parker, RL.  1977.  The Fréchet derivative for the one-dimensional electromagnetic induction problem. Geophysical Journal of the Royal Astronomical Society. 49:543-547.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1977.tb03723.x   AbstractWebsite

Summary. From consideration of the higher order terms, it is shown that the magneto-telluric response is Fréchet differentiable with respect to conductivity; this result remains valid for discontinuous profiles, which is not so in the case of the corresponding free-oscdlation problem for the elastic earth. The remainder term in the Fréchet formula is shown to be O|δσ|2 and a numerical estimate is made of the bounding constant for a restricted class of conductivity models.

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.