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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.

Banks, RJ, Parker RL, Huestis SP.  1977.  Isostatic compensation on a continental scale: local versus regional mechanisms. Geophysical Journal of the Royal Astronomical Society. 51:431-452.: Blackwell Publishing Ltd   10.1111/j.1365-246X.1977.tb06927.x   AbstractWebsite

Summary. Using the techniques of linear and quadratic programming, it can be shown that the isostatic response function for the continental United States, computed by Lewis & Dorman (1970), is incompatible with any local compensation model that involves only negative density contrasts beneath topographic loads. We interpret the need for positive densities as indicating that compensation is regional rather than local. The regional compensation model that we investigate treats the outer shell of the Earth as a thin elastic plate, floating on the surface of a liquid. The response of such a model can be inverted to yield the absolute density gradient in the plate, provided the flexural rigidity of the plate and the density contrast between mantle and topography are specified. If only positive density gradients are allowed, such a regional model fits the United States response data provided the flexural rigidity of the plate lies between 1021 and 1022 N m. The fit of the model is insensitive to the mantle/ load density contrast, but certain bounds on the density structure can be established if the model is assumed correct. In particular, the maximum density increase within the plate at depths greater than 34 kin must not exceed 470 kg m−3; this can be regarded as an upper bound on the density contrast at the Mohorovicic discontinuity. The permitted values of the flexural rigidity correspond to plate thicknesses in the range 5–10 km, yet deformations at depths greater than 20 km are indicated by other geophysical data. We conclude that the plate cannot be perfectly elastic; its effective elastic moduli must be much smaller than the seismically determined values. Estimates of the stress-differences produced in the earth by topographic loads, that use the elastic plate model, together with seismically determined elastic parameters, will be too large by a factor of four or more.

Barbour, AJ, Parker RL.  2014.  psd: Adaptive, sine multitaper power spectral density estimation for R. Computers & Geosciences. 63:1-8.   10.1016/j.cageo.2013.09.015   AbstractWebsite

We present an R package for computing univariate power spectral density estimates with little or no tuning effort. We employ sine multitapers, allowing the number to vary with frequency in order to reduce mean square error, the sum of squared bias and variance, at each point. The approximate criterion of Riedel and Sidorenko (1995) is modified to prevent runaway averaging that otherwise occurs when the curvature of the spectrum goes to zero. An iterative procedure refines the number of tapers employed at each frequency. The resultant power spectra possess significantly lower variances than those of traditional, non-adaptive estimators. The sine tapers also provide useful spectral leakage suppression. Resolution and uncertainty can be estimated from the number of degrees of freedom (twice the number of tapers). This technique is particularly suited to long time series, because it demands only one numerical Fourier transform, and requires no costly additional computation of taper functions, like the Slepian functions. It also avoids the degradation of the low-frequency performance associated with record segmentation in Welch's method. Above all, the adaptive process relieves the user of the need to set a tuning parameter, such as time-bandwidth product or segment length, that fixes frequency resolution for the entire frequency interval; instead it provides frequency-dependent spectral resolution tailored to the shape of the spectrum itself. We demonstrate the method by applying it to continuous borehole strainmeter data from a station in the Plate Boundary Observatory, namely station B084 at the Pinon Flat Observatory in southern California. The example illustrates how pad elegantly handles spectra with large dynamic range and mixed-bandwidth features-features typically found in geophysical datasets. (C) 2013 Elsevier Ltd. All rights reserved.

Berger, J, Agnew DC, Parker RL, Farrell WE.  1979.  Seismic system calibration 2. Cross-spectral calibration using random binary signals. Bulletin of the Seismological Society of America. 69:271-288. AbstractWebsite
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.

Bullard, EC, Parker RL.  1970.  Electromagnetic induction in a thin strip. The sea Pt. 1, Vol. 4, New concepts of sea floor evolution. Regional observations concepts. :695-730., New York: Interscience Publ. Abstract