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Hildebrand, JA, Parker RL.  1987.  Paleomagnetism of Cretaceous Pacific Seamounts revisited. Journal of Geophysical Research-Solid Earth and Planets. 92:12695-12712.   10.1029/JB092iB12p12695   AbstractWebsite

The paleomagnetism of Cretaceous Pacific seamounts is reexamined. Herein techniques for nonuniform magnetic modeling are applied to determine paleomagnetic pole positions and their associated confidence limits. Modeling techniques are presented for reconstruction of both uniform and nonuniform components of the seamount magnetization. The uniform component yields an estimate of the paleomagnetic pole position, and the nonuniform component accounts for irregularities in the seamount magnetization. A seminorm minimization approach constructs maximally uniform magnetizations and is used to represent seamount interiors. A statistical modeling approach constructs random nonuniform magnetizations and is used to determine the confidence limits associated with each pole position. Mean paleopoles are calculated for groups of seamounts, including their associated error bounds. The mean paleopole for seven reliably dated Upper Cretaceous seamounts is located close to the position predicted by Pacific-hotspot relative motion. The paleopole for five seamounts with Cretaceous minimum dates is located west of the hotspotpredicted apparent polar wander path and may represent a Lower Cretaceous or Upper Jurassic pole.

McKenzie, D, Parker RL.  1974.  Plate tectonics in ω space. Earth and Planetary Science Letters. 22:285-293.   10.1016/0012-821x(74)90137-x   AbstractWebsite

The relative angular velocity vectors of the plates covering the earth form a three-dimensional closed polyhedron, for which we propose the name geohedron. All forms of plate evolution produce simple changes in the geohedron. Corresponding bodies exist for relative angular accelerations and an attempt is made to determine the value of the relative accelerations of the plates forming a single triple junction when they are governed by kinematic effects alone, but the resulting values do not agree with the available observations.

Shure, L, Parker RL, Langel RA.  1985.  A preliminary harmonic spline model from Magsat data. Journal of Geophysical Research-Solid Earth and Planets. 90:1505-1512.   10.1029/JB090iB13p11505   AbstractWebsite

We present a preliminary main field model for 1980 derived from a carefully selected subset of Magsat vector measurements using the method of harmonic splines. This model (PHS (80) for preliminary harmonic splines) is the smoothest model (in the sense that the rms radial field at the core surface is minimum) consistent with the measurements (with an rms misfit of 10 nT to account for crustal and external fields as well as noise in the measurement procedure). Therefore PHS (80) is more suitable for studies of the core than models derived with the traditional least squares approach (e.g., GSFC (9/80)). We compare characteristics of the harmonic spline spectrum, topology of the core field and especially the null-flux curves (loci where the radial field is zero) and the flux through patches bounded by such curves. PHS (80) is less complex than GSFC (9/80) and is therefore more representative of that part of the core field that the data constrain.

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.