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Jeffrey J. Love

Publications and source records attributed to Jeffrey J. Love.

100 records · Page 6Linked to original sources
USGS2007

Principal component analysis in paleomagnetism

When studying the mean and variance of paleomagnetic data it is a common practice to employ principal component analysis (Jolliffe, 2002 ). The theory of this method is related to the mathematics quantifying the moment of inertia of a set of particles of mass about some reference point of interest. For the purposes of data analysis, principal component analysis was first promoted by Pearson ( 1901 ) and Hotelling ( 1933 ), and it also often associated with Karhunen ( 1947 ) and Loéve ( 1977 ). Principal component analysis is widely applied in crystallography (e.g., Schomaker et al ., 1959 ). In paleomagnetism (e.g., Mardia, 1972 ; Kirschvink, 1980 ), it finds application in studies of the average paleofield, paleosecular variation, demagnetization, and magnetic susceptibility. Here we discuss and demonstrate principal component analysis in application to full paleomagnetic vectorial data and, separately, to paleomagnetic directional data.

Book chapter↗
USGS2007

Statistical methods for paleovector analysis

Our concern is with the statistical description of paleomagnetic vectors and the estimation of their mean and variance. These vectors may come from a number of different rock units or archeological samples, representing a range of acquisition times, and be useful for studies of the mean paleomagnetic field and paleosecular variation ; alternatively, the vectors may come from individual measurements taken from a given rock unit or archeological sample, representing the same moment of acquisition, and be useful for studying the acquisition process itself. Directional data of a particular polarity are usually analyzed with a Fisher distribution (1953), and data of mixed polarities are usually analyzed with a Bingham distribution (1964). Occasionally, other directional distributions are used. For example, Bingham ( 1983 ) considered the projection of a three‐dimensional (3D), scalar‐variance Gaussian distribution onto the unit sphere, something he called the “angular‐Gaussian” distribution. More recently, Khokhlov et al. ( 2001 ) considered a generalization of the angular‐Gaussian distribution, one with a covariance matrix, which they used to analyze directional data from a number of sites. With respect to intensity data, they have traditionally been treated separately from paleodirections, analyzed with normal, log‐normal, or gamma distributions. Here, for data of either a particular polarity or of mixed polarities, we summarize these works, and that of Love and Constable ( 2003 ), who developed a full‐vector, scalar‐variance, Gaussian‐statistical framework for treating directional and intensity data simultaneously and self‐consistently.

Book chapter↗
USGS2007

The International Geomagnetic Reference Field, 2005

This is a set of five world charts showing the declination, inclination, horizontal intensity, vertical component, and total intensity of the Earth's magnetic field at mean sea level at the beginning of 2005. The charts are based on the International Geomagnetic Reference Field (IGRF) main model for 2005 and secular change model for 2005-2010. The IGRF is referenced to the World Geodetic System 1984 ellipsoid. Additional information about the USGS geomagnetism program is available at: http://geomag.usgs.gov/

Scientific Investigations Map↗
USGS2006

Statistical modeling of storm-level Kp occurrences

We consider the statistical modeling of the occurrence in time of large Kp magnetic storms as a Poisson process, testing whether or not relatively rare, large Kp events can be considered to arise from a stochastic, sequential, and memoryless process. For a Poisson process, the wait times between successive events occur statistically with an exponential density function. Fitting an exponential function to the durations between successive large Kp events forms the basis of our analysis. Defining these wait times by calculating the differences between times when Kp exceeds a certain value, such as Kp ??? 5, we find the wait-time distribution is not exponential. Because large storms often have several periods with large Kp values, their occurrence in time is not memoryless; short duration wait times are not independent of each other and are often clumped together in time. If we remove same-storm large Kp occurrences, the resulting wait times are very nearly exponentially distributed and the storm arrival process can be characterized as Poisson. Fittings are performed on wait time data for Kp ??? 5, 6, 7, and 8. The mean wait times between storms exceeding such Kp thresholds are 7.12, 16.55, 42.22, and 121.40 days respectively.

Geophysical Research Letters↗
USGS2006

National Geomagnetism Program: Current Status & Five-Year Plan, 2006-2010

Executive Summary: The U.S. Geological Survey's Geomagnetism Program serves the scientific community and the broader public by collecting and distributing magnetometer data from an array of ground-based observatories and by conducting scientific analysis on those data. Preliminary, variational time-series can be collected and distributed in near-real time, while fully calibrated, absolute time-series are distributed after processing. The data are used by the civilian and military parts of the Federal Government, by private industry, and by academia, for a wide variety of purposes of both immediately practical importance and long-term scientific interest, including space-weather diagnosis and related hazard mitigation, mapping of the magnetic field and measurement of its activity, and research on the nature of the Earth's interior and the near-Earth space environment. This document reviews the current status of the Program, in terms of its situation within the Government and within the scientific community; summarizes the Program's operations, its staffing situation, and its facilities; describes the diversity of uses of Program magnetometer data; and presents a plan for the next 5 years for enhancing the Program's data-based services, developing products, and conducting scientific research.

Open-File Report↗
USGS2004

Book review: Earth’s magnetism in the age of sail

For many centuries, the source, behavior, and even the essential nature of geomagnetism were enigmatic. Despite this, the effect of geomagnetism was familiar, by imparting a directional preference on the magnetized needle of the compass and providing a useful, if somewhat annoyingly complicated, reference for navigators. Although the compass seems to have first been invented in China, it was the Europeans who made the most systematic early studies of magnetism, who made the first elaborate and practical usage of the compass, and who developed most of the early theories as to the cause of the compass needle’s north-seeking tendency. From the centuries of the Middle Ages, through the late 16th century of the Renaissance, to the 17th century of philosophical enlightenment and the 18th century of discovery, the subject of magnetism and, more specifically, geomagnetism, evolved from a hodgepodge of mystical beliefs into something that we can today recognize as the object of modern scientific pursuit. Those same centuries witnessed the great transoceanic sailing voyages undertaken by European nations for reasons of exploration, territorial claim, religious mission, and mercantile trade. Naturally, the navigator’s compass, and therefore geomagnetism, played an important role in these developments. This romantic intersection of science and history is the subject of Earth’s Magnetism in the Age of Sail , a pleasantly written and scholarly book by A.R.T. Jonkers.

Physics of the Earth and Planetary Interiors↗
USGS2003

Paleointensity in Hawaiian Scientific Drilling Project Hole (HSDP2): Results from submarine basaltic glass

Paleointensity estimates based on the high quality Thellier‐Thellier data from the early Brunhes (420–780 ka) are rare (only 30 in the published literature). The Second Hawaiian Scientific Drilling Project (HSDP2) drill hole recovered submarine volcanics spanning the approximate time period of 420–550 ka. These are of particular interest for absolute paleointensity studies owing to the abundance of fresh submarine basaltic glass, which can preserve an excellent record of ancient geomagnetic field intensity. We present here new results of Thellier‐Thellier paleointensity experiments that nearly double the number of reliable paleointensity data available for the early Brunhes. We also show that the magnetizations of the associated submarine basalts are dominated by viscous magnetizations and therefore do not reflect the true ancient geomagnetic field intensity at the time of extrusion. The viscous contamination is particularly severe because of a combination of low blocking temperatures in the basalts and relatively high temperatures in the deeper parts of the drill core. Our new data, when placed on the approximate timescale available for HSDP and HSDP2, are at odds with other contemporaneous paleointensity data. The discrepancy can be reconciled by adjusting the HSDP timescales to be younger by about 35 kyr.

Geochemistry, Geophysics, Geosystems↗
USGS2003

Gaussian statistics for palaeomagnetic vectors

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Geophysical Journal International↗