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Tauxe, L, Kylstra N, Constable C.  1991.  Bootstrap Statistics for Paleomagnetic Data. Journal of Geophysical Research-Solid Earth and Planets. 96:11723-11740.   10.1029/91jb00572   AbstractWebsite

The power and utility of paleomagnetic analyses stem largely from the ability to quantify such parameters as the degree of rotation of a rock body, or the orientation of an anisotropy axis. Until recently, estimates for uncertainty in these paleomagnetically determined parameters derived from assumptions concerning the underlying parametric distribution functions of the data. In many geologically important situations, the commonly used parametric distribution functions fail to model the data adequately and the uncertainty estimates so obtained are unreliable. Such essentials as the test for common mean require data sets consistent with a spherically symmetric underlying distribution; their application in inappropriate circumstances can result in flawed interpretations. Moreover, the almost universally used approximation for a cone of 95% confidence for the mean of a sample drawn from a Fisher distribution is quite biased even for moderate dispersions (kappa = 25). The availability of inexpensive, powerful computers makes possible the empirical estimation of confidence regions by means of data resampling techniques such as the bootstrap. These resampling schemes replace analytical solutions with repeated simple calculations. We describe a bootstrap approach for the calculation of uncertainties for means or principal directions of paleomagnetic data. The method is tested on means of simulated Fisher distributions with known parameters and is found to be reliable for data sets with more than about 25 elements. Because a Fisher distribution is not assumed, the approach is applicable to a wide range of paleomagnetic data and can be used equally well on directions or associated virtual poles. We also illustrate bootstrap techniques for the discrimination of directions and for the fold test which enable the use of these powerful tests on the wider range of data sets commonly obtained in paleomagnetic investigations.

Tauxe, L, Constable C, Johnson CL, Koppers AAP, Miller WR, Staudigel H.  2003.  Paleomagnetism of the southwestern USA recorded by 0-5 Ma igneous rocks. Geochemistry Geophysics Geosystems. 4   10.1029/2002gc000343   AbstractWebsite

The issue of permanent nondipole contributions to the time-averaged field lies at the very heart of paleomagnetism and the study of the ancient geomagnetic field. In this paper we focus on paleomagnetic directional results from igneous rocks of the southwestern U. S. A. in the age range 0-5 Ma and investigate both the time-averaged field and its variability about the mean value. Several decades of work in the southwestern United States have resulted in the publication of paleomagnetic data from over 800 individual paleomagnetic sites. As part of a new investigation of the San Francisco Volcanics, we collected paleomagnetic samples from 47 lava flows, many of which have been previously dated. The new data combined with published data are highly scattered. Contributions to the scatter were considered, and we find that removal of data sets from tectonically active areas and judicious selection according to Fisher's [1953] precision parameter results in an axially symmetric data distribution with normal and reverse modes that are indistinguishable from antipodal. Monte Carlo simulations suggest that a minimum of 5 samples per site are needed to estimate the precision parameter sufficiently accurately to allow its use as a determinant of data quality. Numerical simulations from statistical paleosecular variation models indicate the need for several hundred paleomagnetic sites to get an accurate determination of the average field direction and are also used to investigate the directional bias that results from averaging unit vectors rather than using the full field vector. Average directions for the southwestern U. S. A. show small deviations from a geocentric axial dipole field, but these cannot be considered statistically significant. Virtual geomagnetic pole (VGP) dispersions are consistent with those from globally distributed observations analyzed by McElhinny and McFadden [1997]. However, a systematic investigation of the effect of imposing a cutoff on VGPs with large deviations from the geographic axis indicates that while it may reduce bias in calculating the average direction, such a procedure can result in severe underestimates of the variance in the geomagnetic field. A more satisfactory solution would be to use an unbiased technique for joint estimation of the mean direction and variance of the field distribution.

Tauxe, L, Shaar R, Jonestrask L, Swanson-Hysell NL, Minnett R, Koppers AAP, Constable CG, Jarboe N, Gaastra K, Fairchild L.  2016.  PmagPy: Software package for paleomagnetic data analysis and a bridge to the Magnetics Information Consortium (MagIC) Database. Geochemistry, Geophysics, Geosystems. 17:2450-2463.   10.1002/2016GC006307   Abstract

The Magnetics Information Consortium (MagIC) database provides an archive with a flexible data model for paleomagnetic and rock magnetic data. The PmagPy software package is a cross-platform and open-source set of tools written in Python for the analysis of paleomagnetic data that serves as one interface to MagIC, accommodating various levels of user expertise. PmagPy facilitates thorough documentation of sampling, measurements, data sets, visualization, and interpretation of paleomagnetic and rock magnetic experimental data. Although not the only route into the MagIC database, PmagPy makes preparation of newly published data sets for contribution to MagIC as a byproduct of normal data analysis and allows manipulation as well as reanalysis of data sets downloaded from MagIC with a single software package. The graphical user interface (GUI), Pmag GUI enables use of much of PmagPy's functionality, but the full capabilities of PmagPy extend well beyond that. Over 400 programs and functions can be called from the command line interface mode, or from within the interactive Jupyter notebooks. Use of PmagPy within a notebook allows for documentation of the workflow from the laboratory to the production of each published figure or data table, making research results fully reproducible. The PmagPy design and its development using GitHub accommodates extensions to its capabilities through development of new tools by the user community. Here we describe the PmagPy software package and illustrate the power of data discovery and reuse through a reanalysis of published paleointensity data which illustrates how the effectiveness of selection criteria can be tested.

Tauxe, L, Constable C, Stokking L, Badgley C.  1990.  Use of Anisotropy to Determine the Origin of Characteristic Remanence in the Siwalik Red Beds of Northern Pakistan. Journal of Geophysical Research-Solid Earth and Planets. 95:4391-4404.   10.1029/JB095iB04p04391   AbstractWebsite

It is often difficult or impossible to determine the origin of the characteristic remanent magnetization of red beds from the bulk remanence alone. However, anisotropy of remanence or susceptibility is strongly controlled by the statistical alignment of hematite grains; this in turn may reflect the development of the magnetic fabric of the sediment over time, so the shape of the anisotropy ellipsoid may provide clues to the origin of remanence. In this work, we make a study of the anisotropy of magnetic susceptibility (AMS) in Siwalik red beds of Miocene age from northern Pakistan. Comparison of the results with detailed petrographic studies and other information suggests that advanced soil development leads to the destruction of primary fabrics and often with it, a coherent magnetization. Furthermore, it should be possible to use AMS fabric information to quantify the degree of pedogenesis in these Miocene soils. We attempted to determine the anisotropy of isothermal remanence (AIR) but found AMS to be the technique of choice because of apparent changes in coercivity during AIR experiments. We interpret the AIR data as resulting from metastable domains in hematite grains which change domain state during the AIR experiment.