Publications

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2004
Gee, JS, Meurer WP, Selkin PA, Cheadle MJ.  2004.  Quantifying three-dimensional silicate fabrics in cumulates using cumulative distribution functions. Journal of Petrology. 45:1983-2009.   10.1093/petrology/egh045   AbstractWebsite

We present a new method for quantifying three-dimensional silicate fabrics and the associated uncertainties from grain orientation data on three orthogonal sections. Our technique is applied to the orientation of crystallographic features and, hence, yields a fabric related to the lattice-preferred orientation, although the method could be applied to shape-preferred orientations or strain analysis based on passive linear markers. The orientation data for each section are represented by their cumulative distribution function, and an iterative procedure is used to find the symmetric second-rank strain tensor that will simultaneously satisfy the cumulative distribution functions observed on each section. For samples with well-developed fabrics, this technique provides a much closer match to the sectional data than do previous techniques based on eigenparameter analysis of two-dimensional orientation data. Robust uncertainty estimates are derived from a non-parametric bootstrap resampling scheme. The method is applied to two cumulates: one with a well-developed fabric and the other with a weak fabric, from the Stillwater complex, Montana. The silicate petrofabric orientations obtained for these samples compare favorably with independent direct estimates of the volume fabric from electron backscatter diffraction and magnetic techniques.

1998
Tauxe, L, Gee JS, Staudigel H.  1998.  Flow directions in dikes from anisotropy of magnetic susceptibility data: The bootstrap way. Journal of Geophysical Research-Solid Earth. 103:17775-17790.   10.1029/98jb01077   AbstractWebsite

One of the first applications of anisotropy of magnetic susceptibility (AMS) was an attempt to determine flow directions from mafic dikes [Khan, 1962]. Since the seminal work of Knight and Walker [1988] defining the expected behavior of AMS in response to magma flow, there has been increasing interest in using AMS for this purpose. Here we present a quantitative method for interpretation of AMS data from dikes, using a parametric bootstrap. First, dikes must be sampled with at least five land preferrably more) samples from within 10 cm of the dike margin. The distributions of the eigenvalues and eigenvectors of the AMS tensor are delineated by calculating eigenparameters of many bootstrapped paradata sets. We generate paradata sets by first selecting a sample at random, then calculating a replacement set of data by drawing tensor elements from normal distributions with the mean and standard deviation of the entire site. The bounds containing 95% of the eigenparameters of the bootstrapped data serve as confidence limits for the parameter of interest. Classification of dikes proceeds as follows: Sites whose maximum and intermediate eigenvalues could not be distinguished are deemed uninterpretable. In addition, sites with principal eigenvectors with angles > 45 degrees away from the dike margin (inverse) or with markedly different directions on either side of the dike (scissored) are excluded. The remaining dikes are classified as having unique flow direction information if the principal eigenvectors from at least one side are distinct from the dike plane based on the distribution of the bootstrapped principal eigenvectors. If neither side has principal eigenvectors distinct from the dike plane, the dikes are classified as having lineation information only. A study comprising 251 dikes from the Troodos ophiolite has 151 sites with directional data, 38 sites with lineations only, 7 inverse sites, 5 scissored sites, and 55 sites not fitting into any other category. The flow directions interpreted from the data were generally southerly, toward a fossil transform zone.