Frederick W. Vollmer

An application of eigenvalue methods to structural domain analysis

The subdivision of a geologic map into structural domains involves the location of regions in which the rock fabric has certain geometrical characteristics; typically, foliation data should share a common axis. The location of such domains involves working interactively with map and equal-area projections of the data set, a tedious and often subjective process. Eigenvector methods can quantify this type of analysis. A set of four eigenvalue-based indexes assists in discriminating among fabric distributions, particularly between strong and weak cylindrical distributions. These indexes form the basis of a triangular diagram for distinguishing among point, girdle, random, and cylindrical fabrics. A domain search proceeds by subdividing the data set and attempting to maximize the total cylindricity, or other characteristic. The method has been applied to a set of foliation data from a fold nappe in the Western Gneiss Region of the Norwegian Caledonides. The resulting domains define a late fold that refolds the recumbent nappe. Lineation and fold-axis data from the area support the results of the domain search. This method may be valuable in other areas of complex geometry.

Structures of the Medial Ordovician Flysch of Eastern New York: Deformation of Synorogenic Deposits in an Overthrust Environment

Synchronous deposition and deformation of the flysch deposits of eastern New York occurred during the westward overthrusting of the Taconic Allochthon in medial Ordovician time. An observed spatial west to east increase in the intensity of deformation is believed to represent the progressive development of structures through time. Folding initiated as upright kinks and buckles with fold axes north-south and approximately horizontal. Fold axes then rotated towards an east-west shear direction with fold tightness and asymmetry increasing and fold axial planes rotating to the west. Shear zones with a phacoidally cleaved fabric and small thrust faults strengthened the east over west structural asymmetry. After attaining intermediate dips (roughly 45°) the fold axial planes began to rotate back toward vertical and lose asymmetry. Bulk flattening and shear competed in the microstructural development of the flysch with slaty cleavage and phacoidal cleavage the corresponding end-products. Shear zones and thrust faults evolved into master faults, producing a large-scale imbricate structure in the flysch. Melange originated both as tectonically broken formations and as disrupted olistostromic deposits. The dominant mechanism for melunge formation appears to have been the disruption of interbedded graywacke and shale sequences under large strains. Imbrication of the original stratigraphic sequence has allowed the incorporation of older rocks, including shelf carbonate, into the melange as blocks and large slivers. The progressive sequence of structures observed within the flysch of eastern New York represents deformation within the leading edge of an accretionary prism developed over continental lithosphere.

A computer model of sheath-nappes formed during crustal shear in the Western Gneiss Region, central Norwegian Caledonides

Abstract The eastern Western Gneiss Region of central Norway is part of the deepest exposed Norwegian Caledonides, where basement gneisses and an overlying thrust-nappe sequence have been folded into large fold-nappes. Structural analysis of a fold-nappe within the central part of the district (the Grovudal area) suggests that it has a strongly sheath-like form, and that other fold-nappes of the Western Gneiss Region may also have sheath-like forms. The structural history within the Grovudal area is dominated by intense east-directed subhorizontal shear in an overthrust sense, followed by asymmetric refolding with an easterly vergence. A computer-generated kinematic model was developed to test whether the regional interference patterns could be explained by sheath-fold development during this type of deformation. The computer model shows that the major regional interference patterns could have been formed by such a kinematic history, but does not rule out other possibile histories. The proposed kinematic history is, however, compatible with the regional tectonic history of the main Caledonian nappe pile, suggesting that the complex nappe interference patterns typical of the region were formed in a kinematically simple, but intense, ductile deformation associated with Caledonian continental imbrication.

C program for automatic contouring of spherical orientation data using a modified Kamb method

Abstract Kambs method for contouring density diagrams is a simple technique for the preliminary analysis and comparison of orientation data distributions. The method is based on the departure from a uniform distribution, and, unlike the Schmidt method, the dependence of contours on sample size is limited. Several improvements can be made, particularly with regard to the implementation of automatic contouring. To reduce smoothing, the expected count for a random sample drawn from a uniform distribution can be decreased. This gives more localized density estimates that can improve the resolution of features. Density estimates are done directly on the sphere for accuracy. This also permits contouring on stereographic and other nonequal area projections, and accommodates vectorial data. Weighting functions provide better density estimates and increase the smoothness of contour lines. These concepts are implemented in the C program Sphere Contour. Options include selection of data rotation, linear or planar data, equal area or stereographic projection, upper or lower hemisphere, and scatter diagrams. Graphics output is either to the screen (MS-DOS) or to a computer-aided drafting file (AutoCAD DXF). The program is modified easily for other computer systems and graphics devices.

Early deformation in the Svecokarelian greenstone belt of the Kiruna iron district, northern Sweden

Abstract The Proterozoic iron ores of the Kiruna district, northern Sweden, occur as discontinous lenses of magnetite and hematite up to 4 kilometers in length within a sequence of felsic porphyries. The association of low-grade felsic volcanics and sedimentary rocks with basaltic pillow lavas and granitic rocks shows a strong similarity to typical Archean greenstone belts. Primary younging indicators, bedding/cleavage relationships, and minor fold symmetries through the district suggest that the area occupies the eastern limb of a major antiform, cored by granitic rocks to the west. A steep regional cleavage, inhomogeneously developed through the district, suggests one major episode of compressional deformation. The cleavage and associated flattened clasts indicate a compression direction plunging 10°WNW. Elongate clasts, boudins, and fibrous veins indicate a strong extension plunging 60°SSE, parallel to fold hinge lines. Boudinage of the major ore bodies to produce their present distribution is compatib...

ANTEVS: a quantitative varve sequence cross-correlation technique with examples from the Northeastern USA

Varve correlation by hand was successfully applied by Ernst Antevs to establish the New England Varve Chronology, which has since been updated to form the North American Varve Chronology (NAVC). Although these methodologies are successful, numerical techniques can assist in finding and evaluating correlations. A quantitative numerical method for varve correlation using time-series Fourier analysis and cross-correlation is proposed and implemented in the computer program ANTEVS (Automatic Numerical Time-series Evaluation of Varve Sequences). The technique is demonstrated by correlating several varve sequences in the northeastern USA. Tests on NAVC data from the Hudson and Connecticut River Valleys show strong positive local and regional cross-correlations, confirming the methods validity. Guidelines for the evaluation of the correlation are determined by cross-testing NAVC sequences, suggesting minimum values for the cross-correlation statistic r, and z-score, a measure of its variation. Field relationships and careful examination of the data graphs and correlograms, however, must accompany numerical analysis. We then apply the method to previously uncorrelated sequences. A Champlain Valley varve sequence at Whallonsburg, NY, is compared with the NAVC, and to another Champlain Valley sequence at Keeseville, NY. No match is found with the NAVC, although none was expected as the sequences are of slightly different ages. A weak correlation is found between the two Champlain Valley sequences. This correlation is not significant and disagrees with the stratigraphic interpretation of the sites. We suggest that an overly strong local sedimentary signal at one of the sites masks the regional signal necessary for positive cross-correlation.

Automatic contouring of geologic fabric and finite strain data on the unit hyperboloid

Abstract Fabric and finite strain analysis, an integral part of studies of geologic structures and orogenic belts, is commonly done by the analysis of particles whose shapes can be approximated as ellipses. Given a sample of such particles, the mean and confidence intervals of particular parameters can be calculated, however, taking the extra step of plotting and contouring the density distribution can identify asymmetries or modes related to sedimentary fabrics or other factors. A common graphical strain analysis technique is to plot final ellipse ratios, R f , versus orientations, ϕ f on polar Elliott or R f / ϕ plots to examine the density distribution. The plot may be contoured, however, it is desirable to have a contouring method that is rapid, reproducible, and based on the underlying geometry of the data. The unit hyperboloid, H 2 , gives a natural parameter space for two-dimensional strain, and various projections, including equal-area and stereographic, have useful properties for examining density distributions for anisotropy. An index, I a , is given to quantify the magnitude and direction of anisotropy. Elliott and R f / ϕ plots can be understood by applying hyperbolic geometry and recognizing them as projections of H 2 . These both distort area, however, so the equal-area projection is preferred for examining density distributions. The algorithm presented here gives fast, accurate, and reproducible contours of density distributions calculated directly on H 2 . The algorithm back-projects the data onto H 2 , where the density calculation is done at regular nodes using a weighting value based on the hyperboloid distribution, which is then contoured. It is implemented as an Octave compatible MATLAB function that plots ellipse data using a variety of projections, and calculates and displays contours of their density distribution on H 2 .