An application of eigenvalue methods to structural domain analysis

Abstract

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.

Strain within the ultrahigh-pressure Western Gneiss region of Norway recorded by quartz CPOs

“…For a semi-quantitative measure of the degree to which a CPO defines a maximum or a girdle, we use Pfch5 (Mainprice 2005) to calculate the P, G and R indices of the c-axis distribution (Woodcock 1977;Vollmer 1990;Ulrich & Mainprice 2005). The magnitudes of the indices reflect how well the data define a point (P), girdle (G) or random (R) prism <a> slip basal <a> slip basal <a> + prism <a> "mixed <a>" slip prism [c] slip [c] <a>…”

Descriptive tools for the analysis of texture projects with large datasets using MTEX : strength, symmetry and components

“…Later Lisle (1985) used a characteristic developed by Mardia (1972) and more recently by Mardia & Jupp (2000): I = (15n/2) (l 2 1 + l 2 2 + l 2 3 − 1/3). Unfortunately the equation was misprinted in Lisle (1985) and was reproduced with the error in Vollmer (1990) where the value of I depends on the pole figure symmetry, the maximum value is 5.00 for a perfect point maximum and 0.3125 for a girdle.…”

Full-field predictions of ice dynamic recrystallisation under simple shear conditions

“…3 , and Vollmer, 1990). Eigenvalues were calculated according to Woodcock (1977) (see Llorens et al, 2016).…”