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Orientation tensor fabric intensity and shape

Source: R/fabric_plots.R
vollmer.Rd

Fabric intensity and shape parameters of the orientation tensor based on Vollmer (1990)

Usage

vollmer(x)

Arguments

x

object of class "Vec3", "Line", "Ray", "Plane", "Pair", or "Fault", where the rows are the observations and the columns are the coordinates.

Value

numeric vector containing the fabric shape and intensity indices:

P

Point (Vollmer 1990). Range: (0, 1)

G

Girdle (Vollmer 1990). Range: (0, 1)

R

Random (Vollmer 1990). Range: (0, 1)

B

Cylindricity (Vollmer 1990). Range: (0, 1)

C

Cylindricity or Fabric strength (Woodcock 1977). Range: (0, Inf)

I

Cylindricity or Fabric intensity (Lisle 1985). Range: (0, 5)

D

"Distance" from uniformity, linear from R to P, and R to G (Vollmer 2020). Range: (0, 1). End members are: uniform D = 0, girdle D = 0.5, cluster D = 1. The 99% level for a test against uniformity for a sample size of 300 is D = 0.1.

U

Uniformity statistic of Mardia (1972)

References

Lisle, Richard J. (1985): "The use of the orientation tensor for the description and statistical testing of fabrics." Journal of Structural Geology 7.1: 115-117.

Mardia, Kantilal Varichand. (1975): "Statistics of directional data." Journal of the Royal Statistical Society Series B: Statistical Methodology 37.3: 349-371.

Vollmer, Frederick W. (1990): "An application of eigenvalue methods to structural domain analysis." Geological Society of America Bulletin 102.6: 786-791.

Vollmer, Frederick W. (2020): "Representing Progressive Fabric Paths on a Triangular Plot Using a Fabric Density Index and Crystal Axes Eigenvector Barycenters." Geological Society of America Abstracts. Vol. 52.

Woodcock, N. H. (1977): "Specification of fabric shapes using an eigenvalue method." Geological Society of America Bulletin 88.9: 1231-1236.

See also

shape_params(), ortensor(), vollmer_plot()

Examples

set.seed(20250411)
mu <- Line(120, 50)
x <- rvmf(100, mu = mu, k = 1)
vollmer(x)
#>           P           G           R           B           C           I 
#>  0.13716550  0.06777223  0.79506227  0.20493773  0.49800008  2.45026231 
#>           D           U 
#>  0.15687782 12.30532499 

# Pair objects:
vollmer(simongomez)
#>            P            G            R            B            C            I 
#>   0.06798346   0.93155564   0.20395038   0.99953910   2.18056889   2.42554552 
#>            D            U 
#>   0.52339268 109.57596054