ort-eigen: Decomposition of Orientation Tensor in 2D

In tectonicr: Analyzing the Orientation of Maximum Horizontal Stress

Decomposition of Orientation Tensor in 2D

Description

Spectral decomposition of the 2D orientation tensor into two Eigenvectors and corresponding Eigenvalues provides provides a measure of location and a corresponding measure of dispersion, respectively.

Usage

ot_eigen2d(x, w = NULL, scale = FALSE)

principal_direction(x, w = NULL)

axial_strength(x, w = NULL)

axial_dispersion(x, w = NULL)

Arguments

x	numeric. Axial angular data (in degrees).
w	(optional) Weights. A vector of positive numbers and of the same length as x.
scale	logical. Whether the Eigenvalues should be scaled so they sum up to 1. Only applicable when weighting are specified, otherwise the eigenvalues are always scaled.

Details

The Eigenvalues (\lambda_1 > \lambda_2) can be interpreted as the fractions of the variance explained by the orientation of the associated Eigenvectors. The two perpendicular Eigenvectors (a_1, a_2) are the "principal directions" with respect to the highest and the lowest concentration of orientation data.

The strength of the orientation is the largest eigenvalue \lambda_1 normalized by the sum of the eigenvalues (scale=TRUE). Then \lambda_2 = 1-\lambda_1 is a measure of dispersion of 2D orientation data with respect to a_1.

Value

ot_eigen2d returns a list of the Eigenvalues and the axial angles corresponding to the Eigenvectors. principal_direction(), axial_strength() and axial_dispersion() are convenience functions to return the orientation of the largest eigenvalue, the orientation strength, the axial dispersion respectively.

Note

Eigenvalues and Eigenvectors of the orientation tensor (inertia tensor) are also called "principle moments of inertia" and "principle axes of inertia", respectively.

See Also

ortensor2d()

Examples

test <- rvm(100, mean = 0, k = 10) / 2
ot_eigen2d(test)

data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
sa_eig <- ot_eigen2d(sa.por$azi.PoR, w = weighting(san_andreas$unc), scale = TRUE)
print(sa_eig)

rose(sa.por$azi.PoR, muci = FALSE)
rose_line(sa_eig$vectors,
  col = c("red", "green"),
  radius = sa_eig$values, lwd = 2
)
graphics::legend("topright",
  legend = round(sa_eig$values, 2),
  col = c("red", "green"), lty = 1
)

principal_direction(sa.por$azi.PoR)

axial_strength(sa.por$azi.PoR)

axial_dispersion(sa.por$azi.PoR)

tectonicr documentation built on Dec. 12, 2025, 9:06 a.m.