Orientation tensor

3D orientation tensor, which characterize data distribution using eigenvalue method. See (Watson 1966, Scheidegger 1965).

Usage

# S3 method for class 'spherical'
ortensor(x, norm = TRUE, w = NULL)

ortensor(x, norm = TRUE, w = NULL)

Arguments

x: object of class "Vec3", "Line", "Ray", or "Plane", where the rows are the observations and the columns are the coordinates.
norm: logical. Whether the tensor should be normalized or not.
w: numeric. weightings

Value

matrix

Details

The normalized orientation tensor is given as $$D = \frac{1}{n} (x_i, y_i, z_i) (x_i, y_i, z_i)^T$$

References

Watson, G. S. (1966). The Statistics of Orientation Data. The Journal of Geology, 74(5), 786–797.

Scheidegger, A. E. (1964). The tectonic stress and tectonic motion direction in Europe and Western Asia as calculated from earthquake fault plane solutions. Bulletin of the Seismological Society of America, 54(5A), 1519–1528. https://doi.org/10.1785/BSSA05405A1519

Examples

set.seed(20250411)
x <- rfb(100, mu = Line(120, 50), k = 1, A = diag(c(10, 0, 0)))
ortensor(x, w = runif(nrow(x)))
#>             [,1]        [,2]        [,3]
#> [1,]  0.15892037 -0.19509505 -0.09467572
#> [2,] -0.19509505  0.74173788 -0.05769709
#> [3,] -0.09467572 -0.05769709  0.97105679