Skip to contents

Orientation tensor

Source: R/ortensor.R
ortensor.Rd

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

Usage

is.ortensor(object)

as.ortensor(object)

ortensor(x, norm, w, shift)

# S3 method for class 'Vec3'
ortensor(x, norm = TRUE, w = NULL, shift = NULL)

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

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

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

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

Arguments

object

3x3 matrix

x

object of class "Vec3", "Line", "Ray", "Plane", "Pair", or "Fault", 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

shift

logical. Only for "Pair" objects: Tensor is by default shifted towards positive eigenvalues, so it could be used as Scheidegger orientation tensor for plotting. When original Lisle tensor is needed, set shift to FALSE.

Value

ortensor() returns an object of class "ortensor"

is.ortensor returns TRUE if x is an "ortensor" object, and FALSE otherwise.

as.ortensor coerces a 3x3 matrix into an "ortensor" object.

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. doi:10.1785/BSSA05405A1519

Lisle, R. (1989). The Statistical Analysis of Orthogonal Orientation Data. The Journal of Geology, 97(3), 360-364.

See also

inertia_tensor()

Other ortensor: ot_eigen(), strain_shape

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)))
#> Orientation tensor
#>            [,1]        [,2]        [,3]
#> [1,]  0.1953747 -0.22524425 -0.09751770
#> [2,] -0.2252442  0.69749852 -0.01237374
#> [3,] -0.0975177 -0.01237374  1.10031778

test <- as.ortensor(diag(3))
is.ortensor(test)
#> [1] TRUE

# Orientation tensor for Pairs
ortensor(angelier1990$TYM)
#> Orientation tensor
#>             [,1]        [,2]        [,3]
#> [1,] -0.33014781  0.17226487 -0.03483861
#> [2,]  0.17226487 -0.15036372 -0.06174581
#> [3,] -0.03483861 -0.06174581  0.48051152