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Flinn Diagram

Source: R/fabric_plots.R
flinn_plot.Rd

Plots the strain ratios X/Y against Y/Z and shows the strain intensity and the strain symmetry after Flinn (1965)

Usage

flinn_plot(
  x,
  main = "Flinn diagram",
  R.max = NULL,
  log = FALSE,
  add = FALSE,
  ...
)

# Default S3 method
flinn_plot(
  x,
  main = "Flinn diagram",
  R.max = NULL,
  log = FALSE,
  add = FALSE,
  ...
)

# S3 method for class 'ortensor'
flinn_plot(x, ...)

# S3 method for class 'ellipsoid'
flinn_plot(x, ...)

# S3 method for class 'spherical'
flinn_plot(x, ...)

# S3 method for class 'list'
flinn_plot(x, ...)

Arguments

x

accepts the following objects: a two-column matrix where first column is the ratio of maximum strain and intermediate strain (X/Y) and second column is the the ratio of intermediate strain and minimum strain (Y/Z); objects of class "Vec3", "Line", "Ray", "Plane", "ortensor" and "ellipsoid" objects. Tensor objects can also be lists of such objects ("ortensor" and "ellipsoid").

main

character. The main title (on top).

R.max

numeric. Maximum aspect ratio for scaling.

log

logical. Whether the axes should be in logarithmic scale.

add

logical. Should data be plotted to an existing plot?

...

plotting arguments passed to graphics::points()

Value

list. Relative magnitudes of X, Y and Z (Z=1).

Details

Strain symmetry (Flinn 1965): $$k = \frac{s_1/s_2 - 1}{s_2/s_3 - 1}$$ where \(s_1 \geq s_2 \geq s_3\) the semi-axis lengths of the ellipsoid. The value ranges from 0 to \(\infty\), and is 0 for oblate ellipsoids (flattening), 1 for plane strain and \(\infty\) for prolate ellipsoids (constriction).

and strain intensity (Flinn 1965): $$d = \sqrt{(s_1/s_2 - 1)^2 + (s_2/s_3 - 1)^2}$$

References

Flinn, D. (1965). On the Symmetry Principle and the Deformation Ellipsoid. Geological Magazine, 102(1), 36–45. doi:10.1017/S0016756800053851

See also

ellipsoid() class, ortensor() class, flinn() for Flinn's strain parameters.

Other fabric-plot: hsu_plot(), vollmer-plot, woodcock_plot()

Examples

data(holst)
R_XY <- holst[, "R_XY"]
R_YZ <- holst[, "R_YZ"]
flinn_plot(cbind(R_XY, R_YZ), log = FALSE, col = "#B63679", pch = 16)

flinn_plot(cbind(R_XY, R_YZ), log = TRUE, col = "#B63679", pch = 16, type = "b")


# ellipsoid objects
hossack_ell <- lapply(seq.int(nrow(hossack1968)), function(i) {
  ellipsoid_from_stretch(hossack1968[i, 3], hossack1968[i, 2], hossack1968[i, 1])
})
flinn_plot(hossack_ell, col = "#B63679", pch = 16, log = TRUE)


set.seed(20250411)
mu <- Line(120, 50)
x <- rvmf(100, mu = mu, k = 1)
flinn_plot(x, R.max = 2)

set.seed(20250411)
y <- rvmf(100, mu = mu, k = 20)
flinn_plot(ortensor(y), col = "red", R.max = 2, add = TRUE)