7. Strain and Vorticity Analysis

Tobias Stephan

2025-09-15

library(structr)

Import some R-phi data

data(ramsay)
head(ramsay)
#>         R   phi
#> [1,] 1.52 27.59
#> [2,] 1.33 36.91
#> [3,] 1.78 27.31
#> [4,] 1.51 17.73
#> [5,] 1.70 24.45
#> [6,] 1.39 45.84

Calculate densities in Rf-Phi space:

out <- hypercontour(ramsay, angfmt = "deg", proj = 'rfp')

Rf/phi plot

image(out$x, out$y, out$z, asp = ifelse(out$proj != 'rfp', 1, NA),
  ylim = c(1, out$rmax),
  xlab = bquote(varphi*' ('*degree*')'), ylab = bquote(R[f]),
  main = 'Rf/phi plot', 
 col = viridis::viridis(50)
 )
contour(out$x, out$y, out$z, add = TRUE, lwd = .5)
points(out$points, col = "grey", pch = 16, cex = .5)

Equidistant polar plot:

out2 <- hypercontour(ramsay, angfmt = "deg", proj = 'eqd')
 
# calculate some colors
levels <- pretty(range(out2$z, na.rm = TRUE), 20)
cols <- viridis::viridis(n = length(levels) - 1)
 
plot(out2$x, y = out2$y, 'n', xlab = NULL, ylab = NULL, asp = 1, axes = FALSE, ann = FALSE)
graphics::.filled.contour(out2$x, out2$y, out2$z, levels = levels, col = cols)
# points(out2$points, col = "grey", cex = .5)
lines( out2$frame, lwd = 2)
title(main = 'Elliot plot')

Vorticity analysis

The rigid grain net after (Jessup et al. 2007) plots the distribution the strain ratio (R) of orientation (phi) of porphyroclast over the theoretical distribution of tailless clasts. The plot estimates the critical threshold Rc marking the transition between the stable-sink position and infinitely rotating porphyroclasts. This threshold can be interpreted as the the mean kinmatic vorticity number. Here the Rc is estimated using the bootstrap method described in Stephan et al. (2025).

ramsay_shift <- ramsay
ramsay_shift[, 2] <- tectonicr::circular_mean(ramsay[, 2]) - ramsay[, 2] # assuming the mean orientation resembles the foliation

RGN_plot(ramsay_shift, col = "#B63679")
title(main = 'Rigid Grain Net')