Uncertainties of direction stress inversion after Yamaji and Sato (2006)

Bootstrap resampling to evaluate solution precision (Section 6). Yields B stress tensors from resampled datasets. The dispersion of these tensors on \(S^5\) approximates the noise level of the data (Eq. 37).

Usage

slip_inversion_yamaji_sato_boot(
  x,
  weights = NULL,
  n_iter = 100L,
  conf.level = 0.95,
  flip = FALSE,
  ...
)

Arguments

x

object of class "Pair" or "Fault" with at least 4 rows.

weights

numeric. Weightings for the faults. Must have the same length as x

n_iter

integer. Number of bootstrap replicates (100 by default)

conf.level

numeric. Confidence level of the interval (0.95 by default)

flip

logical. Flip if you want to have the negative stress tensor, i.e. sigma 1 and 3 will be flipped.

...

optional parameters passed to confidence_ellipse()

Value

List identical to slip_inversion_michael() and additional list entries:

theta

length-B vector of angular stress distances from optimal

dispersion

mean angular stress distance (Theta-bar); approximates the noise level p of the data (Fig. 8 of paper)

sd

standard deviation of Theta values

D_bar

mean Orife-Lisle distance from optimal

DM_bar

mean Michael distance from optimal

See also

slip_inversion_yamaji_sato()

Examples

set.seed(20250411)

# Use Angelier examples:
nx <- length(angelier1990)
par(mfrow = c(2, length(angelier1990)/2))

invisible(lapply(seq_len(nx), function(i) {
  # inversion
  x <- angelier1990[[i]]
  res <- slip_inversion_yamaji_sato_boot(x, n_iter = 100, n = 1000, res = 100)

  # some stress shape
  phi_val <- round(res$phi_CI, 2)

  # misfit
  rup_val <- round(res$rup_CI, 2)

  # Plot the faults (color-coded by RUP%) and show the principal stress axes
  stereoplot(guides = FALSE)
  stereo_shmax(res$SHmax)
  fault_plot(x, col = assign_col(res$misfit$rup))
  stereo_confidence(res$principal_axes_CI$sigma1, col = 2)
  stereo_confidence(res$principal_axes_CI$sigma2, col = 3)
  stereo_confidence(res$principal_axes_CI$sigma3, col = 4)
  text(res$principal_axes, label = rownames(res$principal_axes), col = 2:4, adj = -.25)
  legend("topleft", col = 2:4, legend = rownames(res$principal_axes), pch = 16)
  title(
  main = names(angelier1990)[i],
  sub = bquote(atop(varphi ~ "(95% CI)" == "[" * .(phi_val[1]) * "," ~ .(phi_val[2]) * "]",
  ~ bar("RUP") ~ "(95% CI)" == "[" * .(rup_val[1]) * "," ~ .(rup_val[2]) * "] %")
  ))
}))