Stress Inversion for Fault-Slip Data

Convenience function for direction inversion of fault-slip data to derive the reduced stress tensor.

Usage

slip_inversion(
  x,
  method = c("michael", "angelier", "hansen", "yamaji", "wissi"),
  ...
)

Arguments

x: "Fault" object where the rows are the observations, and the columns the coordinates. Object must be complete, i.e. no NA values. For Michael's, Angelier's, and Yamaji-Sato's methods, at least 4 rows of fault measurements are required, while Hansen's method requires at least 7.
method: character. The inversion algorithm, one of "michael" (the default) for a bootstrapped linear inversion after Micheal (1984), "angelier" for an iterative direct inversion after Angelier (1990) and Mostafa (2005), "yamaji" for direct inversion using the 5d parameter space after Yamaji and Sato (2006), "hansen" for direct inversion using the 9d parameter space after Hansen (2013), and "wissi" for the Weighted Iterative Sigma-Space Inversion (WISSI).
...: arguments passed to slip_inversion_angelier(), slip_inversion_michael(), slip_inversion_yamaji_sato(), slip_inversion_hansen(), or slip_inversion_wissi() depending on method.

Value

a named list with the following components:

stress_tensor: "ellipsoid" object. Best-fit devitoric stress tensor in input coordinate frame
principal_axes: "Line" objects. Orientation of the principal stress axes as unit vectors (max to min)
tensor_params: the four tensor parameters (Eq. 4.87)
principal_vals: eigenvalues of the stress tensor (\(\sigma_1 >= \sigma_2 >= \sigma_3\))
stress_shape: list Stress shape ratio. See stress_shape().
misfit: list. Misfit parameters. See slip_inversion_misfit().
SHmax: numeric. Direction of maximum horizontal stress (in degrees)
tau_mean: numeric. Average resolved shear stress on each plane. Should be close to 1.
stress_components: matrix. The resolved shear and normal stresses, the slip and dilation tendency on each plane. See tau2shearnorm() and tau2tendency().
n_iter: number of Mostafa iterations performed
method: character. The inversion method used, equal to method argument.

References

Angelier, J. (1990). Inversion of field data in fault tectonics to obtain the regional stress—III. A new rapid direct inversion method by analytical means. Geophys. J. Int, 103, 363–376. doi:10.1111/j.1365-246X.1990.tb01777.x

Hansen, J. A. (2013). Direct inversion of stress, strain or strain rate including vorticity: A linear method of homogenous fault-slip data inversion independent of adopted hypothesis. Journal of Structural Geology, 51, 3–13. doi:10.1016/j.jsg.2013.03.014

Michael, A. J. (1984). Determination of stress from slip data: Faults and folds. Journal of Geophysical Research: Solid Earth, 89(B13), 11517–11526. doi:10.1029/JB089iB13p11517

Yamaji, A., & Sato, K. (2006). Distances for the solutions of stress tensor inversion in relation to misfit angles that accompany the solutions. Geophysical Journal International, 167(2), 933–942. doi:10.1111/j.1365-246X.2006.03188.x

Examples

set.seed(20250411)

# Use Angelier 1990 examples
nx <- length(angelier1990)

par(mfrow = c(nx/2, nx/2), mar = c(4, 1, 4, 1))
invisible(lapply(seq_len(nx), function(i) {
  x <- angelier1990[[i]]

  # Inversion after Michael (1984)
  res_michael <- slip_inversion(x, method = "michael", n_iter = 100, n = 100, res = 100)

  # Inversion after Angelier (1990)
  res_angelier <- slip_inversion(x, method = "angelier")
  
  res_yamaji <- slip_inversion(x, method = "yamaji")

  res_hansen <- slip_inversion(x, method = "hansen", type = "6d")
  
  res_wissi <- slip_inversion(x, method = 'wissi')

  stereoplot(title = names(angelier1990)[i], guides = FALSE)
  fault_plot(x, col = "gray80")
  points(res_michael$principal_axes, pch = 1:3, col = 2)
  points(res_angelier$principal_axes, pch = 1:3, col = 3)
  points(res_yamaji$principal_axes, pch = 1:3, col = 4)
  points(res_hansen$principal_axes, pch = 1:3, col = 5)
  points(res_wissi$principal_axes, pch = 1:3, col = 6)
  legend("topleft",
    pch = 1,
    legend = c("Michael (1984)", "Angelier (1990)", "Yamaji & Sato (2006)", 
      "Hansen (2013)", "WISSI"),
    col = 2:6, cex = 0.8
  )
  legend("bottom",
    pch = 1:3,
    legend = c("S1", "S2", "S3"),
    horiz = TRUE,
    cex = 0.8
  )
}))

Usage

Arguments

Value

References

See also

Examples