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Stress Inversion for Fault-Slip Data

Source: R/stress_inversion.R
slip_inversion.Rd

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

Usage

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

Arguments

x

"Fault" object where the rows are the observations, and the columns the coordinates. Object must be cmpolete, i.e. no NA values. For Michael's and Angelier'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), and "hansen" for direct inversion using the 9d parameter space after Hansen (2013).

...

arguments passed to slip_inversion_angelier(), slip_inversion_michael(), or slip_inversion_hansen() 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. https://doi.org/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. https://doi.org/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. https://doi.org/10.1029/JB089iB13p11517

See also

Other stress-inversion: Fault_PT(), slip_inversion_angelier(), slip_inversion_hansen(), slip_inversion_hansen_boot(), slip_inversion_michael(), slip_inversion_simple()

Examples

set.seed(20250411)
# Use Angelier examples
par(mfrow = c(1, length(angelier1990)))
invisible(lapply(angelier1990, function(x) {
  # 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_hansen <- slip_inversion(x, method = "hansen", type = "6d")

  stereoplot(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_hansen$principal_axes, pch = 1:3, col = 4)
  legend("topleft",
    pch = 1,
    legend = c("Michael (1984)", "Angelier (1990)", "Hansen (2013)"),
    col = 2:4
  )
  legend("bottomright",
    pch = 1:3,
    legend = c("S1", "S2", "S3")
  )
}))