Subgrain‐Size Piezometer Calibrated for EBSD

Calculates differential stress using the Subgrain‐Size Piezometer of Goddard et al. (2020). Uses Monte Carlo sampling for propagating parameter uncertainties in flow model.

Usage

subgrainsize_piezometry(
  lambda,
  sd = NULL,
  calibrated = TRUE,
  min = c("q", "fo90", "fo50"),
  sim = 1e+06,
  propagate_err = TRUE
)

Arguments

lambda

mean line intercept length in μm or units object.

sd

(optional) Standard deviation of lambda

calibrated

logical. Whether the calibration of Holyoke and Kronenberg (2010) is considered or not.

min

character. The Mineral uses. one of "q" for quartz, "fo90" for Olive with 90% Forsterite, or "fo50" for Olivine with 50% Forsterite.

sim

non-negative number. Number of Monte Carlo simulations

propagate_err

logical. Whether errors of the flow law parameters should be propagated. TRUE by default.

Value

list. Differential stress in MPa. If Monte Carlo Simulation was used, and object of class "MCS" is returned (see summary() for detailed description of output). The piezometer produce log-normal distributed estimates considering the uncertainties in the equation parameter. Hence it is recommended to report the median (or geometric mean), and the interpercentile range.

Details

The sub-grain size piezometer is $$\frac{\lambda}{b} = 10^a \left(\frac{\sigma}{\mu}\right)^b$$ where \(\lambda\) is the mean line intercept length, \(b\) is the Burgers vector, \(\sigma\) is the differential stress, \(\mu\) is the shear modulus, and \(a\) and \(b\) are the empirical exponents.

References

Goddard, R. M., Hansen, L. N., Wallis, D., Stipp, M., Holyoke, C. W., Kumamoto, K. M., & Kohlstedt, D. L. (2020). A Subgrain‐Size Piezometer Calibrated for EBSD. Geophysical Research Letters, 47(23). https://doi.org/10.1029/2020GL090056

See also

grainsize_piezometry(), units::set_units()

Examples

set.seed(20250411)
subgrainsize_piezometry(9, min = "fo50") |> summary() # 420 MPa
#> Statistical summary of 1000000 Monte Carlo simulations
#> 
#> Median:                      560 MPa 
#> 95% interpercentile range:   34 - 3600 MPa 
#> Standard error in log-space: 0.000516207
#> Student's t-Test:            p<0.05
subgrainsize_piezometry(18, min = "q") |> summary() # 240 MPa
#> Statistical summary of 1000000 Monte Carlo simulations
#> 
#> Median:                      220 MPa 
#> 95% interpercentile range:   11 - 1500 MPa 
#> Standard error in log-space: 0.00054436
#> Student's t-Test:            p<0.05