Grain-Size Piezometry

Calculates differential stress from grain size. Uses Monte Carlo sampling for propagating parameter uncertainties in flow model.

Usage

grainsize_piezometry(
  d,
  sd = NULL,
  model = c("Stipp-reg2-3", "Stripp-reg1", "Cross-1", "Cross-sliding"),
  sim = 1e+06,
  propagate_err = TRUE
)

Arguments

d

numeric. Grain size in μm or units object

sd

(optional) Standard deviation of d

model

character. One of

"Stipp-reg2-3": Piezometer for dislocation creep regime 2 and 3 (for deviatoric stress <368 MPa) after Stipp and Tullis (2003)
"Stripp-reg1": Piezometer for dislocation creep regime 1 (deviatoric stress ≥368 MPa) after Stipp and Tullis (2003)
"Cross-1": Piezometer after Cross et al. (2017) for 1 μm step size resolution in EBSD data
"Cross-sliding": Sliding resolution piezometer after Cross et al. 2017. According to authors, more accurately estimates stress in fine-grained (<10 μm) samples

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

General formula for grain-size piezometer is: $$\sigma = \left(\frac{d}{k}\right)^\frac{1}{n}$$ where $\sigma$ is the differential stress, $d$ is the grain size, and $k$ and $n$ are empirical parameters.

References

Stipp, M., & Tullis, J. (2003). The recrystallized grain size piezometer for quartz. Geophysical Research Letters, 30(21), 1–5. https://doi.org/10.1029/2003GL018444

Cross, A. J., Prior, D. J., Stipp, M., & Kidder, S. (2017). The recrystallized grain size piezometer for quartz: An EBSD-based calibration. Geophysical Research Letters, 44(13), 6667–6674. https://doi.org/10.1002/2017GL073836

Examples

set.seed(20250411)
grainsize_piezometry(12.2) |> summary() # 92
#> Statistical summary of 1000000 Monte Carlo simulations
#> 
#> Median:                      92 MPa 
#> 95% interpercentile range:   49 - 190 MPa 
#> Standard error in log-space: 0.000151644
#> Student's t-Test:            p<0.05
grainsize_piezometry(31) |> summary() # 44
#> Statistical summary of 1000000 Monte Carlo simulations
#> 
#> Median:                      44 MPa 
#> 95% interpercentile range:   24 - 86 MPa 
#> Standard error in log-space: 0.00014041
#> Student's t-Test:            p<0.05