Direction of Maximum Horizontal Stress in PoR reference system

Models the direction of maximum horizontal stress \(\sigma_{Hmax}\) in the Euler pole (Pole of Rotation) coordinate reference system. When type of plate boundary is given, it also gives the deviation from the theoretically predicted azimuth of \(\sigma_{Hmax}\), the deviation, and the normalized \(\chi^2\) statistics.

Usage

PoR_shmax(df, PoR, type = c("none", "in", "out", "right", "left"))

Arguments

df

data.frame containing the coordinates of the point(s) (lat, lon), the direction of \(\sigma_{Hmax}\) azi and its standard deviation unc (optional)

PoR

"data.frame" or object of class "euler.pole" containing the geographical coordinates of the Euler pole

type

Character. Type of plate boundary (optional). Can be "out", "in", "right", or "left" for outward, inward, right-lateral, or left-lateral moving plate boundaries, respectively. If "none" (the default), only the PoR-equivalent azimuth is returned.

Value

Either a numeric vector of the azimuths in the transformed coordinate system (in degrees), or a "data.frame" with

azi.PoR

the transformed azimuths (in degrees),

prd

the predicted azimuths (in degrees),

dev

the deviation between the transformed and the predicted azimuth (in degrees),

nchisq

the Norm \(\chi^2\) test statistic, and

cdist

the angular distance between the transformed and the predicted azimuth.

Details

The azimuth of \(\sigma_{Hmax}\) in the pole of rotation reference system is approximate 0 (or 180), 45, 90, 135 degrees if the stress is sourced by an outward, sinistral, inward, or dextral moving plate boundary, respectively. directions of \(\sigma_{Hmax}\) with respect to the four plate boundary types.

References

Stephan, T., Enkelmann, E., and Kroner, U. "Analyzing the horizontal orientation of the crustal stress adjacent to plate boundaries". Sci Rep 13. 15590 (2023). doi:10.1038/s41598-023-42433-2 .

See also

model_shmax() to compute the theoretical direction of \(\sigma_{Hmax}\) in the geographical reference system. deviation_shmax() to compute the deviation of the modeled direction from the observed direction of \(\sigma_{Hmax}\). norm_chisq() to calculate the normalized \(\chi^2\) statistics. circular_distance() to calculate the angular distance.

Examples

data("nuvel1")
# North America relative to Pacific plate:
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")

data("san_andreas")
res <- PoR_shmax(san_andreas, PoR, type = "right")
head(res)
#>    azi.PoR prd        dev       nchisq       cdist
#> 1 162.2848 135  27.284805 0.0919087122 0.210143277
#> 2 137.7446 135   2.744584 0.0009299678 0.002292849
#> 3 119.5840 135 -15.416011 0.0293399256 0.070663207
#> 4 131.1908 135  -3.809243 0.0017913992 0.004413592
#> 5 152.3277 135  17.327717 0.0370678728 0.088706703
#> 6 109.7786 135 -25.221400 0.0785332091 0.181575875