Azimuth Conversion from Geographical to PoR Coordinate Reference System

Transforms azimuths and 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 circular distance, and the normalized \(\chi^2\) statistics.

Usage

PoR_azimuth(x, PoR, axial = TRUE)

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

Arguments

x

sf object or a data.frame containing the coordinates of the point(s) (lat, lon). x must contain the direction of \(\sigma_{Hmax}\) as column azi and its standard deviation as unc (the latter is optional)

PoR

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

axial

logical. Whether the azimuth is axial (0-180) or directional (0-360).

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

PoR_azimuth returns numeric vector of the transformed azimuth in degrees. PoR_shmax returns 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
#> 1 173.240166 135   38.24017 0.18053214 0.38311043
#> 2   1.058195 135 -133.94180 2.21486507 0.51846479
#> 3 147.609558 135   12.60956 0.01962975 0.04765752
#> 4 163.607388 135   28.60739 0.10103489 0.22925429
#> 5 152.233017 135   17.23302 0.03666381 0.08776909
#> 6 150.611386 135   15.61139 0.03008832 0.07242085