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
#> 1 173.240166 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
```