# Theoretical Direction of Maximum Horizontal Stress in the geographical reference system.

Source:`R/model_shmax.R`

`model_shmax.Rd`

Models the direction of maximum horizontal stress \(\sigma_{Hmax}\) along great circles, small circles, and loxodromes at a given point or points according to the relative plate motion in the geographical coordinate reference system.

## Arguments

- df
`data.frame`

containing the coordinates of the point(s) (`lat`

,`lon`

).- euler
`"data.frame"`

or object of class`"euler.pole"`

containing the geographical coordinates of the Euler pole

## Value

`data.frame`

- gc
Azimuth of modeled \(\sigma_{Hmax}\) following great circles

- sc
Small circles

- ld.cw
Clockwise loxodromes

- ld.ccw
Counter-clockwise loxodromes

## Details

\(\sigma_{Hmax}\) following *great circles* is the
(initial) bearing between the given point and the pole of relative plate
motion. \(\sigma_{Hmax}\) along *small circles*, clockwise, and
counter-clockwise *loxodromes* is 90\(^{\circ}\),
+45\(^{\circ}\), and 135\(^{\circ}\)
(-45\(^{\circ}\)) to this great circle bearing, respectively.

## 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

`deviation_shmax()`

to compute the deviation of the modeled direction
from the observed direction of \(\sigma_{Hmax}\).
`PoR_shmax()`

to calculate the azimuth of \(\sigma_{Hmax}\)
in the pole of rotation reference system.

## Examples

```
data("nuvel1")
# North America relative to Pacific plate:
euler <- subset(nuvel1, nuvel1$plate.rot == "na")
# the point where we mant to model the SHmax direction:
point <- data.frame(lat = 45, lon = 20)
model_shmax(point, euler)
#> sc ld.ccw gc ld.cw
#> 1 42.45436 87.45436 132.4544 177.4544
```