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

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.

Usage

model_shmax(df, euler)

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.

Author

Tobias Stephan

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