knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )

This vignette teaches you how to plot the trajectories of the predicted stress directions.

library(tectonicr) library(ggplot2) # load ggplot library library(sf)

Relative plate motions from a set of (global) plate motions can be retrieved by transforming the set of the Euler rotations parameters to equivalent rotations.

The NUVEL1 data set offers the global plate motions relative to the Pacific plate (DeMets et al. 1990). In order to extract the plate motions between two other plates (e.g. all plates relative to Eurasia), one has to transform the rotations in to a new, equivalent reference system (i.e. all rotation with respect to (wrt.) Eurasia).

In **tectonicr** this can be done with `equivalent_rotation()`

:

data("nuvel1") nuvel1.eu <- equivalent_rotation(nuvel1, fixed = "eu") head(nuvel1.eu)

Alternatively, the PB2002 model by Bird (2003) is also provided as an ready-to use example dataset for global plate motions.

data("pb2002") pb2002.eu <- equivalent_rotation(pb2002, fixed = "eu") head(pb2002.eu)

To visualize the theoretical trajectories of the direction of $\sigma_{Hmax}$
(great circles, small circles, and loxodomes), we need to transform the
locations from the geographical coordinate system into the *PoR* coordinate
system. The transformations are done through the function functions
`geographical_to_PoR()`

and `PoR_to_geographical()`

. They are the base of the
functions `eulerpole_smallcircles()`

, `eulerpole_greatcircles()`

, and
`eulerpole_loxodromes()`

that allow to draw the theoretical trajectories in
geographical coordinates.

Function `eulerpole_smallcircles(x, gridsize)`

returns small circles as as
simple feature(`sf`

) by giving a `data.frame`

of the PoR
coordinates in lat and lon (`x`

) and the number of small circles (`n`

).

For example the small circles around the pole of the relative motion of the Indian plate relative to the Eurasian plate (transformed from the from the NUVEL1 model).

por <- subset(nuvel1.eu, nuvel1$plate.rot == "in") # India relative to Eurasia

The `returnclass`

option in `eulerpole_smallcircles()`

provides the output
types `"sf"`

(for a simple feature) and `"sp"`

(`Spatial*`

object) for the
small circles.

To eventually plot the small circles with `ggplot`

, I recommend to extract a
`sf`

feature and plot the it with `geom_sf()`

:

por.sm <- eulerpole_smallcircles(por) data("plates") # load plate boundary data set # world <- rnaturalearth::ne_countries(scale = "small", returnclass = "sf") ggplot() + # geom_sf(data = world, alpha = .5) + geom_sf( data = plates, color = "red", alpha = .5 ) + labs(title = "India relative to Eurasia", subtitle = "source: NUVEL1") + geom_sf( data = por.sm, aes(lty = "small circles"), color = "darkblue", fill = NA, alpha = .5 ) + geom_point( data = por, aes(lon, lat), shape = 21, colour = "lightblue", size = 2, fill = "darkblue", stroke = 1 ) + geom_point( data = euler, aes(lon + 180, -lat), shape = 21, colour = "lightblue", size = 2, fill = "darkblue", stroke = 1 ) + coord_sf(default_crs = "WGS84", crs = sf::st_crs("ESRI:54030"))

Great circles are lines that cut the small circles at 90$^{\circ}$ and
the PoR. Function `eulerpole_greatcircles(x, n)`

returns great
circles as `sf`

object by giving a `data.frame`

of the Pole of Rotation (PoR)
coordinates in lat and lon (`x`

) and the number of great circles `n`

,
or the great circle angles (`360/d`

).

por.gm <- eulerpole_greatcircles(por) ggplot() + # geom_sf(data = world, alpha = .5) + geom_sf( data = plates, color = "red", alpha = .5 ) + labs(title = "India relative to Eurasia", subtitle = "source: NUVEL1") + geom_sf( data = por.sm, aes(lty = "small circles"), color = "darkblue", alpha = .5 ) + geom_sf( data = por.gm, aes(lty = "great circles"), color = "darkblue" ) + geom_point( data = por, aes(lon, lat), shape = 21, colour = "lightblue", size = 2, fill = "darkblue", stroke = 1 ) + geom_point( data = por, aes(lon + 180, -lat), shape = 21, colour = "lightblue", size = 2, fill = "darkblue", stroke = 1 ) + coord_sf(default_crs = "WGS84", crs = sf::st_crs("ESRI:54030"))

Loxodrome (also called Rhumb Line) is a curve cutting the small circles at a constant angle. Thus, small and great circles are 0$^{\circ}$ and 90$^{\circ}$ loxodromes, respectively.

Function `eulerpole_loxodromes(x, n)`

returns loxodromes as
`sf`

object by giving a `data.frame`

of the PoR
coordinates in lat and lon (`x`

) and the angle between the loxodromes, the
direction, and the sense.

por.ld <- eulerpole_loxodromes(x = por, angle = 45, n = 10, cw = TRUE) ggplot() + labs(title = "India relative to Eurasia", subtitle = "source: NUVEL1") + # geom_sf(data = world, alpha = .5) + geom_sf( data = plates, color = "red", alpha = .5 ) + geom_sf( data = por.sm, aes(lty = "small circles"), color = "darkblue", alpha = .5 ) + geom_sf( data = por.ld, aes(lty = "clockwise loxodromes"), color = "darkblue" ) + geom_point( data = por, aes(lon, lat), shape = 21, colour = "lightblue", size = 2, fill = "darkblue", stroke = 1 ) + geom_point( data = por, aes(lon + 180, -lat), shape = 21, colour = "lightblue", size = 2, fill = "darkblue", stroke = 1 ) + coord_sf(default_crs = "WGS84", crs = sf::st_crs("ESRI:54030"))

Bird, Peter. 2003. “An Updated Digital Model of Plate Boundaries”
*Geochemistry, Geophysics, Geosystems* 4 (3).
doi: 10.1029/2001gc000252.

DeMets, C., R. G. Gordon, D. F. Argus, and S. Stein. 1990. “Current Plate Motions”
*Geophysical Journal International* 101 (2): 425–78.
doi: 10.1111/j.1365-246x.1990.tb06579.x.

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