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Construct \(\sigma_{Hmax}\) lines that are following small circles, great circles, or loxodromes of an Euler pole for the relative plate motion.

Usage

eulerpole_paths(x, type = c("sc", "gc", "ld"), n = 10, angle, cw)

eulerpole_smallcircles(x, n = 10)

eulerpole_greatcircles(x, n = 10)

eulerpole_loxodromes(x, n = 10, angle = 45, cw)

Arguments

x

Either an object of class "euler.pole" or "data.frame" containing coordinates of Euler pole in lat, lon, and rotation angle (optional).

type

Character string specifying the type of curves to export. Either "sm" for small circles (default), "gc" for great circles, or "ld" for loxodromes.

n

Number of equally spaced curves; n = 10 by default (angular distance between curves: 180 / n)

angle

Direction of loxodromes; angle = 45 by default.

cw

logical. Sense of loxodromes: TRUE for clockwise loxodromes (left-lateral displaced plate boundaries). FALSE for counterclockwise loxodromes (right-lateral displaced plate boundaries).

Value

sf object

Details

Maximum horizontal stress can be aligned to three types of curves related to relative plate motion:

Small circles

Lines that have a constant distance to the Euler pole. If x contains angle, output additionally gives absolute velocity on small circle (degree/Myr -> km/Myr).

Great circles

Paths of the shortest distance between the Euler pole and its antipodal position.

Loxodromes

Lines of constant bearing, i.e. curves cutting small circles at a constant angle.

Author

Tobias Stephan

Examples

data("nuvel1")
por <- subset(nuvel1, nuvel1$plate.rot == "na") # North America relative to
# Pacific plate

eulerpole_smallcircles(por)
#> Simple feature collection with 11 features and 2 fields
#> Geometry type: GEOMETRY
#> Dimension:     XY
#> Bounding box:  xmin: -180 ymin: -84.709 xmax: 180 ymax: 84.709
#> Geodetic CRS:  WGS 84
#> # A tibble: 11 × 3
#>                                                           geometry     d abs_vel
#>  *                                                  <GEOMETRY [°]> <dbl>   <dbl>
#>  1 LINESTRING (101.833 -48.709, 101.833 -48.709, 101.833 -48.709,…     0     0  
#>  2 LINESTRING (101.833 -30.709, 102.4799 -30.71571, 103.1265 -30.…   -18    26.9
#>  3 LINESTRING (101.833 -12.709, 102.9175 -12.72024, 104.0016 -12.…   -36    51.2
#>  4 MULTILINESTRING ((101.833 5.291, 103.2953 5.275842, 104.757 5.…   -54    70.4
#>  5 MULTILINESTRING ((101.833 23.291, 103.6965 23.27168, 105.5586 …   -72    82.8
#>  6 MULTILINESTRING ((101.833 41.291, 104.228 41.26618, 106.6194 4…    90    87.1
#>  7 MULTILINESTRING ((101.833 59.291, 105.1832 59.25627, 108.521 5…    72    82.8
#>  8 MULTILINESTRING ((101.833 77.291, 108.4309 77.22258, 114.9037 …    54    70.4
#>  9 LINESTRING (-78.167 84.709, -89.46284 84.59139, -99.79473 84.2…    36    51.2
#> 10 LINESTRING (-78.167 66.709, -79.57283 66.69442, -80.97315 66.6…    18    26.9
#> 11 LINESTRING (-78.167 48.709, -78.167 48.709, -78.167 48.709, -7…     0     0  
eulerpole_greatcircles(por)
#> Simple feature collection with 11 features and 1 field
#> Geometry type: GEOMETRY
#> Dimension:     XY
#> Bounding box:  xmin: -180 ymin: -89.991 xmax: 180 ymax: 89.991
#> Geodetic CRS:  WGS 84
#> # A tibble: 11 × 2
#>        d                                                                geometry
#>  * <dbl>                                                          <GEOMETRY [°]>
#>  1     0 LINESTRING (101.833 -48.709, 101.833 -48.609, 101.833 -48.509, 101.833…
#>  2    36 LINESTRING (101.833 -48.709, 101.7441 -48.62806, 101.6554 -48.54706, 1…
#>  3    72 LINESTRING (101.833 -48.709, 101.689 -48.67801, 101.5451 -48.64684, 10…
#>  4   108 LINESTRING (101.833 -48.709, 101.6888 -48.73981, 101.5444 -48.77044, 1…
#>  5   144 LINESTRING (101.833 -48.709, 101.7438 -48.78987, 101.6543 -48.87067, 1…
#>  6     0 LINESTRING (101.833 -48.709, 101.833 -48.809, 101.833 -48.909, 101.833…
#>  7    36 MULTILINESTRING ((101.833 -48.709, 101.9222 -48.78987, 102.0117 -48.87…
#>  8    72 MULTILINESTRING ((101.833 -48.709, 101.9772 -48.73981, 102.1216 -48.77…
#>  9   108 MULTILINESTRING ((101.833 -48.709, 101.977 -48.67801, 102.1209 -48.646…
#> 10   144 MULTILINESTRING ((101.833 -48.709, 101.9219 -48.62806, 102.0106 -48.54…
#> 11     0 MULTILINESTRING ((101.833 -48.709, 101.833 -48.609, 101.833 -48.509, 1…
eulerpole_loxodromes(x = por, angle = 45, n = 10, cw = FALSE)
#> Simple feature collection with 15 features and 1 field
#> Geometry type: GEOMETRY
#> Dimension:     XY
#> Bounding box:  xmin: -180 ymin: -82.82221 xmax: 180 ymax: 82.82221
#> Geodetic CRS:  WGS 84
#> # A tibble: 15 × 2
#>        d                                                                geometry
#>  * <dbl>                                                          <GEOMETRY [°]>
#>  1   108 LINESTRING (-78.07054 66.58404, -78.01693 66.51323, -77.96404 66.44238…
#>  2   144 LINESTRING (101.6024 77.35336, 101.3391 77.42378, 101.0733 77.49398, 1…
#>  3     0 LINESTRING (101.833 41.291, 101.7388 41.36167, 101.6444 41.43227, 101.…
#>  4    36 LINESTRING (101.3044 5.933699, 101.2458 6.003953, 101.1871 6.074159, 1…
#>  5    72 LINESTRING (101.6185 -30.1275, 101.5917 -30.05698, 101.5648 -29.98648,…
#>  6   108 LINESTRING (101.7399 -48.5214, 101.7063 -48.4543, 101.6725 -48.38724, …
#>  7   144 LINESTRING (101.5909 -48.59325, 101.5042 -48.55193, 101.4174 -48.5107,…
#>  8     0 LINESTRING (101.5338 -48.70929, 101.4266 -48.70954, 101.3195 -48.70986…
#>  9    36 LINESTRING (101.591 -48.82535, 101.5043 -48.86716, 101.4177 -48.90905,…
#> 10    72 MULTILINESTRING ((101.7412 -48.89695, 101.7086 -48.96434, 101.6762 -49…
#> 11   108 MULTILINESTRING ((101.9268 -48.89653, 101.961 -48.96356, 101.9956 -49.…
#> 12   144 LINESTRING (102.0762 -48.82424, 102.1639 -48.86512, 102.2519 -48.9058,…
#> 13     0 LINESTRING (102.1322 -48.70793, 102.2393 -48.70703, 102.3465 -48.70586…
#> 14    36 LINESTRING (102.0739 -48.59215, 102.1596 -48.54991, 102.245 -48.50747,…
#> 15    72 LINESTRING (101.9241 -48.52098, 101.9561 -48.45352, 101.9878 -48.38601…
eulerpole_loxodromes(x = por, angle = 30, cw = TRUE)
#> Simple feature collection with 13 features and 1 field
#> Geometry type: GEOMETRY
#> Dimension:     XY
#> Bounding box:  xmin: -180 ymin: -85.21953 xmax: 180 ymax: 85.21953
#> Geodetic CRS:  WGS 84
#> # A tibble: 13 × 2
#>        d                                                                geometry
#>  * <dbl>                                                          <GEOMETRY [°]>
#>  1   144 LINESTRING (101.5141 -47.93824, 101.4813 -47.85449, 101.4487 -47.77068…
#>  2     0 LINESTRING (100.8943 -48.20753, 100.7944 -48.15215, 100.6949 -48.09657…
#>  3    36 LINESTRING (100.6237 -48.6678, 100.4929 -48.66181, 100.3621 -48.65551,…
#>  4    72 LINESTRING (100.8139 -49.14575, 100.7018 -49.19187, 100.5894 -49.23775…
#>  5   108 LINESTRING (101.4023 -49.45697, 101.3538 -49.53763, 101.3048 -49.61821…
#>  6   144 LINESTRING (102.1618 -49.47885, 102.1969 -49.5624, 102.2319 -49.64599,…
#>  7     0 MULTILINESTRING ((102.7905 -49.20269, 102.8946 -49.25631, 102.9989 -49…
#>  8    36 MULTILINESTRING ((103.044 -48.73753, 103.1752 -48.74063, 103.3065 -48.…
#>  9    72 MULTILINESTRING ((102.8344 -48.26342, 102.9424 -48.21527, 103.0504 -48…
#> 10   108 MULTILINESTRING ((102.251 -47.95948, 102.2967 -47.87845, 102.3424 -47.…
#> 11   144 MULTILINESTRING ((101.833 -21.06283, 101.8579 -20.97623, 101.883 -20.8…
#> 12     0 MULTILINESTRING ((101.833 41.291, 101.8996 41.37758, 101.9664 41.46413…
#> 13    36 LINESTRING (-78.167 76.35517, -78.26446 76.26854, -78.36015 76.18185, …
eulerpole_smallcircles(data.frame(lat = 30, lon = 10))
#> Simple feature collection with 11 features and 1 field
#> Geometry type: GEOMETRY
#> Dimension:     XY
#> Bounding box:  xmin: -180 ymin: -84 xmax: 180 ymax: 84
#> Geodetic CRS:  WGS 84
#> # A tibble: 11 × 2
#>                                                                   geometry     d
#>  *                                                          <GEOMETRY [°]> <dbl>
#>  1 LINESTRING (-170 -30, -170 -30, -170 -30, -170 -30, -170 -30, -170 -30…     0
#>  2 MULTILINESTRING ((-170 -12, -169.4314 -12.00774, -168.8632 -12.03093, …   -18
#>  3 MULTILINESTRING ((-170 6, -168.9363 5.985529, -167.8735 5.942134, -166…   -36
#>  4 MULTILINESTRING ((-170 24, -168.4063 23.97832, -166.8145 23.91332, -16…   -54
#>  5 MULTILINESTRING ((-170 42, -167.6973 41.96867, -165.3999 41.87482, -16…   -72
#>  6 MULTILINESTRING ((-170 60, -166.4035 59.95107, -162.8282 59.80475, -15…    90
#>  7 MULTILINESTRING ((-170 78, -161.8144 77.88851, -153.9057 77.56006, -14…    72
#>  8 LINESTRING (10 84, -3.638991 83.81339, -15.74781 83.28465, -25.60532 8…    54
#>  9 LINESTRING (10 66, 7.401912 65.96464, 4.822514 65.85889, 2.279844 65.6…    36
#> 10 LINESTRING (10 48, 9.169016 47.98869, 8.339768 47.9548, 7.51398 47.898…    18
#> 11 LINESTRING (10 30, 10 30, 10 30, 10 30, 10 30, 10 30, 10 30, 10 30, 10…     0