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 = 45, 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 = 10by default (angular distance between curves:180 / n)- angle
Direction of loxodromes;
angle = 45by default.- cw
logical. Sense of loxodromes:
TRUEfor clockwise loxodromes (left-lateral displaced plate boundaries).FALSEfor counterclockwise loxodromes (right-lateral displaced plate boundaries).
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
xcontainsangle, 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.
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