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Description:

platemotion 0.1.7

Welcome to the platemotion package

The platemotion package is an archive of scientific routines for handling tectonic plate motion. Currently, operations on plate include:

Calculate the geometrical and physical properties of plates, such as area, centroid, moment of inertia tensor
Calculate velocities of points given Euler pole parameters
Estimate the euler pole based on ITRF2014 velocity field

How to Install

Install cartopy from conda by conda install cartopy

On Linux, macOS and Windows architectures, the binary wheels can be installed using pip by executing one of the following commands:

pip install platemotion
pip install platemotion --upgrade # to upgrade a pre-existing installation

How to use
Initialize a plate
from platemotion import Plate
# define a tectonic plate from a spherical polygon file
plate_an = Plate.from_file('platemotion/data/NnrMRVL_PltBndsLatLon/an',skiprows=1)

Set Euler pole
from astropy import units as u

#omega = np.array([-0.0914,-0.5283,0.7547])*u.mas/u.yr
#plate_an.set_omega(omega,'cartesian')

omega = [59.4*u.deg,236.5*u.deg,0.23*u.deg/u.Ma]
plate_an.set_omega(omega,'spherical')
#plate_an.set_name('Antarctica')

Calculate the area of the spherical polygon over the Earth with an averaged radius of 6371km.
from pprint import pprint
pprint(plate_an.info)

{'H_cartesian': <Quantity [-6.27283273e+26, -8.49556792e+26, 5.41130833e+26] kg km2 / Ma>,
'H_spherical': (<Latitude 27.13117643 deg>,
<Longitude 233.55912584 deg>,
<Quantity 1.18661435e+27 kg km2 / Ma>),
'area': <Quantity 58149691.98644825 km2>,
'centroid': (<Quantity -83.61081032 deg>,
<Quantity 57.80052887 deg>,
<Quantity 880.96785844 km>),
'compactness': 0.39900007941415533,
'density': <Quantity 3.1 g / cm3>,
'inertia': <Quantity [ 6.77582676e+29, 5.99961382e+29, 1.85826885e+29,
-2.60236951e+28, 2.67935794e+28, 4.15067565e+28] kg km2>,
'inertia_mag': <Quantity 9.27275284e+29 kg km2>,
'inertia_tensor': <Quantity [[ 6.77582676e+29, -2.60236951e+28, 2.67935794e+28],
[-2.60236951e+28, 5.99961382e+29, 4.15067565e+28],
[ 2.67935794e+28, 4.15067565e+28, 1.85826885e+29]] kg km2>,
'omega_cartesian': <Quantity [-0.06462052, -0.09763096, 0.19797067] deg / Ma>,
'omega_spherical': (<Latitude 59.4 deg>,
<Longitude 236.5 deg>,
<Quantity 0.23 deg / Ma>),
'perimeter': <Quantity 40281.70946992 km>,
'polygon': instance of class Sphericalpolygon,
'thickness': <Quantity 100. km>}

plate_an.plot()

Calculate velocities of points
location = [-60*u.deg,-90*u.deg,0*u.m]
v = plate_an.velocity_at(location,'geodetic')
pprint(v.info)

{'azimuth': <Quantity 70.63835275 deg>,
'en': <Quantity [20.41947555, 7.17547259] mm / yr>,
'speed': <Quantity 21.64352994 mm / yr>,
'xyz': <Quantity [20.41947555, -6.20366278, 3.60582514] mm / yr>}

locations = [[-45,69]*u.deg,[-67,80]*u.deg,[200,500]*u.m]
v = plate_an.velocity_at(locations,'geodetic')
pprint(v.info)

{'azimuth': <Quantity [ 62.30457157, 105.22683355] deg>,
'en': <Quantity [[20.67102344, 10.85042608],
[19.0385182 , -5.1822267 ]] mm / yr>,
'speed': <Quantity [23.34572673, 19.73121001] mm / yr>,
'xyz': <Quantity [[ 22.01554216, 1.03807964, 7.6981329 ],
[-17.90989462, 8.06639686, -1.86803771]] mm / yr>}

Plate Motion Model
Currently, only NNR-MORVEL56 and GSRMv2.1 are avaliable.
NNR-MORVEL56
from platemotion import PlateMotion

nnr_model = PlateMotion.loadmodel('NNR-MORVEL56') # GSRMv2.1
nnr_model_summmary = nnr_model.summary

Loading plates from NNR-MORVEL56: 100%|##########| 56/56 [03:04<00:00, 3.30s/it]

nnr_model_summmary

Plate
Ab
ωx
ωy
ωz
Lat.(°N)
Lon.(°E)
ω(°/Ma)
Hx
Hy
...
Q12
Q13
Q23
‖Q‖F(10^27 km^2 kg)
Area(km^2)
Perimeter(km)
Compactness
Lat.(°N).2
Lon.(°E).2
Depth(km)

0
Amur
am
-0.073
-0.113
0.265
63.17
237.18
0.297
-13.153
-229.643
...
14.674
18.550
-26.198
93.227
5.303403e+06
10623.85
0.58
46.14
125.62
79.07

1
Antarctica
an
-0.049
-0.092
0.227
65.42
241.89
0.250
-431.464
-773.526
...
-26.024
26.794
41.507
927.275
5.814969e+07
40281.71
0.40
-83.61
57.80
880.97

2
Arabia
ar
0.364
-0.054
0.421
48.88
351.51
0.559
153.309
-306.945
...
-24.914
-15.093
-15.853
86.263
4.904200e+06
10634.77
0.54
23.68
47.06
75.05

3
Australia
au
0.414
0.323
0.352
33.86
37.94
0.632
2167.411
3190.055
...
114.401
-110.930
123.123
615.306
3.739861e+07
29918.84
0.49
-31.50
132.34
577.37

4
Capricorn
cp
0.399
0.170
0.426
44.44
23.09
0.608
694.008
129.685
...
-11.050
3.668
23.291
144.348
8.265942e+06
13287.27
0.58
-14.30
82.93
123.16

5
Caribbean
ca
-0.011
-0.233
0.165
35.20
267.38
0.286
-51.417
-1.557
...
9.196
-2.662
8.713
52.144
2.964782e+06
8998.46
0.46
15.03
286.85
76.10

6
Cocos
co
-0.602
-0.882
0.543
26.93
235.69
1.198
-332.681
55.068
...
-2.831
0.543
5.180
51.788
2.931807e+06
8083.46
0.56
8.37
265.35
47.43

7
Eurasia
eu
-0.042
-0.141
0.168
48.85
253.50
0.223
-648.252
-1573.417
...
-18.161
-108.899
-158.461
781.347
4.855785e+07
41567.75
0.32
59.05
58.30
789.50

8
India
in
0.346
-0.020
0.419
50.37
356.71
0.544
845.422
-409.581
...
-29.136
-6.688
-30.894
215.867
1.243504e+07
17113.95
0.52
12.98
77.49
162.86

9
Juan de Fuca
jf
0.373
0.647
-0.590
-38.31
60.04
0.951
-1.570
7.031
...
-0.767
0.978
1.272
4.556
2.563227e+05
3312.65
0.29
45.43
232.47
7.96

10
Lwandle
lw
0.062
-0.165
0.225
51.89
290.48
0.286
170.963
-83.923
...
-22.135
18.412
15.150
83.574
4.753637e+06
11706.88
0.43
-28.19
39.21
78.38

11
Macquarie
mq
0.734
0.143
0.866
49.19
11.05
1.144
16.662
26.215
...
0.415
-1.620
0.748
5.694
3.202684e+05
2816.44
0.51
-58.68
155.19
5.42

12
Nazca
nz
-0.092
-0.473
0.503
46.23
258.94
0.696
-277.314
-785.905
...
-6.458
-1.516
-57.931
277.199
1.610124e+07
20148.02
0.48
-19.92
267.84
220.52

13
North America
na
0.034
-0.205
-0.018
-4.85
279.36
0.209
250.269
-1767.046
...
33.802
-1.855
202.376
889.564
5.543143e+07
34361.85
0.53
57.92
273.92
798.28

14
Nubia
nb
0.072
-0.183
0.216
47.68
291.56
0.292
-5.864
-8.229
...
2.150
-0.184
0.108
6.893
3.881402e+05
3835.33
0.33
-2.52
148.63
13.03

15
Pacific
pa
-0.121
0.263
-0.583
-63.58
114.70
0.651
-2678.327
5362.521
...
-219.343
39.545
-29.332
1589.318
1.045938e+08
48335.51
0.45
1.57
202.75
1452.00

16
Philippine Sea
ps
0.540
-0.329
-0.655
-46.02
328.64
0.910
47.495
232.842
...
29.776
13.610
-14.116
95.663
5.443797e+06
11279.45
0.53
18.34
133.46
81.35

17
Rivera
ri
-1.265
-4.063
1.570
20.25
252.71
4.536
0.189
0.019
...
-0.319
0.122
0.390
1.795
1.008984e+05
1481.84
0.58
20.04
252.60
1.67

18
Sandwich
SW
0.944
-0.708
-0.680
-29.94
323.13
1.362
15.337
-16.817
...
0.269
0.928
-0.480
3.280
1.844105e+05
1822.73
0.70
-57.80
332.63
2.73

19
Scotia
SC
-0.038
-0.130
0.056
22.52
253.85
0.146
-12.880
-48.905
...
2.908
6.123
-7.381
30.066
1.700716e+06
7724.24
0.36
-57.29
309.58
42.37

20
Somalia
sm
0.021
-0.217
0.259
49.95
275.48
0.339
398.115
-243.385
...
-79.112
12.643
18.315
248.311
1.440102e+07
19256.05
0.47
-7.98
51.20
210.07

21
South America
sa
-0.039
-0.093
-0.042
-22.62
247.17
0.109
-557.774
-536.392
...
172.790
91.516
-86.113
670.920
4.072691e+07
33048.47
0.43
-20.60
314.20
553.87

22
Sunda
su
-0.019
-0.216
0.258
50.06
264.98
0.337
-149.553
-120.216
...
35.293
3.342
-8.597
155.795
8.916227e+06
14027.20
0.56
5.01
111.10
118.89

23
Sur
sr
-0.033
-0.084
-0.057
-32.50
248.68
0.107
-13.203
-18.912
...
0.998
6.254
-1.510
19.487
1.098150e+06
5189.20
0.51
-55.12
346.52
17.86

24
Yangtze
yz
-0.068
-0.135
0.298
63.03
243.38
0.334
-22.130
-85.981
...
8.500
4.928
-9.974
38.979
2.201941e+06
7134.39
0.54
27.26
116.18
33.46

25
Aegean Sea
AS
-0.063
0.098
0.041
19.43
122.87
0.124
-5.102
6.648
...
-0.990
-1.760
-0.822
5.724
3.218650e+05
2356.17
0.73
36.97
25.06
4.38

26
Altiplano
AP
0.051
-0.482
-0.056
-6.58
276.02
0.488
-18.993
-12.488
...
3.114
1.050
-2.768
14.777
8.321276e+05
3858.38
0.70
-17.34
290.56
13.05

27
Anatolia
AT
0.827
0.415
0.780
40.11
26.66
1.210
4.371
-12.327
...
-2.028
-2.945
-1.907
10.229
5.756255e+05
3345.52
0.65
38.24
32.92
8.66

28
Balmoral Reef
BR
-0.171
0.133
-0.439
-63.74
142.06
0.490
4.558
4.858
...
0.164
-0.615
0.044
3.475
1.953799e+05
2131.61
0.54
-15.06
175.87
3.28

29
Banda Sea
BS
-1.298
2.106
-0.064
-1.49
121.64
2.475
19.274
18.959
...
4.074
-0.434
0.599
12.347
6.959325e+05
4968.34
0.35
-4.90
125.71
18.99

30
Birds Head
BH
-0.112
0.602
-0.514
-40.00
100.50
0.799
28.056
23.877
...
3.264
-0.099
0.103
9.336
5.256390e+05
3577.94
0.52
-1.24
131.99
12.28

31
Burma
BU
0.457
-2.169
-0.238
-6.13
281.90
2.229
34.713
-0.845
...
0.435
0.066
-0.989
9.146
5.153850e+05
4033.03
0.40
9.00
93.98
17.43

32
Caroline
CL
0.055
0.171
-0.580
-72.78
72.05
0.607
27.128
50.084
...
9.291
0.807
-0.676
27.099
1.528196e+06
5301.21
0.68
3.17
140.55
22.45

33
Conway Reef
CR
-3.627
0.605
-1.367
-20.40
170.53
3.923
1.573
8.483
...
0.147
-0.562
0.052
2.570
1.444575e+05
1859.82
0.52
-19.21
174.75
2.55

34
Easter
EA
3.927
9.495
4.785
24.97
67.53
11.334
-9.163
3.009
...
-0.644
-0.322
-0.725
2.970
1.669842e+05
1783.03
0.66
-24.57
246.07
2.25

35
Futuna
FT
-4.892
0.165
-1.434
-16.33
178.07
5.101
0.127
2.444
...
-0.014
-0.100
-0.004
0.570
3.201157e+04
919.36
0.48
-14.97
182.13
0.74

36
Galapagos
GP
0.841
5.417
0.242
2.53
81.18
5.487
-0.852
0.222
...
-0.036
0.001
0.006
0.260
1.462437e+04
576.37
0.55
1.87
258.32
0.22

37
Juan Fernandez
JZ
6.099
17.454
12.589
34.25
70.74
22.368
-12.130
0.294
...
-0.286
-0.201
-0.527
1.738
9.767412e+04
1239.13
0.80
-33.34
249.09
1.27

38
Kermadec
KE
1.787
0.202
1.508
39.99
6.46
2.347
-15.633
20.010
...
-0.063
-2.855
-0.017
8.951
5.053495e+05
4775.62
0.28
-33.02
180.67
29.97

39
Manus
MN
-44.689
25.521
-3.301
-3.67
150.27
51.569
0.192
0.318
...
0.044
-0.006
0.003
0.146
8.220170e+03
413.71
0.60
-3.53
150.50
0.13

40
Maoke
MO
-0.035
0.749
0.191
14.25
92.67
0.774
8.776
10.312
...
0.718
-0.064
0.058
2.051
1.153029e+05
1647.84
0.53
-3.42
138.15
2.07

41
Mariana
MA
-0.950
0.860
0.250
11.05
137.84
1.306
5.003
15.579
...
2.232
1.264
-0.872
7.474
4.207784e+05
3548.51
0.42
17.88
145.44
11.97

42
Molucca Sea
MS
1.988
-2.957
0.134
2.15
303.91
3.566
2.414
0.796
...
2.410
-0.060
0.084
7.431
4.181131e+05
3268.02
0.49
-1.13
123.48
7.63

43
New Hebrides
NH
2.453
-0.284
0.025
0.57
353.40
2.469
35.290
12.374
...
1.198
-2.322
0.387
11.433
6.434675e+05
3514.29
0.65
-17.88
170.44
9.71

44
Niuafo'ou
NI
-3.293
-0.318
-0.190
-3.29
185.51
3.314
-5.920
-2.304
...
-0.108
-0.428
-0.032
2.211
1.242883e+05
1768.19
0.50
-16.69
184.34
2.28

45
North Andes
ND
-0.060
-0.093
0.035
17.73
237.32
0.116
-16.894
-3.936
...
2.939
-0.376
1.269
17.222
9.718156e+05
5368.42
0.42
6.33
284.76
26.51

46
North Bismarck
NB
-0.369
0.479
-0.606
-45.04
127.64
0.856
11.278
14.723
...
2.150
-0.184
0.108
6.893
3.881402e+05
3835.33
0.33
-2.52
148.63
13.03

47
Okhotsk
OK
-0.008
-0.198
0.116
30.30
267.72
0.229
4.668
-136.269
...
6.616
15.485
-9.127
53.486
3.037119e+06
9459.60
0.42
51.24
148.99
67.44

48
Okinawa
ON
-1.522
1.374
1.497
36.12
137.92
2.539
-12.180
-25.417
...
1.555
1.024
-1.303
5.768
3.247068e+05
3384.93
0.36
27.33
127.95
11.58

49
Panama
PM
-0.110
-0.248
0.165
31.35
246.10
0.317
-8.867
-0.210
...
0.511
-0.081
0.521
4.866
2.737256e+05
2593.99
0.51
8.94
278.88
6.54

50
Shetland
SL
-0.136
-0.101
0.207
50.71
216.53
0.268
-1.489
-2.725
...
0.089
0.194
-0.324
1.286
7.226161e+04
1235.12
0.60
-61.90
301.00
1.57

51
Solomon Sea
SS
-1.107
1.291
-0.085
-2.87
130.62
1.703
7.874
16.113
...
0.651
-0.180
0.093
2.289
1.286602e+05
1775.52
0.51
-7.26
152.54
2.43

52
South Bismarck
SB
6.837
-4.254
0.972
6.88
328.11
8.111
-3.581
-4.769
...
1.707
-0.292
0.177
5.495
3.090909e+05
2784.42
0.50
-5.06
148.73
5.57

53
Timor
TI
-0.741
1.704
-0.144
-4.44
113.50
1.864
23.658
19.560
...
2.047
-0.383
0.537
6.276
3.532757e+05
3246.87
0.42
-8.67
125.80
11.15

54
Tonga
TO
8.021
0.628
3.902
25.87
4.48
8.942
-16.446
-10.117
...
-0.274
-0.994
-0.095
4.508
2.536195e+05
2747.12
0.42
-19.48
185.57
7.53

55
Woodlark
WL
-1.086
1.364
0.003
0.10
128.52
1.744
26.558
47.235
...
2.536
-0.548
0.337
8.027
4.530879e+05
5058.21
0.22
-6.59
146.83
28.15

56 rows × 27 columns
Build a Plate Motion Model based on ITRF2014 velocity field
from platemotion import ITRF_PlateMotion
# use NNR-MORVEL56 plate boundaries
platemodel = ITRF_PlateMotion('NNR-MORVEL56')

Screen out sites with an observation time of more than 3 years ... Finished
Eliminate sites with velocity uncertainty greater than 1mm/yr ... Finished
Eliminate sites affected by the post-earthquake deformation ... Finished
Exclude sites with the second invariant strain rate greater than 1e-10 based on gsrmv2.1 ... Finished
Exclude sites with the vertical displacement rate greater than 0.75mm/yr based on ICE-6G_D(VM5a) ... Finished
Assign sites to plates ... Finished
Estimating Euler Pole ... Finished

pprint(platemodel.eu.epr)

{'num_sites': 136,
'omega_cartesian': <Quantity [-0.02592416, -0.14672679, 0.20901511] deg / Ma>,
'omega_cartesian_std': <Quantity [8.49222294e-05, 3.32043179e-05, 1.05751362e-04] deg / Ma>,
'omega_spherical': (<Latitude 54.51629211 deg>,
<Longitude 259.98020722 deg>,
<Quantity 0.25668683 deg / Myr>),
'omega_spherical_std': (<Quantity 0.01517495 deg>,
<Quantity 0.03223431 deg>,
<Quantity 8.85943626e-05 deg / Myr>),
'rms': <Quantity [0.33554098, 0.32477936] mm / yr>}

platemodel.eu.sites

CODE
PT
DOMES
STATION DESCRIPTION
Geod. Lat. °N
Lat. °N
Lon. °E
H
SOLN
REF_EPOCH
...
STAX_STD
STAY_STD
STAZ_STD
VELX_STD
VELY_STD
VELZ_STD
ve
vn
ve_res
vn_res

0
AJAC
A
10077M005
Ajaccio, France
41.927444
41.736196
8.762611
98.8
2
10:001:00000
...
0.59986E-03
0.58068E-03
0.53876E-03
0.34092E-04
0.37461E-04
0.34696E-04
0.021088
0.016058
1.936000e-04
0.000373

1
AMBL
A
19967M001
Ambrumesnil, FR
49.859361
49.669592
0.994306
129.9
1
10:001:00000
...
0.58646E-03
0.56964E-03
0.55445E-03
0.63379E-04
0.41625E-04
0.68454E-04
0.017454
0.015939
-1.016939e-06
-0.000324

2
ARGI
A
10117M002
Argir, Tórshavn, Faro
61.997361
61.837525
353.216472
110.2
1
10:001:00000
...
0.56975E-03
0.55433E-03
0.61036E-03
0.67557E-04
0.47148E-04
0.10893E-03
0.011754
0.017084
-4.035166e-05
0.000543

3
ARTU
A
12362M001
ARTU 12362M001
56.429806
56.252264
58.560444
247.6
1
10:001:00000
...
0.56576E-03
0.58116E-03
0.54879E-03
0.32262E-04
0.34318E-04
0.32609E-04
0.025272
0.006188
-4.640728e-04
0.000138

4
BEA2
A
10079S001
Port-Vendres, France
42.515306
42.323661
3.136694
108.2
1
10:001:00000
...
0.65645E-03
0.58472E-03
0.58795E-03
0.15452E-03
0.63419E-04
0.13409E-03
0.020631
0.015778
9.087333e-04
-0.000355

...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...
...

131
WTZZ
A
14201M014
WTZZ 14201M014
49.144194
48.953689
12.878889
665.9
3
10:001:00000
...
0.58338E-03
0.57389E-03
0.54538E-03
0.30691E-04
0.36384E-04
0.32602E-04
0.020297
0.015552
1.736272e-04
0.000290

132
YEBE
A
13420M001
YEBE 13420M001
40.524889
40.334908
356.911361
972.8
1
10:001:00000
...
0.59871E-03
0.57837E-03
0.53645E-03
0.31429E-04
0.37409E-04
0.33017E-04
0.018894
0.016412
-1.166159e-04
-0.000035

133
ZEEB
A
13174M001
Zeebrugge, Belgium
51.335833
51.147958
3.208222
60.3
2
10:001:00000
...
0.58028E-03
0.56775E-03
0.55188E-03
0.35170E-04
0.36910E-04
0.38767E-04
0.017532
0.015357
-4.851948e-07
-0.000772

134
ZWE2
A
12330M003
ZWE2 12330M003
55.699278
55.519899
36.758389
208.2
2
10:001:00000
...
0.56790E-03
0.57494E-03
0.55162E-03
0.33546E-04
0.36547E-04
0.39024E-04
0.022651
0.011871
-4.586815e-04
0.000525

135
ZWEN
A
12330M001
Zwenigorod, Russia
55.699278
55.519899
36.758611
205.0
4
10:001:00000
...
0.57802E-03
0.58197E-03
0.58189E-03
0.33618E-04
0.36611E-04
0.39084E-04
0.022659
0.011874
-4.503503e-04
0.000527

136 rows × 26 columns
### Relative motion of plates
pa_plate = platemodel.pa
na_plate = platemodel.na
# euler pole of North America w.r.t. Pacific
pa_na = na_plate.fixed_ref(pa_plate)
pprint(pa_na)

{'omega_cartesian': <Quantity [ 0.11831538, -0.48878796, 0.58888957] deg / Ma>,
'omega_cartesian_std': <Quantity [0.00016247, 0.00016937, 0.0001375 ] deg / Ma>,
'omega_spherical': (<Latitude 49.50311891 deg>,
<Longitude 283.60721239 deg>,
<Quantity 0.77440502 deg / Ma>),
'omega_spherical_std': (<Quantity 0.01157821 deg>,
<Quantity 0.01855507 deg>,
<Quantity 0.00015158 deg / Ma>)}

Change log

0.1.7 — Mar 9, 2021

Added calculation of relative motion of plates

0.1.6 — Mar 8, 2021

The first release

Reference
Argus, Donald F., Richard G. Gordon, and Charles DeMets. "Geologically current motion of 56 plates relative to the no‐net‐rotation reference frame." Geochemistry, Geophysics, Geosystems 12.11 (2011).
Kreemer, Corné, Geoffrey Blewitt, and Elliot C. Klein. "A geodetic plate motion and Global Strain Rate Model." Geochemistry, Geophysics, Geosystems 15.10 (2014): 3849-3889.
Altamimi, Zuheir, et al. "ITRF2014: A new release of the International Terrestrial Reference Frame modeling nonlinear station motions." Journal of Geophysical Research: Solid Earth 121.8 (2016): 6109-6131.