platemotion 0.1.7

A package to handle the tectonic plate motion

Welcome to the platemotion package

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

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

How to Install

1. Install cartopy from conda by conda install cartopy

2. 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.