Package: platemotion
Welcome to the platemotion packageThe 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 tensorCalculate velocities of points given Euler pole parametersEstimate the euler pole based on ITRF2014 velocity fieldHow to InstallInstallcartopyfrom conda byconda install cartopyOn Linux, macOS and Windows architectures, the binary wheels can be installed usingpipby executing one of the following commands:pip install platemotion
pip install platemotion --upgrade # to upgrade a pre-existing installationHow to useInitialize a platefromplatemotionimportPlate# define a tectonic plate from a spherical polygon fileplate_an=Plate.from_file('platemotion/data/NnrMRVL_PltBndsLatLon/an',skiprows=1)Set Euler polefromastropyimportunitsasu#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.frompprintimportpprintpprint(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 pointslocation=[-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 ModelCurrently, onlyNNR-MORVEL56andGSRMv2.1are avaliable.NNR-MORVEL56fromplatemotionimportPlateMotionnnr_model=PlateMotion.loadmodel('NNR-MORVEL56')# GSRMv2.1nnr_model_summmary=nnr_model.summaryLoading plates from NNR-MORVEL56: 100%|##########| 56/56 [03:04<00:00,  3.30s/it]nnr_model_summmaryPlateAbωxωyωzLat.(°N)Lon.(°E)ω(°/Ma)HxHy...Q12Q13Q23‖Q‖F(10^27 km^2 kg)Area(km^2)Perimeter(km)CompactnessLat.(°N).2Lon.(°E).2Depth(km)0Amuram-0.073-0.1130.26563.17237.180.297-13.153-229.643...14.67418.550-26.19893.2275.303403e+0610623.850.5846.14125.6279.071Antarcticaan-0.049-0.0920.22765.42241.890.250-431.464-773.526...-26.02426.79441.507927.2755.814969e+0740281.710.40-83.6157.80880.972Arabiaar0.364-0.0540.42148.88351.510.559153.309-306.945...-24.914-15.093-15.85386.2634.904200e+0610634.770.5423.6847.0675.053Australiaau0.4140.3230.35233.8637.940.6322167.4113190.055...114.401-110.930123.123615.3063.739861e+0729918.840.49-31.50132.34577.374Capricorncp0.3990.1700.42644.4423.090.608694.008129.685...-11.0503.66823.291144.3488.265942e+0613287.270.58-14.3082.93123.165Caribbeanca-0.011-0.2330.16535.20267.380.286-51.417-1.557...9.196-2.6628.71352.1442.964782e+068998.460.4615.03286.8576.106Cocosco-0.602-0.8820.54326.93235.691.198-332.68155.068...-2.8310.5435.18051.7882.931807e+068083.460.568.37265.3547.437Eurasiaeu-0.042-0.1410.16848.85253.500.223-648.252-1573.417...-18.161-108.899-158.461781.3474.855785e+0741567.750.3259.0558.30789.508Indiain0.346-0.0200.41950.37356.710.544845.422-409.581...-29.136-6.688-30.894215.8671.243504e+0717113.950.5212.9877.49162.869Juan de Fucajf0.3730.647-0.590-38.3160.040.951-1.5707.031...-0.7670.9781.2724.5562.563227e+053312.650.2945.43232.477.9610Lwandlelw0.062-0.1650.22551.89290.480.286170.963-83.923...-22.13518.41215.15083.5744.753637e+0611706.880.43-28.1939.2178.3811Macquariemq0.7340.1430.86649.1911.051.14416.66226.215...0.415-1.6200.7485.6943.202684e+052816.440.51-58.68155.195.4212Nazcanz-0.092-0.4730.50346.23258.940.696-277.314-785.905...-6.458-1.516-57.931277.1991.610124e+0720148.020.48-19.92267.84220.5213North Americana0.034-0.205-0.018-4.85279.360.209250.269-1767.046...33.802-1.855202.376889.5645.543143e+0734361.850.5357.92273.92798.2814Nubianb0.072-0.1830.21647.68291.560.292-5.864-8.229...2.150-0.1840.1086.8933.881402e+053835.330.33-2.52148.6313.0315Pacificpa-0.1210.263-0.583-63.58114.700.651-2678.3275362.521...-219.34339.545-29.3321589.3181.045938e+0848335.510.451.57202.751452.0016Philippine Seaps0.540-0.329-0.655-46.02328.640.91047.495232.842...29.77613.610-14.11695.6635.443797e+0611279.450.5318.34133.4681.3517Riverari-1.265-4.0631.57020.25252.714.5360.1890.019...-0.3190.1220.3901.7951.008984e+051481.840.5820.04252.601.6718SandwichSW0.944-0.708-0.680-29.94323.131.36215.337-16.817...0.2690.928-0.4803.2801.844105e+051822.730.70-57.80332.632.7319ScotiaSC-0.038-0.1300.05622.52253.850.146-12.880-48.905...2.9086.123-7.38130.0661.700716e+067724.240.36-57.29309.5842.3720Somaliasm0.021-0.2170.25949.95275.480.339398.115-243.385...-79.11212.64318.315248.3111.440102e+0719256.050.47-7.9851.20210.0721South Americasa-0.039-0.093-0.042-22.62247.170.109-557.774-536.392...172.79091.516-86.113670.9204.072691e+0733048.470.43-20.60314.20553.8722Sundasu-0.019-0.2160.25850.06264.980.337-149.553-120.216...35.2933.342-8.597155.7958.916227e+0614027.200.565.01111.10118.8923Sursr-0.033-0.084-0.057-32.50248.680.107-13.203-18.912...0.9986.254-1.51019.4871.098150e+065189.200.51-55.12346.5217.8624Yangtzeyz-0.068-0.1350.29863.03243.380.334-22.130-85.981...8.5004.928-9.97438.9792.201941e+067134.390.5427.26116.1833.4625Aegean SeaAS-0.0630.0980.04119.43122.870.124-5.1026.648...-0.990-1.760-0.8225.7243.218650e+052356.170.7336.9725.064.3826AltiplanoAP0.051-0.482-0.056-6.58276.020.488-18.993-12.488...3.1141.050-2.76814.7778.321276e+053858.380.70-17.34290.5613.0527AnatoliaAT0.8270.4150.78040.1126.661.2104.371-12.327...-2.028-2.945-1.90710.2295.756255e+053345.520.6538.2432.928.6628Balmoral ReefBR-0.1710.133-0.439-63.74142.060.4904.5584.858...0.164-0.6150.0443.4751.953799e+052131.610.54-15.06175.873.2829Banda SeaBS-1.2982.106-0.064-1.49121.642.47519.27418.959...4.074-0.4340.59912.3476.959325e+054968.340.35-4.90125.7118.9930Birds HeadBH-0.1120.602-0.514-40.00100.500.79928.05623.877...3.264-0.0990.1039.3365.256390e+053577.940.52-1.24131.9912.2831BurmaBU0.457-2.169-0.238-6.13281.902.22934.713-0.845...0.4350.066-0.9899.1465.153850e+054033.030.409.0093.9817.4332CarolineCL0.0550.171-0.580-72.7872.050.60727.12850.084...9.2910.807-0.67627.0991.528196e+065301.210.683.17140.5522.4533Conway ReefCR-3.6270.605-1.367-20.40170.533.9231.5738.483...0.147-0.5620.0522.5701.444575e+051859.820.52-19.21174.752.5534EasterEA3.9279.4954.78524.9767.5311.334-9.1633.009...-0.644-0.322-0.7252.9701.669842e+051783.030.66-24.57246.072.2535FutunaFT-4.8920.165-1.434-16.33178.075.1010.1272.444...-0.014-0.100-0.0040.5703.201157e+04919.360.48-14.97182.130.7436GalapagosGP0.8415.4170.2422.5381.185.487-0.8520.222...-0.0360.0010.0060.2601.462437e+04576.370.551.87258.320.2237Juan FernandezJZ6.09917.45412.58934.2570.7422.368-12.1300.294...-0.286-0.201-0.5271.7389.767412e+041239.130.80-33.34249.091.2738KermadecKE1.7870.2021.50839.996.462.347-15.63320.010...-0.063-2.855-0.0178.9515.053495e+054775.620.28-33.02180.6729.9739ManusMN-44.68925.521-3.301-3.67150.2751.5690.1920.318...0.044-0.0060.0030.1468.220170e+03413.710.60-3.53150.500.1340MaokeMO-0.0350.7490.19114.2592.670.7748.77610.312...0.718-0.0640.0582.0511.153029e+051647.840.53-3.42138.152.0741MarianaMA-0.9500.8600.25011.05137.841.3065.00315.579...2.2321.264-0.8727.4744.207784e+053548.510.4217.88145.4411.9742Molucca SeaMS1.988-2.9570.1342.15303.913.5662.4140.796...2.410-0.0600.0847.4314.181131e+053268.020.49-1.13123.487.6343New HebridesNH2.453-0.2840.0250.57353.402.46935.29012.374...1.198-2.3220.38711.4336.434675e+053514.290.65-17.88170.449.7144Niuafo'ouNI-3.293-0.318-0.190-3.29185.513.314-5.920-2.304...-0.108-0.428-0.0322.2111.242883e+051768.190.50-16.69184.342.2845North AndesND-0.060-0.0930.03517.73237.320.116-16.894-3.936...2.939-0.3761.26917.2229.718156e+055368.420.426.33284.7626.5146North BismarckNB-0.3690.479-0.606-45.04127.640.85611.27814.723...2.150-0.1840.1086.8933.881402e+053835.330.33-2.52148.6313.0347OkhotskOK-0.008-0.1980.11630.30267.720.2294.668-136.269...6.61615.485-9.12753.4863.037119e+069459.600.4251.24148.9967.4448OkinawaON-1.5221.3741.49736.12137.922.539-12.180-25.417...1.5551.024-1.3035.7683.247068e+053384.930.3627.33127.9511.5849PanamaPM-0.110-0.2480.16531.35246.100.317-8.867-0.210...0.511-0.0810.5214.8662.737256e+052593.990.518.94278.886.5450ShetlandSL-0.136-0.1010.20750.71216.530.268-1.489-2.725...0.0890.194-0.3241.2867.226161e+041235.120.60-61.90301.001.5751Solomon SeaSS-1.1071.291-0.085-2.87130.621.7037.87416.113...0.651-0.1800.0932.2891.286602e+051775.520.51-7.26152.542.4352South BismarckSB6.837-4.2540.9726.88328.118.111-3.581-4.769...1.707-0.2920.1775.4953.090909e+052784.420.50-5.06148.735.5753TimorTI-0.7411.704-0.144-4.44113.501.86423.65819.560...2.047-0.3830.5376.2763.532757e+053246.870.42-8.67125.8011.1554TongaTO8.0210.6283.90225.874.488.942-16.446-10.117...-0.274-0.994-0.0954.5082.536195e+052747.120.42-19.48185.577.5355WoodlarkWL-1.0861.3640.0030.10128.521.74426.55847.235...2.536-0.5480.3378.0274.530879e+055058.210.22-6.59146.8328.1556 rows × 27 columnsBuild a Plate Motion Model based on ITRF2014 velocity fieldfromplatemotionimportITRF_PlateMotion# use NNR-MORVEL56 plate boundariesplatemodel=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 ... Finishedpprint(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.sitesCODEPTDOMESSTATION DESCRIPTIONGeod. Lat. °NLat. °NLon. °EHSOLNREF_EPOCH...STAX_STDSTAY_STDSTAZ_STDVELX_STDVELY_STDVELZ_STDvevnve_resvn_res0AJACA10077M005Ajaccio, France41.92744441.7361968.76261198.8210:001:00000...0.59986E-030.58068E-030.53876E-030.34092E-040.37461E-040.34696E-040.0210880.0160581.936000e-040.0003731AMBLA19967M001Ambrumesnil, FR49.85936149.6695920.994306129.9110:001:00000...0.58646E-030.56964E-030.55445E-030.63379E-040.41625E-040.68454E-040.0174540.015939-1.016939e-06-0.0003242ARGIA10117M002Argir, Tórshavn, Faro61.99736161.837525353.216472110.2110:001:00000...0.56975E-030.55433E-030.61036E-030.67557E-040.47148E-040.10893E-030.0117540.017084-4.035166e-050.0005433ARTUA12362M001ARTU 12362M00156.42980656.25226458.560444247.6110:001:00000...0.56576E-030.58116E-030.54879E-030.32262E-040.34318E-040.32609E-040.0252720.006188-4.640728e-040.0001384BEA2A10079S001Port-Vendres, France42.51530642.3236613.136694108.2110:001:00000...0.65645E-030.58472E-030.58795E-030.15452E-030.63419E-040.13409E-030.0206310.0157789.087333e-04-0.000355..................................................................131WTZZA14201M014WTZZ 14201M01449.14419448.95368912.878889665.9310:001:00000...0.58338E-030.57389E-030.54538E-030.30691E-040.36384E-040.32602E-040.0202970.0155521.736272e-040.000290132YEBEA13420M001YEBE 13420M00140.52488940.334908356.911361972.8110:001:00000...0.59871E-030.57837E-030.53645E-030.31429E-040.37409E-040.33017E-040.0188940.016412-1.166159e-04-0.000035133ZEEBA13174M001Zeebrugge, Belgium51.33583351.1479583.20822260.3210:001:00000...0.58028E-030.56775E-030.55188E-030.35170E-040.36910E-040.38767E-040.0175320.015357-4.851948e-07-0.000772134ZWE2A12330M003ZWE2 12330M00355.69927855.51989936.758389208.2210:001:00000...0.56790E-030.57494E-030.55162E-030.33546E-040.36547E-040.39024E-040.0226510.011871-4.586815e-040.000525135ZWENA12330M001Zwenigorod, Russia55.69927855.51989936.758611205.0410:001:00000...0.57802E-030.58197E-030.58189E-030.33618E-040.36611E-040.39084E-040.0226590.011874-4.503503e-040.000527136 rows × 26 columns### Relative motion of platespa_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 log0.1.7 — Mar 9,  2021Added calculation of relative motion of plates0.1.6 — Mar 8,  2021The first releaseReferenceArgus, 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.