---------------------------------------------------------------------------- Table 1. Nubia-South America noise-reduced finite rotations ---------------------------------------------------------------------------- Chron Lat. Long. Omega REDBACK rotation covariances --------------------------------------------- N E deg. S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- 1n 60.35 321.26 0.221 307.9 -245.9 313.5 198.4 -254.0 325.7 2n 60.60 320.99 0.507 319.1 -233.2 284.0 195.7 -253.4 335.9 2An.1 60.77 320.80 0.741 382.8 -232.2 251.2 206.9 -273.3 386.4 2An.3 60.94 320.60 1.046 480.2 -213.7 167.6 211.0 -288.5 453.4 3n.1 61.01 320.52 1.227 529.0 -186.9 92.1 201.2 -282.6 479.0 3n.4 61.09 320.41 1.550 641.7 -152.2 -32.1 195.1 -287.2 548.7 3An.1 61.14 320.35 1.798 833.5 -191.8 -58.4 249.9 -368.8 714.8 3An.2 61.17 320.31 2.030 1007.6 -196.8 -142.6 277.1 -416.4 847.6 4n.1 61.19 320.28 2.312 1244.7 -169.4 -325.0 288.7 -451.7 1011.2 4n.2 61.20 320.26 2.521 1539.4 -201.8 -427.9 348.8 -547.1 1248.7 4A 61.21 320.26 2.881 2299.6 -351.4 -577.2 548.6 -842.6 1897.1 5n.1 61.21 320.27 3.131 2964.0 -481.4 -718.8 719.2 -1093.1 2459.8 5n.2 61.16 320.35 3.621 4382.4 -698.3 -1167.1 1031.9 -1562.5 3635.0 5An.2 61.05 320.52 4.221 5607.5 -645.6 -2072.4 1112.9 -1744.3 4557.0 5AC 60.89 320.74 4.773 5782.1 -339.4 -2835.9 886.3 -1489.9 4563.2 5AD 60.76 320.92 5.154 5713.9 -232.8 -3037.7 795.4 -1378.5 4491.9 5Cn.1 60.57 321.19 5.752 5887.5 -259.5 -3165.1 828.4 -1424.2 4699.2 5D 60.39 321.44 6.313 6213.4 -359.3 -3254.9 932.4 -1560.1 5062.7 5E 60.28 321.60 6.692 6432.6 -299.8 -3571.2 899.8 -1535.7 5257.9 6ny 60.17 321.74 7.019 6708.5 -207.7 -3989.2 843.9 -1489.3 5482.6 6no 60.02 321.96 7.485 7381.1 -157.4 -4631.8 842.1 -1522.4 6045.3 6An.2 59.82 322.20 7.960 8320.8 -374.6 -4957.4 1063.6 -1809.0 6904.4 6Bn.1 59.54 322.52 8.463 8992.2 -777.1 -4751.2 1407.7 -2203.4 7612.4 7n.1 58.79 323.29 9.432 6906.6 -664.4 -3640.2 1131.5 -1741.7 6020.6 7n.2 58.60 323.48 9.649 6272.3 -571.0 -3393.1 1001.8 -1554.3 5493.1 8n.1 58.38 323.71 9.913 5729.3 -478.6 -3212.5 879.4 -1381.2 5044.6 8n.2 58.07 324.02 10.287 5273.3 -351.7 -3171.6 738.4 -1197.0 4684.6 9ny 57.93 324.17 10.469 5161.3 -292.0 -3226.8 681.7 -1129.9 4608.3 9no 57.64 324.49 10.897 4995.0 -172.0 -3385.7 573.6 -1006.7 4518.7 10n.1 57.55 324.61 11.073 4880.9 -145.9 -3371.0 542.4 -964.9 4440.3 10n.2 57.47 324.71 11.249 4749.6 -134.1 -3314.4 520.3 -930.6 4344.8 11n.1 57.35 324.90 11.629 4296.3 -167.7 -2945.5 501.3 -868.4 3975.1 11n.2 57.28 325.03 11.959 3772.0 -258.6 -2399.0 517.5 -831.8 3512.1 12ny 57.23 325.14 12.220 3349.5 -349.4 -1917.3 544.9 -815.9 3128.3 12no 57.20 325.21 12.407 3062.7 -399.0 -1612.2 555.3 -797.8 2867.1 13ny 57.06 325.53 13.317 2257.0 -195.4 -1464.2 313.4 -474.2 2169.0 13no 57.02 325.62 13.551 2620.2 -135.5 -1908.1 288.8 -474.0 2554.4 -------------------------------------------------------------------------------- These noise-reduced finite rotations, which reconstruct the South America plate onto the Nubia plate, were derived via a REDBACK analysis of the best-fitting rotations in Supplemental Table 2. The rotation angles Omega are positive CCW. The Cartesian rotation covariances, which specify the 2-D position uncertainty when rotating points from the Nubia onto the South America plate or vice versa, have units of 10^-10 radians^2. See the footnotes to Table 1 in the main document for information on how to build the rotation covariance matrix from the six covariance elements in the table. ---------------------------------------------------------------------------- Table 2. South America-Nubia noise-reduced stage angular velocities ---------------------------------------------------------------------------- Age(y) Age(o) Lat. Long. omega Covariances --------------------------------------------- Ma Ma N E dg/Myr S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- 0.000 0.781 60.35 321.26 -0.284 3.96 -3.15 8.67 2.54 -6.95 19.65 0.781 1.778 60.79 320.79 -0.287 1.16 -0.79 1.83 0.67 -1.53 4.59 1.778 2.581 61.15 320.36 -0.292 1.31 -0.75 1.41 0.66 -1.27 4.07 2.581 3.596 61.34 320.11 -0.300 1.21 -0.65 1.13 0.58 -1.06 3.51 3.596 4.187 61.40 320.01 -0.306 1.28 -0.69 1.16 0.65 -1.09 3.68 4.187 5.235 61.41 319.98 -0.308 1.23 -0.67 1.25 0.62 -1.16 3.77 5.235 6.033 61.42 319.95 -0.310 1.61 -0.88 1.70 0.79 -1.58 5.05 6.033 6.733 61.39 319.99 -0.331 2.37 -1.36 2.85 1.20 -2.60 8.12 6.733 7.528 61.34 320.06 -0.356 2.66 -1.30 2.16 1.13 -2.17 7.23 7.528 8.108 61.35 320.09 -0.359 2.88 -1.26 1.90 1.14 -2.03 6.90 8.108 9.105 61.28 320.22 -0.361 2.97 -1.18 1.58 1.05 -1.84 6.38 9.105 9.786 61.14 320.46 -0.366 4.25 -1.88 3.01 1.65 -3.15 10.50 9.786 11.056 60.89 320.85 -0.386 5.22 -2.47 4.53 2.12 -4.51 14.40 11.056 12.474 60.38 321.56 -0.423 4.13 -1.68 2.36 1.50 -2.66 9.15 12.474 13.739 59.66 322.50 -0.437 3.38 -1.33 1.04 1.22 -1.45 5.99 13.739 14.609 59.15 323.18 -0.438 7.36 -2.08 -1.03 1.66 -0.91 7.00 14.609 15.974 58.99 323.52 -0.439 3.74 -1.45 0.68 1.24 -1.26 5.92 15.974 17.235 58.62 324.05 -0.445 4.40 -1.62 0.66 1.33 -1.38 6.56 17.235 18.056 58.40 324.39 -0.462 6.46 -2.53 1.76 2.04 -2.60 11.01 18.056 18.748 58.19 324.68 -0.473 8.31 -3.11 1.63 2.49 -2.85 12.70 18.748 19.722 57.75 325.19 -0.479 9.70 -3.49 1.65 2.85 -3.06 13.91 19.722 20.709 56.79 326.10 -0.482 11.76 -4.26 2.41 3.56 -3.94 17.45 20.709 21.767 55.21 327.45 -0.477 13.23 -4.26 -0.07 3.58 -2.55 15.32 21.767 23.962 52.36 329.76 -0.445 12.32 -3.35 -2.85 2.36 -0.67 9.49 23.962 24.474 50.75 331.12 -0.430 23.41 -5.36 -9.15 3.57 0.83 13.02 24.474 25.099 50.40 331.50 -0.428 22.33 -4.51 -9.90 2.98 1.29 10.80 25.099 25.987 50.13 331.90 -0.427 19.49 -3.55 -9.34 2.56 1.42 8.76 25.987 26.420 50.13 332.14 -0.426 21.83 -3.59 -10.85 3.00 1.76 9.37 26.420 27.439 50.78 332.02 -0.424 17.08 -2.44 -8.29 2.37 1.11 7.40 27.439 27.859 52.10 331.48 -0.423 20.79 -2.41 -10.20 2.87 1.24 8.61 27.859 28.278 52.84 331.13 -0.422 19.26 -2.12 -9.29 2.65 1.00 8.10 28.278 29.183 53.98 330.53 -0.421 12.20 -1.45 -5.29 1.85 0.29 5.96 29.183 29.970 54.84 330.08 -0.420 10.36 -1.53 -3.76 1.96 -0.03 6.17 29.970 30.591 55.15 329.96 -0.421 10.20 -1.79 -3.09 2.24 -0.28 7.00 30.591 31.034 55.27 329.96 -0.423 19.26 -7.99 13.53 6.72 -11.96 39.30 31.034 33.157 55.33 330.12 -0.429 12.68 -3.00 -1.29 3.45 -1.67 12.24 33.157 33.705 55.17 330.57 -0.429 28.69 -6.69 2.94 9.13 -7.22 34.17 -------------------------------------------------------------------------------- These noise-reduced angular velocities specify South America plate motion in a Nubia plate frame of reference for time intervals given in the first two columns. The angular velocities and covariances, which are outputs of the REDBACK software (Iaffaldano et al. 2014), were determined from a REDBACK analysis of the finite rotations in Supplemental Table 2. The angular rotation rates omega are positive anti-clockwise and have units of degrees per million years. The Cartesian angular velocity covariances are calculated in a Nubia-fixed reference frame and have units of 10^-8 radians^2 Myr^-2. See Table 1 for instructions on constructing the six covariance matrix elements. ---------------------------------------------------------------------------- Table 3. South America-North America noise-reduced finite rotations ---------------------------------------------------------------------------- Chron Lat. Long. Omega Scaled rotation covariances --------------------------------------------- N E deg. S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- 1n 9.53 -56.96 -0.104 0.8 -0.1 0.2 0.4 -0.5 0.6 2n 10.55 -57.15 -0.242 0.9 0.0 0.0 0.4 -0.6 0.7 2An.1 11.35 -57.21 -0.357 1.0 0.0 -0.1 0.5 -0.7 0.9 2An.3 12.57 -57.04 -0.512 1.2 0.1 -0.3 0.6 -0.8 1.2 3n.1 13.21 -56.87 -0.606 1.4 0.2 -0.5 0.7 -0.9 1.4 3n.4 14.04 -56.55 -0.776 1.6 0.4 -0.9 0.8 -1.2 1.9 3An.1 14.48 -56.30 -0.907 2.0 0.5 -1.0 1.0 -1.5 2.5 3An.2 15.10 -56.02 -1.033 2.3 0.5 -1.2 1.2 -1.7 3.0 4n.1 15.49 -55.75 -1.186 2.7 0.5 -1.2 1.1 -1.7 3.3 4n.2 15.51 -55.62 -1.300 3.3 0.4 -1.0 1.2 -1.8 3.7 4A 15.50 -55.41 -1.498 5.0 0.3 -0.7 1.5 -2.2 5.1 5n.1 15.55 -55.27 -1.637 6.8 0.3 -0.3 1.9 -2.7 6.7 5n.2 16.14 -54.97 -1.911 10.3 0.4 -0.4 2.8 -3.9 10.3 5An.2 17.47 -54.72 -2.246 13.9 1.0 -1.2 3.6 -5.4 14.3 5AC 18.05 -54.82 -2.536 16.9 1.7 -1.0 3.8 -5.8 16.3 5AD 17.75 -55.15 -2.712 19.7 1.5 1.2 3.6 -5.3 16.3 5Cn.1 17.37 -55.75 -2.958 20.9 -0.5 3.1 3.2 -5.3 15.4 5D 17.24 -56.15 -3.175 20.0 -2.0 3.2 3.2 -5.7 14.8 5E 17.36 -56.30 -3.318 19.8 -2.6 3.0 3.3 -6.0 14.7 6ny 17.57 -56.36 -3.438 21.9 -3.5 4.1 3.8 -6.9 16.5 6no 17.98 -56.42 -3.582 25.4 -6.5 6.4 6.9 -11.1 21.9 -------------------------------------------------------------------------------- These finite rotations, which reconstruct the North America plate onto the South America plate, were determined by combining North America-Nubia noise-reduced rotations from DeMets et al. (2015a) with Nubia-South America noise-reduced rotations from Table 1. Rotation angles Omega are positive anticlockwise. The Cartesian rotation covariances, which are tied to the North America plate, specify the 2-D uncertainty in the location of the North America plate upon its rotation onto the South America plate. The covariances, which have units of 10^-8 radians^2, have been reduced by a factor of 16 so as to approximate the scatter in results obtained from the best-fitting North America-South America rotations. ---------------------------------------------------------------------------- Table 4. Antarctica-South America closure-derived rotations: Best-fitting and noise-reduced ---------------------------------------------------------------------------- Chron Lat. Long. Omega Scaled rotation covariances --------------------------------------------- N E deg. S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- Best-fitting finite rotations 1n -87.73 40.65 0.201 1.4 -0.7 -0.6 0.6 -0.1 0.9 2n -87.40 39.34 0.468 6.8 2.1 -9.4 1.5 -2.4 19.0 2An.1 -84.21 39.84 0.740 14.5 3.5 -8.8 2.4 -0.8 14.8 2An.3 -84.78 24.60 1.054 17.2 5.6 -18.1 4.4 -4.1 29.3 3n.1 -84.12 29.80 1.236 21.4 7.0 -23.9 5.2 -4.8 42.7 3n.4 -85.74 58.33 1.508 26.0 7.8 -28.8 5.4 -7.6 45.3 3An.1 -86.68 59.57 1.679 23.0 4.4 -25.2 5.1 -3.6 41.1 3An.2 -86.69 81.99 1.836 32.0 7.0 -36.4 4.5 -7.6 56.7 4n.1 -85.54 97.44 2.125 39.7 9.9 -44.8 6.7 -12.9 66.3 4n.2 -85.71 90.32 2.308 46.3 7.8 -48.7 8.6 -14.2 78.4 4A -85.26 72.62 2.726 75.6 10.5 -71.3 13.4 -24.0 97.3 5n.1 -85.35 72.60 2.894 93.1 31.5 -95.0 18.4 -39.2 121.6 5n.2 -85.64 91.33 3.290 33.3 7.2 -31.1 5.1 -8.0 45.9 5An.2 -85.10 86.78 3.858 40.0 8.8 -40.2 7.4 -13.6 60.5 5AC -84.99 84.56 4.422 33.6 5.9 -25.8 7.2 -8.4 34.4 5AD -83.58 107.44 4.733 42.3 8.6 -37.3 9.4 -10.6 50.1 5Cn.1 -84.18 89.92 5.418 231.6 45.0 -251.7 40.0 -91.3 366.7 6ny -84.10 104.34 6.456 502.5 23.7 -321.5 31.6 -28.1 271.9 6no -83.65 133.85 6.405 75.5 27.6 -46.0 46.8 -14.8 73.4 Noise-reduced finite rotations 1n -85.92 36.10 0.206 11.4 -7.8 3.0 5.9 -2.7 9.3 2n -85.91 40.81 0.475 13.5 -7.7 2.4 6.3 -1.9 10.7 2An.1 -85.86 43.53 0.700 16.9 -7.7 2.1 7.2 -1.3 13.2 2An.3 -85.85 47.54 0.993 22.6 -7.3 1.2 8.4 0.1 17.3 3n.1 -85.89 50.12 1.164 26.2 -6.9 -0.1 9.1 1.5 19.6 3n.4 -86.05 58.00 1.462 30.9 -6.5 -2.6 9.8 2.5 22.7 3An.1 -86.11 66.12 1.685 39.7 -9.5 -5.5 12.6 3.0 28.9 3An.2 -86.06 72.70 1.894 50.1 -11.8 -9.3 15.5 5.1 35.8 4n.1 -85.93 77.70 2.151 57.3 -10.6 -11.8 16.6 5.5 41.1 4n.2 -85.84 79.63 2.341 64.4 -10.0 -12.3 17.9 4.0 46.8 4A -85.73 81.30 2.670 81.6 -10.3 -11.6 22.0 -1.2 61.5 5n.1 -85.66 82.52 2.895 96.7 -11.1 -12.3 25.5 -5.7 74.0 5n.2 -85.46 86.84 3.337 127.0 -11.5 -17.1 31.5 -15.0 99.1 5An.2 -85.06 93.79 3.885 153.9 -4.9 -29.6 33.9 -18.7 119.9 5AC -84.71 98.95 4.392 160.3 8.5 -35.9 31.3 -12.6 124.7 5AD -84.49 102.09 4.743 168.7 16.2 -31.3 33.3 -5.4 132.6 5Cn.1 -84.22 106.26 5.291 209.6 24.4 -16.8 46.8 12.1 166.8 6ny -83.56 119.01 6.343 332.9 83.5 63.4 84.3 68.8 285.6 6no -83.32 133.62 6.622 322.3 69.2 30.5 67.4 42.3 267.7 -------------------------------------------------------------------------------- These finite rotations reconstruct the Antarctic plate relative to the South America plate. The rotations labeled "best-fitting" are determined from the best-fitting Nubia-South America rotations in Supplemental Table 2 and best-fitting Nubia-Antarctic rotations from Table 2 of DeMets et al. (2015b). Rotations for chrons C5D and C5E were not estimated due to insufficient shipboard coverage of these two magnetic anomalies along the western third of the Southwest Indian Ridge. The rotations The rotations labeled "noise-reduced", our preferred estimates, are determined from noise-reduced Nubia-South America rotations in Table 1 and noise-reduced Nubia-Antarctic rotations from Supplemental Table 1 of DeMets et al. (2015b). All rotation angles Omega are positive CCW. All the covariances are Cartesian and have units of 10^-8 radians^2. Both sets of covariances are tied to the Antarctic plate and specify the uncertainty in the location of the Antarctic plate upon its rotation onto the South America plate. Instructions for reconstructing the covariance matrix are given in Table 1 footnotes. ---------------------------------------------------------------------------- NOTE: Supplemental Table 1 is not reproduced in this text document. ---------------------------------------------------------------------------- ---------------------------------------------------------------------------- Supplemental Table 2. Nubia-South America best-fitting finite rotations ---------------------------------------------------------------------------- Chron DOF Lat. Long. Omega Covariances from bootstrap procedure ----------------------------------------------- N E deg. S_xx S_xy S_xz S_yy S_yz S_zz --------------------------------------------------------------------------------------- 1n 3574 60.09 321.45 -0.219 4.9 -1.4 1.1 4.0 0.1 6.9 2n 1206 61.11 321.44 -0.513 66.9 11.8 -1.2 49.2 3.6 34.1 2An.1 1072 62.55 317.74 -0.757 887.3 202.4 -238.9 100.0 -47.8 108.8 2An.3 1141 63.13 320.23 -1.038 161.6 24.1 -50.9 87.0 19.8 73.5 3n.1 813 62.62 319.37 -1.223 167.3 8.8 -40.3 65.1 4.9 45.0 3n.4 996 61.22 320.28 -1.549 168.8 40.1 -23.9 105.9 -5.5 41.8 3An.1 774 61.89 320.53 -1.776 260.1 26.2 -46.2 239.2 38.1 74.4 3An.2 752 61.51 319.62 -2.007 301.4 65.1 -46.4 104.3 -3.6 77.7 4n.1 854 59.99 321.10 -2.303 210.1 57.3 -16.0 76.4 4.1 48.4 4n.2 619 61.29 320.11 -2.498 447.5 35.2 -47.2 108.3 -15.5 114.7 4A 950 61.33 320.03 -2.868 425.9 26.4 -34.0 105.4 -16.7 202.2 5n.1 705 61.32 319.72 -3.120 342.8 43.2 -47.5 98.3 -2.5 106.3 5n.2 1234 61.08 320.54 -3.617 774.4 135.2 -95.1 148.8 5.8 132.3 5An.2 1447 61.80 319.55 -4.193 1039.5 152.5 -178.9 166.1 18.4 122.1 5AC 1394 61.82 319.73 -4.750 881.0 -18.4 -33.7 310.0 28.5 99.1 5AD 1011 59.84 321.39 -5.163 505.5 72.9 -10.2 393.0 51.2 54.4 5Cn.1 1291 60.95 320.71 -5.729 508.9 120.5 -31.3 324.7 -1.4 91.0 5D 1127 59.98 321.61 -6.278 344.2 36.0 -48.9 215.3 3.7 175.4 5E 853 60.24 321.67 -6.661 517.7 -66.6 -15.0 195.0 -22.1 170.4 6ny 753 60.49 321.59 -7.023 660.8 -69.5 -81.8 194.5 -42.2 285.7 6no 929 60.61 321.57 -7.467 530.1 15.7 -76.1 171.8 -15.8 113.9 6An.2 1047 60.41 321.76 -7.972 670.0 -32.5 -83.9 222.6 -16.3 233.7 6Bn.1 1042 60.01 322.34 -8.479 1354.1 378.0 -287.2 734.3 -43.4 448.9 7n.1 1862 58.52 323.54 -9.464 1045.9 411.7 -200.3 971.7 85.8 427.4 7n.2 359 58.92 323.21 -9.620 653.0 293.0 -50.9 768.5 32.8 291.9 8n.1 677 58.44 323.63 -9.962 960.7 43.8 11.6 836.4 -50.4 525.7 8n.2 579 57.91 324.07 -10.252 685.1 -11.3 142.7 448.6 -62.0 320.2 9ny 561 58.20 324.01 -10.534 861.3 -21.1 11.9 597.0 -46.9 330.9 9no 630 57.24 324.68 -10.868 496.1 86.8 -40.3 432.1 -6.7 321.0 10n.1 420 57.32 324.58 -11.082 537.2 -113.0 20.4 321.0 -20.2 124.6 10n.2 370 57.17 324.83 -11.277 1018.7 -137.5 -37.8 383.3 -43.5 323.9 11n.1 673 57.55 324.84 -11.639 1395.7 -135.5 -25.5 757.7 -74.1 413.7 11n.2 515 57.07 325.18 -11.939 1094.5 -216.2 155.8 552.3 -58.1 362.5 12ny 431 57.23 325.15 -12.161 545.6 -84.4 29.9 406.6 -13.9 175.2 12no 354 57.07 325.35 -12.353 664.7 -128.3 59.5 467.1 -32.5 243.4 13ny 1483 56.85 325.78 -13.373 673.5 15.8 -26.5 808.3 80.2 150.2 13no 352 56.78 325.69 -13.580 1261.4 77.9 -177.4 583.7 -32.0 259.5 --------------------------------------------------------------------------------------- These finite rotations reconstruct movement of the Nubia plate relative to the South America plate and include a 2-km correction for outward displacement. The rotation angles Omega are positive CCW. Each rotation is the mean of 1000 bootstrap solutions (see text). DOF, the degrees of freedom, equals the total number of magnetic reversal, transform fault, and fracture zone flow-line crossings used to estimate the rotation for a given time reduced by the number of estimated parameters. The bootstrap-derived Cartesian rotation covariances, which specify the 2-D position uncertainty when rotating points from the Nubia onto the South America plate or vice versa, have units of 10^-10 radians^2. See the footnotes to Table 1 in the main document for information on how to build the rotation covariance matrix from the six covariance elements in the table. ---------------------------------------------------------------------------- Supplemental Table 3. Nubia-South America noise-reduced stage angular velocities ---------------------------------------------------------------------------- Age(y) Age(o) Lat. Long. omega Covariances -------------------------------------- Ma Ma N E dg/Myr S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- 0.000 0.781 60.35 321.26 0.284 7.23 -5.78 16.04 4.64 -12.87 36.29 0.781 1.778 60.79 320.79 0.287 1.61 -1.16 2.86 0.96 -2.35 6.92 1.778 2.581 61.15 320.37 0.292 1.37 -0.79 1.54 0.71 -1.37 4.37 2.581 3.596 61.35 320.11 0.300 1.27 -0.68 1.19 0.62 -1.10 3.67 3.596 4.187 61.41 320.02 0.306 1.39 -0.77 1.38 0.74 -1.26 4.20 4.187 5.235 61.42 319.99 0.309 1.35 -0.78 1.53 0.71 -1.38 4.42 5.235 6.033 61.43 319.97 0.311 1.73 -1.00 2.02 0.89 -1.84 5.80 6.033 6.733 61.40 320.01 0.331 2.33 -1.38 2.86 1.21 -2.59 8.14 6.733 7.528 61.36 320.07 0.355 2.52 -1.33 2.27 1.16 -2.18 7.24 7.528 8.108 61.35 320.11 0.359 2.79 -1.33 1.99 1.17 -2.04 7.00 8.108 9.105 61.28 320.24 0.361 2.92 -1.26 1.64 1.09 -1.83 6.48 9.105 9.786 61.13 320.46 0.367 4.08 -1.90 2.93 1.65 -3.07 10.37 9.786 11.056 60.88 320.81 0.387 4.88 -2.42 4.30 2.07 -4.28 13.87 11.056 12.474 60.36 321.45 0.423 3.96 -1.74 2.35 1.54 -2.57 9.07 12.474 13.739 59.62 322.28 0.436 3.53 -1.54 0.97 1.41 -1.34 6.21 13.739 14.609 59.04 322.89 0.438 9.02 -3.18 -2.03 2.27 -0.29 7.84 14.609 15.974 58.94 323.17 0.438 4.01 -1.86 0.52 1.54 -1.02 6.19 15.974 17.235 58.53 323.64 0.446 4.36 -2.00 0.76 1.63 -1.25 6.81 17.235 18.056 58.29 323.93 0.463 6.27 -3.00 1.78 2.40 -2.29 11.05 18.056 18.748 58.07 324.18 0.474 7.93 -3.71 1.34 2.97 -2.27 12.77 18.748 19.722 57.59 324.59 0.479 9.09 -4.17 1.28 3.41 -2.34 13.85 19.722 20.709 56.56 325.28 0.481 10.89 -5.03 1.95 4.20 -2.98 16.89 20.709 21.767 54.86 326.26 0.477 12.35 -5.54 -0.46 4.57 -1.36 15.05 21.767 23.962 51.82 327.91 0.446 10.66 -4.73 -3.11 3.49 0.72 9.34 23.962 24.474 50.09 328.94 0.430 20.23 -8.32 -8.81 5.72 3.13 13.28 24.474 25.099 49.71 329.23 0.429 19.95 -7.82 -9.98 5.22 3.77 11.50 25.099 25.987 49.42 329.58 0.427 16.89 -6.27 -9.15 4.36 3.54 9.14 25.987 26.420 49.41 329.80 0.426 19.31 -6.84 -10.91 5.02 4.26 10.08 26.420 27.439 50.08 329.84 0.425 14.86 -4.98 -8.29 3.87 3.08 7.95 27.439 27.859 51.46 329.64 0.423 18.44 -5.82 -10.39 4.73 3.80 9.40 27.859 28.278 52.23 329.50 0.422 17.11 -5.29 -9.46 4.34 3.36 8.79 28.278 29.183 53.46 329.23 0.421 10.66 -3.43 -5.37 2.91 1.84 6.13 29.183 29.970 54.38 329.05 0.421 8.75 -3.10 -3.63 2.91 1.23 6.25 29.970 30.591 54.70 329.03 0.421 8.37 -3.11 -3.16 3.11 1.14 6.45 30.591 31.034 54.81 329.07 0.423 8.60 -3.29 -3.00 3.39 1.08 6.98 31.034 33.157 54.81 329.28 0.428 9.43 -3.67 -3.34 3.98 1.30 7.82 33.157 33.705 54.58 329.65 0.429 21.19 -7.30 -3.71 9.08 0.17 20.96 -------------------------------------------------------------------------------- These noise-reduced angular velocities specify Nubia plate motion in a South America plate frame of reference for time intervals given in the first two columns. The angular velocities and covariances, which are outputs of the REDBACK software (Iaffaldano et al. 2014), were determined from a REDBACK analysis of the finite rotations in Supplemental Table 2. The angular rotation rates omega are positive anti-clockwise and have units of degrees per million years. The Cartesian angular velocity covariances are calculated in a frame of reference tied to the South America plate and have units of 10^-8 radians^2 Myr^-2. See Table 1 for instructions on constructing the six covariance matrix elements. ---------------------------------------------------------------------------- Supplemental Table 4. North America-South America stage angular velocities ---------------------------------------------------------------------------- Age(y) Age(o) Lat. Long. omega Covariances -------------------------------------- Ma Ma N E dg/Myr S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- 0.781 0.000 9.53 -56.96 0.133 1.33 -0.16 0.25 0.66 0.00 -0.83 1.778 0.781 11.32 -57.30 0.138 1.69 -0.13 0.19 0.86 0.00 -1.08 2.581 1.778 13.04 -57.32 0.144 2.92 -0.01 -0.05 1.50 0.00 -1.93 3.596 2.581 15.36 -56.62 0.153 2.17 0.16 -0.38 1.10 0.00 -1.46 4.187 3.596 16.68 -55.95 0.159 7.42 1.06 -2.32 3.69 0.00 -5.06 5.235 4.187 17.02 -55.36 0.162 2.73 0.59 -1.23 1.36 0.00 -1.92 6.033 5.235 17.02 -54.78 0.165 5.69 1.37 -3.00 2.88 0.00 -4.22 6.733 6.033 19.52 -53.87 0.180 8.72 1.94 -4.59 4.39 0.00 -6.57 7.528 6.733 18.10 -53.91 0.194 7.83 1.49 -3.81 3.55 0.00 -5.44 8.108 7.528 15.67 -54.27 0.195 17.77 2.40 -6.58 6.76 0.00 -10.43 9.105 8.108 15.41 -54.04 0.199 8.37 0.57 -1.68 2.67 0.00 -4.00 9.786 9.105 16.11 -53.78 0.205 25.44 0.94 -2.21 7.32 0.00 -10.43 11.056 9.786 19.62 -53.06 0.216 10.60 0.35 -0.46 2.89 0.00 -4.04 12.474 11.056 24.97 -53.05 0.239 12.01 0.58 -0.80 3.09 0.00 -4.53 13.739 12.474 22.52 -55.55 0.229 19.24 1.48 -1.47 4.46 0.00 -6.81 14.609 13.739 13.52 -59.82 0.205 48.58 3.75 -0.09 9.46 0.00 -14.27 15.974 14.609 13.29 -62.30 0.182 21.90 0.34 2.14 3.50 0.00 -5.54 17.235 15.974 15.48 -61.58 0.173 25.85 -1.82 3.81 3.85 0.00 -6.74 18.056 17.235 20.06 -59.66 0.174 59.35 -7.51 8.83 9.30 0.00 -16.80 18.748 18.056 23.32 -57.76 0.175 87.51 -13.73 14.21 14.30 0.00 -25.94 19.722 18.748 27.88 -57.50 0.150 50.24 -11.24 10.91 10.79 0.00 -18.30 -------------------------------------------------------------------------------- These noise-reduced angular velocities specify North America plate motion in a South America plate frame of reference for time intervals given in the first two columns. The angular velocities and their Cartesian covariances are derived from the rotations given in Table 3 of the main document. The angular rotation rates omega are positive anti-clockwise and have units of degrees per million years. The Cartesian angular velocity covariances are calculated in a frame of reference tied to the South America plate and have units of 10^-8 radians^2 Myr^-2. See Table 1 for instructions on constructing the six covariance matrix elements. ---------------------------------------------------------------------------- Supplemental Table 5. Antarctica-South America stage angular velocities ---------------------------------------------------------------------------- Age(y) Age(o) Lat. Long. omega Covariances -------------------------------------- Ma Ma N E dg/Myr S_xx S_xy S_xz S_yy S_yz S_zz -------------------------------------------------------------------------------- 0.781 0.000 -85.92 36.10 0.263 1.87 -1.28 0.48 0.96 0.00 -0.45 1.778 0.781 -85.89 44.37 0.271 2.50 -1.57 0.54 1.23 0.00 -0.47 2.581 1.778 -85.72 49.02 0.280 4.69 -2.41 0.71 2.12 0.00 -0.50 3.596 2.581 -85.74 56.89 0.288 3.82 -1.47 0.32 1.53 0.00 -0.12 4.187 3.596 -85.93 65.58 0.290 13.91 -4.14 0.32 5.09 0.00 0.46 5.235 4.187 -85.84 89.96 0.285 5.17 -1.26 -0.25 1.74 0.00 0.36 6.033 5.235 -84.75 110.33 0.280 11.00 -2.61 -1.28 3.59 0.00 0.88 6.733 6.033 -84.15 110.42 0.299 18.17 -4.53 -3.00 5.88 0.00 1.72 7.528 6.733 -84.25 103.56 0.324 16.87 -3.74 -3.32 5.19 0.00 1.75 8.108 7.528 -84.61 96.12 0.328 35.93 -6.63 -7.13 10.50 0.00 2.99 9.105 8.108 -84.82 90.68 0.329 14.59 -2.28 -2.41 4.11 0.00 0.33 9.786 9.105 -84.70 94.02 0.330 38.17 -5.32 -5.23 10.50 0.00 -1.36 11.056 9.786 -83.61 105.98 0.349 13.77 -1.70 -1.87 3.62 0.00 -1.23 12.474 11.056 -81.66 116.78 0.388 13.91 -1.16 -2.38 3.30 0.00 -1.58 13.739 12.474 -81.14 120.70 0.403 19.64 -0.33 -4.15 4.04 0.00 -1.80 14.609 13.739 -80.78 124.47 0.404 43.62 1.86 -8.96 8.32 0.00 -2.06 15.974 14.609 -81.03 128.18 0.403 20.45 1.44 -2.55 4.15 0.00 0.44 17.235 15.974 -79.36 139.82 0.397 30.62 3.09 0.34 6.73 0.00 2.99 18.056 17.235 -77.46 146.75 0.394 87.49 12.59 10.29 19.90 0.00 13.24 18.748 18.056 -73.28 162.66 0.346 137.15 25.30 23.94 30.91 0.00 24.78 19.722 18.748 -53.95 196.18 0.347 70.41 13.06 10.27 14.77 0.00 11.40 -------------------------------------------------------------------------------- These noise-reduced angular velocities specify Antarctic plate motion relative to South America for time intervals given in the first two columns. The angular velocities and their Cartesian covariances are derived from the noise-reduced rotations from Table 4 of the main document. The angular rotation rates omega are positive anti-clockwise and have units of degrees per million years. The angular velocity covariances are calculated in a frame of reference tied to the South America plate and have units of 10^-7 radians^2 Myr^-2. See Table 1 for instructions on constructing the six covariance matrix elements.