============================================================= Finding and applying a pole in and to a velocity data set ============================================================= To apply a rotation pole to a velocity can be used to do different things : 1/ rotate a given velocity from one reference frame to another one. assuming V1 is the velocity in Reference Frame 1 (RF1), and you want it in Reference frame 2 (RF2), you just have to apply to V1 the rotation pole of RF2 with respect to RF1. 2/ compute residual velocities within a rigid plate. assuming V is the velocity of a station on a given plate, applying to V the rotation pole of this plate will eave you with the residual velocity of this station (in other terms, how much this station is moving RELATIVE to the plate) 3/ compute the relative motion at plate boundaries. if one plate has rotation pole P1 and a neighbouring plate has pole P2, and a station on plate 1 has velocity V1. then applying P1 to V1 should give 0, and applying P2 to V1 will give the velocity of the station with respect to plate 2. if the station is on the boundary between plate1 and plate2, this velocity is the relative velocity between the 2 plates at that place applying a pole to a given set of vectors is very straightforward ! 1st step : ---------- get a velocity table ! the table should list those numbers in this order : lon lat Veast Vnorth sigVe sigVn correl Site-Name exemple : geodyssea-sol.dat (velocities of GEODYSSEA solution in ITRF2000) ---------------- 128.117 -3.775 12.90 20.24 0.29 0.09 0.058 AMBO 121.436 -1.010 -1.66 7.87 0.23 0.06 -0.106 AMPA 106.849 -6.491 -23.56 -71.13 17.94 5.12 0.042 BAK2 106.849 -6.491 21.68 -8.31 0.10 0.03 -0.056 BAKO 114.680 -8.147 27.50 -11.17 0.26 0.08 0.014 BALI 119.460 -1.427 17.39 -5.72 0.19 0.06 -0.009 BARA 114.791 -3.867 26.09 -9.04 0.26 0.08 0.055 BATU 122.795 -5.471 27.05 11.38 0.22 0.07 0.021 BAUB 102.252 -3.786 25.63 14.58 0.26 0.08 -0.035 BENG 136.248 -1.167 -10.97 89.78 0.40 0.12 0.053 BIAK 116.815 -1.272 22.58 -11.42 0.18 0.06 0.032 BLKP 96.111 22.360 27.75 1.64 1.17 0.38 -0.012 BODA . . . ----------------- 2nd step : =========== apply the pole : a simple command line to invoque the program, with command line arguments. Runstring: applypole infile: velocity file name (input to applypole) outfile: rotated velocity file name (output by applypole) coef: apply a coefficient if velocities are not in mm/yr (1 in most cases) example : applypole geodyssea-sol.dat geodyssea-sol_eurasia.dat 1 the program will then ask for the pole to be applied, suggesting a list of known pole. using the values for Nuvel-!a Eurasia for example (50.6,-112.4,0.23) will rotate the velocities so that they are now relative to Eurasia (as defined in the Nuvel-1a model) training : 1/ using geodyssea-sol.dat file, what is the velocity of station IISC (Bangalore in India) with respect to Eurasia as defined by Calais et al 2003 with pole located latitude 52.3, longitude -107.0, 0.245 2/ using geodyssea-sol.dat file and the Nuvel1A Eurasian pole (50.6,-112.4,0.23), what is the velocity of stations NONN PHUK CHON KUAL TABA TANJ BAKO BUTU BALI BATU CAMP, with respect to Eurasia ? 3/ using the velocities of those stations with respect to Eurasia and the pole of Sundaland with respect to Eurasia (66.7,-27.0,0.090), compute the velocities of those stations with respect to Sundaland. conclusion ? 4/ compute directely the velocities of thoses stations using the geodyssea-sol.dat file and Sundaland pole in ITRF2000 (59.4,-99.3,0.303). compare to previous result. conclusion ? 5/ given the 2 poles : sunda in ITRF2000 : 59.4,-99.3,0.303 Australia in ITRF 2000 : 32.3,39.4,0.614 compute the motion of Australia relative to Sunda at position : lat=-7, lon=105 Finding a pole is easy too. 1st step : ========== get a velocity file (again geodyssea-sol.dat will work fine). extract stations on Sundaland (NONN PHUK CHON KUAL TABA TANJ BAKO BUTU BALI BATU CAMP), and put them in a new file (ie Sunda_ITRF2000.dat) start program findpole, using a simple line command : Runstring: findpole : input velocity file : pole initial start latitude : pole initial start longitude : +/-Dlat step of initial grid : +/-Dlon step of initial grid : Option 1/2/3/4 for minimization 1 : L1 norm minimization 2 : L2 norm (least square) minimization 3 : weighted by distance to pole 4 : weighted by distance to pole times velocity : number of iterations findpole will try to minimize the differences between the velocities in the input file and the velocities predicted by a given pole. the rotation pole of the plate defined by the velocities in the input file is then found by successive iterations. you have to give findpole informations on how to procede to look for this pole. - where to start (lat, lon) should not be too far away from final position - the length of the grid (dlat, dlon) should be adapted to how far you think you are from the final pole example : findpole sunda.dat 57 -102 5 5 2 20 should work fine. ALWAYS TEST YOUR FOUND POLE BY APPLYING IT TO THE INITIAL VECTORS -> SHOULD GIVE SMALL VELOCITIES !!!! training : using the 11 stations NONN PHUK CHON KUAL TABA TANJ BAKO BUTU BALI BATU CAMP 1/ find Sundaland pole in ITRF2000 2/ find Sundaland pole with respect to Nuvel-1a Eurasia 3/ find Sundaland pole with respect to Eurasia defined by Calais et al 2003 (52.3,-107.0,0.245) 4/ one station has high residual velocity (> 4 mm/yr). which one ?. what does this mean ? 5/ start again, using only 10 stations 6/ one station has again high residual velocity (> 3 mm/yr). which one ?. what does this mean ? 7/ start again, using only 9 stations 8/ finally, which stations are located in stable Sundaland ? 9/ what are the velocities of stations XIAN, WUHN, and SHAO with respect to Sundaland. any conclusion from that ? if you have additionnal time, you can try to find poles for South Sulawesi (Makassar) block, and North Sulawesi (Minahassa) block. pick up the stations you like and see what happeneds