==================================================================== Inverting velocities around a fault to find an arctangent profile ==================================================================== to fit an arctangent profile to a given set of vectors around a strike-slip fault is very simple. 1st step : ---------- get a velocity table ! the table should start with a header : the first 2 lines with text describe the data set then, the table should list those numbers in this order : lon lat Veast Vnorth sigVe sigVn correl Site-Name example : fault1.dat -------------------- test data strike slip fault 1. orientation : North 180 degrees 119.000 0.000 0.00 3.29 1.00 1.00 0.000 pt01 119.100 0.000 0.00 4.03 1.00 1.00 0.000 pt02 119.200 0.000 0.00 5.15 1.00 1.00 0.000 pt03 119.300 0.000 0.00 6.99 1.00 1.00 0.000 pt04 119.400 0.000 0.00 10.14 1.00 1.00 0.000 pt05 119.500 0.000 0.00 15.41 1.00 1.00 0.000 pt06 119.600 0.000 0.00 19.86 1.00 1.00 0.000 pt07 119.700 0.000 0.00 23.01 1.00 1.00 0.000 pt08 119.800 0.000 0.00 24.85 1.00 1.00 0.000 pt09 119.900 0.000 0.00 25.97 1.00 1.00 0.000 pt10 120.000 0.000 0.00 26.71 1.00 1.00 0.000 pt11 -------------------- 2nd step : =========== find the best fit arctangent to these velocities ! this is done with program iat, and is done through a simple invocation with command line arguments : Runstring: iat : the input velocity file : the output file with best fit arctangent and other things : the parameter file describing the fault on which the arctangent is applied example : iat fault1.dat fault1.res fault1.par description of input parameter file example : fault1.par ------------- test fault1 iat input parameter file (3 header lines) parameters * comment ----------------------------- 119.5 * longitude of fault start point 0.500 * latitude of fault start point 200.0 * length of fault 180.0 * strike (in degrees from North) -------------- the first 2 lines are header again the 3rd and 4th line contain the position of the starting point of the fault (longitude, latitude) the 5th line contains the length of the fault (in km) the 6th line contains the strike of the fault (in degrees from North) all these values may not be known precisely. what matters is that you find parameters such that your fault is really going to run across your network, approximately where you think is the real line of elastic accumulation. then you can adjust and see what happeneds. AWAS ! there are always 2 identical faults : the one running one direction, and the one running 180 degrees from this direction. only the STARTING point has to be different. description of output file example : fault1.res ------------- least square inversion fault parameters --------------------------------------- strike = 180.0 degrees locking depth = 20.0 km far-field velocity = 30.0 mm/yr residual (rms) = 0.02 mm/yr applied translation vel of = 0.02 mm/yr . SITE longitude latitude Vlon Vlat dVlon dVlat Corr. VEL AZIMUT dist /fault Vpl Vpp dVpl dVpp Vobs Vmodel Vresid ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ pt01 119.00000 0.00000 0.00 3.29 1.0 1.0 0.000 3.3 0. -55.657 3.29 0.00 3.0 3.0 3.27 3.29 -0.02 pt02 119.10000 0.00000 0.00 4.03 1.0 1.0 0.000 4.0 0. -44.527 4.03 0.00 3.0 3.0 4.01 4.03 -0.02 pt03 119.20000 0.00000 0.00 5.15 1.0 1.0 0.000 5.2 0. -33.396 5.15 0.00 3.0 3.0 5.13 5.15 -0.02 pt04 119.30000 0.00000 0.00 6.99 1.0 1.0 0.000 7.0 0. -22.265 6.99 0.00 3.0 3.0 6.97 6.99 -0.02 pt05 119.40000 0.00000 0.00 10.14 1.0 1.0 0.000 10.1 0. -11.136 10.14 0.00 3.0 3.0 10.12 10.15 -0.03 pt06 119.50000 0.00000 0.00 15.41 1.0 1.0 0.000 15.4 0. 0.341 15.41 0.00 3.0 3.0 15.39 15.16 0.23 pt07 119.60000 0.00000 0.00 19.86 1.0 1.0 0.000 19.9 0. 11.136 19.86 0.00 3.0 3.0 19.84 19.85 -0.01 pt08 119.70000 0.00000 0.00 23.01 1.0 1.0 0.000 23.0 0. 22.265 23.01 0.00 3.0 3.0 22.99 23.01 -0.02 pt09 119.80000 0.00000 0.00 24.85 1.0 1.0 0.000 24.9 0. 33.396 24.85 0.00 3.0 3.0 24.83 24.85 -0.02 pt10 119.90000 0.00000 0.00 25.97 1.0 1.0 0.000 26.0 0. 44.527 25.97 0.00 3.0 3.0 25.95 25.97 -0.02 pt11 120.00000 0.00000 0.00 26.71 1.0 1.0 0.000 26.7 0. 55.657 26.71 0.00 3.0 3.0 26.69 26.71 -0.02 ------------- the first text lines contain the parameters of the best fit arctangent - strike of the fault (same than from parameter file, iat does not inver for a new one yet) - locking depth (in km) - far field velocity (in mm/yr) - the total rms of the observed velocities with respect to the modeled velocities - the value of the translation applied to put the original velocities in the correct reference frame (in this frame, the velocity of a point at infinite distance from the fault is zero) then following lines contain all self explained numbers at each station. these values are used to make plots 3rd step : =========== plot the data, best fit arctangent, residual velocities, etc, etc, etc... with program iat.gmt iat.gmt : input file = output file from iat (ie. fault1.res) AWAS: for the test fault plot, make sure you have the following lines commented/uncommented # parameters for test fault set lmin = "-70" set lmax = "70" set ropt = "118.9/120.1/-0.5/0.50" set copt = "n" ## parameters for Palu fault #set lmin = "-30" #set lmax = "40" #set ropt = "119.45/120.35/-0.95/-0.40" #set copt = "y" and of course reverse when working on Palu fault training : 1/ compute arctangent profile for a test fault described in fault1.par and fault1.dat it is a fault runing from North to south with velocities // to tha fault what is the locking depth ? the far field velocity ? 2/ compute arctangent profile for a test fault described in fault2.dat (create yourself a fault2.par after you have read the header line of fault2.dat) what is the locking depth ? the far field velocity ? 3/ compute arctangent profile for a test fault described in fault3.dat (create yourself a fault3.par after you have read the header line of fault3.dat) what is the locking depth ? the far field velocity ? 4/ compute arctangent profile for a palu fault described in palu.dat (create yourself a palu.par file with folling numbers : fault starts at point (lon=119.725,lat=-0.600), has a length of 50 km and strikes 158 degrees from north this should not give a good result. why ? find which stations are creating a problem 5/ compute arctangent profiles for the palu data, rejecting stations that create problems what are the results using stations from Wata to PL11 ? from Wata to PL12, from wata to PL12 + tobo ? 6/ if you have time, try to move the fault in the palu.parso that station Loli is on one side or the other. is it better ? is it signficant ? 7/ again, try changinng the strike of the fault a little bit. what are the results ?