Tectonics through GPS
05. 09. - 12. 09. 2007
Exercise 2
Reminder for using the tcsh
Copy the directory ~plattner/GPS-course/Exercis2 to your home. You will find a list
of GPS stations PAsites.dat, which you can plot using the executable file:
PAsites.gmt
You will also find a file PA.dat that contains the velocity data from these stations on
the Pacific plate, in the format of:
SITE
Velocity-East
Velocity-North
Error-East
Error-North
Keep this file as a backup. Copy it to another file PA1.dat with which you work:
Cp PA.dat PA1.dat
You will also find the file site.gd, which contains the position data of each GPS
station.
1.
The position data and the velocity data of GPS stations from the Pacific plate
allow you to invert for the Pacific plate Euler vector, i.e. pole of rotation. Run this
inversion as:
~plattner/bin/vplate1.x < PA1.dat >& PA1.pol
Look at the output PA1.pol:
In the upper part you find observed velocity and uncertainty, plus the
predicted velocity and the residual between observed and predicted velocity
for North and East direction. The lower part gives the modelled velocity (rate
and azimuth cw from north) and the residual velocity, which should be as low
as possible. Below you also find the mean residual rate for all stations. The
last column lists the importance of each station in percent, which should be
more or less equal weighting for all stations.
In the middle of the file you also find information about the Chi² misfit, where
the reduced Chi2 (Chi²/DOF) should have a value of ~1.0 for a good model
(see formular at the end of these sheets)
The last three lines of PA1.pol are the Euler vector in Cartesian Coordinates. Extract
these last 3 lines into a own file:
tail -3 PA1.pol > PA1.vec
Create a file PA1.st, containing PA1.vec and PA.dat
cat PA1.vec > PA1.st
cat PA.dat >> PA1.st
Run a transformation of you’re your observed GPS data from IGb00 into the stable
Pacific plate reference frame:
pvel < PA1.st > PA1.res
Tectonics through GPS
05. 09. - 12. 09. 2007
Automatically create the file map_vel.dat suitable for plotting the residual motion of
each station with respect to the stable Pacific plate. To obtain it, run
vmap PA1.res –diff
Plot the residual motion by running the gmt-script remap.gmt and look at the output
map.ps. The residual motion is shown as a vector, the velocity uncertainty as an error
ellipse representing 95% confidence. For a good representation of the stable Pacific
plate, the residual motion should be insignificant.
The executable script meanresidualrate.x (meanresidualrate.f90) calculates you the
mean residual rate of all 22 stations from your map_vel.dat file.
2.
Improve your stable Pacific plate Euler vector by excluding GPS stations of
which you think they do not represent the stable Pacific plate motion well, e.g.
because the station has a large residual motion. Be careful, there may be many
different other arguments for why you need or not need to exclude a station, ranging
from the noise within the GPS time-series (In the subdirectory GD.ps-files you will
find the SITE.GD.ps files, and you can see the quality of the time-series) over
geological arguments (location is in active deformation zone) to unequal weighting
proportionalities in the inversion.
For each model make an own directory, copy the necessary files into it, to store the
output of your calculations. Run as many models as necessary until you find a
solution you are confident with. Be aware that this process may not only be directed
in “one-way” (it may turn out that sites you have excluded at the beginning later on fit
quiet well).
Prepare a table summarizing all your results as:
Directory Nr. of
name
stations
Chi²/
DOF
Stations used for inversion
Mean
Nr. of stations
residua
with significant
l rate
residual motion
All 22 stations
Mean
Nr. of stations
residual with significant
rate
residual motion
3.
Copy all your Euler vector files PA*.vec into a new directory. Convert the
Cartesian vector information for each Euler vector into a rotation pole location in
geographical coordinates and a rotation rate in degrees/Myr.
~malservisi/bin/getsph < PA1.vec > PA1.sph
PA1.sph gives you 1D and 2D information. Use the 2D information for the following:
Extract the data from all of your PA*.sph files into a single file Poles.dat that contains
additionally the mean residual rate of all 22 stations for each Euler. Poles.dat should
be set up in the following:
Latitude Longitude MeanResidualRate Azimuth Max-Error Min-Error Modelname
Tectonics through GPS
05. 09. - 12. 09. 2007
e.g.
-63.67 109.81 1.10 78.9 56 25 PA1
Sort this file by the Max-Error and Min-Error:
sort –k3 –k6 –r Poles.dat > Poles.dat.sort
Plot the location of the Euler poles and their uncertainty colourcoded by the mean
residual rate, using the gmt script Poleplot.gmt, with the colourscale Col.cpt and
text.txt, which you find in the directory Exercise2. If you want you can adjust the
colourscale using gmt command makecpt (man makecpt) see also Exercise 4 below.
From all the information you have now (mean residual rate of the stations used, mean
residual rate of all 22 stations, plots of your residual motion, plot of the spatial
distribution of the rotationpoles itself), chose your best model. Why do you think this
is the best model? Explain which sites and why you excluded them.
4. GMT (General Mapping Tool) is a script that plots data from a file (e.g. PA.dat).
The GMT script (e.g. PAsites.gmt) is a executable file. By executing it you plot the
data of PA.dat. If you want to change seetings of GMT enter into the executable file
(e.g. vi PAsites.gmt)
Try to get familiar with GMT commands by looking at the GMT manual:
man GMT
Learn about the meaning of the switches –R, -J, -B, -K, -O, -H, -W, -V
_____________________________________________________________________
Chi² = SUM (Δy / σ)²
Chi² = SUM (Modelled value – observed value / Error of the observed value)²
DOF = degrees of freedom (Nr of points – nr. of modelparameters)
Tectonics through GPS
05. 09. - 12. 09. 2007