Tectonics through GPS
05. 09. - 12. 09. 2007
Exercise 6
Reminder to use tcsh
1.
Copy the directory ~plattner/GPS-course/Exercise6/TOPODEF to your
homedirectory. The program topodef.f computes the deformation resulting from a
volume change of a defined source within a halfspace. There are 4(5) different models
that describe the deformation from such a source. We will look at the differences and
compare the model results.
The input file for the program is called paramin.NAME.dat, choose the name for
your model and run the program as RUN.com NAME
The program creates to plots, stored in the directory results:
NAME.profile.ps shows you the horizontal (blue) and vertical (red) displacement at
the specified cross-section.
NAME.V.ps will show you the vertical deformation at the surface and the vector
displacement field.
The inputfile is specified in the following way:
Line Parameter
19
Title
35
nsrc
35
35
35
101
112
129
130
ff
273
284
342
342
347
393
411
428
448
ndval
naval
nset
inod
nlout
npln
nind
fc1 – fc9
Pois, rmu
isrc
par
Meaning
Specify your model NAME
Nr of sources creating the deformation (e.g. 1 Magma chamber,
1 Magma chamber plus 1 pipe)
Nr of parameter values for the horizontal profile (1-47)
Nr of parameter values for the vertical profile (1-47)
Nr of profiles you want to solve for
Specify the parameters for the horizontal profile
Specify the parameters for the vertical profile
Nr of nodes in x and y direction specifying your model area
Nodes along profile(s) (x,y)
Parameters controlling frequency
Poisson ration and shear modulus
Choose model (1-4, see lines 296-337)
Specify the parameters of the chosen model (see lines 296–
337 on what you need to set)
Specify your mesh (nodes)
Specify projection of axes
Scaling information
Units
Indices
1.1
Calculate the deformation from a magma chamber of a radius of 4000 m and a
pressure 107 Pa. The magma chamber should be located at a depth of 8000 m.
a) Use the Mogi-source model and calculate the source strength for the 1st parameter.
b) Use the spherical model for the same settings
1
Tectonics through GPS
05. 09. - 12. 09. 2007
c) Adjust the gmt-script compare.gmt with your model NAMES for the input files and
run it to onbtain a comparison of the vertical deformation resulting from these two
models.
c) Do a similar comparison of the results of a Mogi source and a spherical source
model for a depth of 15000 m. Can you explain why the differences vanish?
1.2
Using the Ellipsoidal source model for a magma chamber with a pressure of
107 Pa and a volume of 268.083 * 109 m³. The Euler angles should be set in a way so
that the angle between the z-axis and c-axis (ellipse minor axis) is 5 degrees, but the
orientation of the ellipse major-axis should be set to 0.0 for both. The depth should
again be 8000m. Compare the model results for different source geometries (draw
sketches of these sources:
a) Ratio of b-axis to axis = 1, ratio of c-axis to a-axis = 1. Compare your results to the
ones obtained from the Mogi source and the spherical model, using the compare.gmt
script.
b) Ratio of b-axis to axis = 0.5, ratio of c-axis to a-axis = 0.5
c) Ratio of b-axis to axis = 0.1, ratio of c-axis to a-axis = 0.1
d) Adjust the compare.gmt script to compare the 3 models.
1.3
The ellipsoidal model with a ratio of 1/0.1 can be rotated to simulate a pipe
(vertical orientation of a ellipse with a small and equal ratio of a/b and
a/c…………………………
1.4. Model a tension crack having a 2 m displacement at a depth of 300 m, and a
horizontal dimension of 500 m and a along-dip dimension of 100 m. The dip should
be orientated 89.9 degrees w.r.t. the horizontal, and the strike 90 degrees ccw from
east.
2