Tectonics through GPS
05. 09. - 12. 09. 2007
Exercise 3
Reminder for using tcsh
1.
Savage and Burford (1973) published an elastic half space model in which the
surface velocity field, representing the strain accumulation across a strike-slip fault,
can be expressed as:
v = (V/pi) atan (x/D)
where:
v is the observed surface-velocity at a point. In our case this is the component of
velocity of a GPS station in the fault-parallel direction.
V is the full relative motion, also named far-field velocity.
x is the distance of the point (in our case GPS station) from the fault.
D is the locking depth of the fault.
Draw the fault trace at the surface this 3D model of a vertical strike-slip fault and
mark the locking depth D of the fault. Draw velocity vectors to the black points.
2.
Assume the full North America – Pacific relative plate motion at a location
along the San Andreas Fault (SAF) to be 52 mm/yr, 100% of this motion being strikeslip.
2.1. Calculate the fault parallel velocity according to Savage & Buford (1973)
model, at distances 0, 2, 5, 10, 25, 50, and 100 km from the fault.
Assume the locking depth is a) 10 km b) 20 km.
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Tectonics through GPS
05. 09. - 12. 09. 2007
2.2
Since you can expect antisymmetry at a perfect strike-slip fault, you can use
simply negative distances -5, -25, etc. and the corresponding negative velocities for
the opposite site of the fault.
For each locking depth, prepare a file (distvelo10.dat and distvelo20.dat) listing the
distances and velocities in the following order: Start with negative distance, zero
distance and then positive distances and their corresponding velocities.
e.g.
-100
-50
-25
-10
-5
-2
0
2
5
10
…
-22.73
-19.70
….
…
…
…
…
…
…
…
…
Plot this data using the GMT script distvelo.gmt, run it to obtain the plot
veloprofile.ps.
3.
In the directory Exercise3 you will find a data-table final_dataset_errorcor
containing GPS data from ~1400 stations located in the Pacific-North American plate
boundary region, mainly southern California.
In the following this position and velocity data is used to identify patterns of strain
accumulation of strike-slip faults, following Savage and Burford (1973). The program
to use is called process_data. It inverts for the best-fitting fault parameters, like
location of the fault (x=0), motion (V), and locking depth (D).
To run such an inversions for a strain accumulation pattern you need to define the
fault-perpendicular direction, and choose which GPS data you want to use. You can
set this in the program process_data by defining a rectangular box, for which you set
the coordinates of its center (In the program named “faultcenter_lon” and
“faultcenter_lat”), the length (“length”), width (“width”) and the azimuth of the
length-axis in degrees clockwise from north (“projection_azimuth”). The projection
azimuth calculates the fault-parallel velocities to use for the inversion.
Another setting is the number of faults you want to invert (since there may be
overlapping strain accumulation patterns from nearby faults). You can give your
models different names (line 12 in the program) to store your results.
3.1.
Run such an inversion for a model called BIGBEND that solves for 1 single
fault, centering your box at -118°E, 34.5°N. Once you run the programm, you can
look at your settings on the plot map_BIGBEND.ps.
a) Orientate the projection_azimuth perpendicular to the San Andreas fault and run
the program for the inversion.
Look also at the surface velocity profile in the plot fit_BIGBEND.ps. This plot shows
the component of velocity in the fault-parallel direction of your chosen GPS stations,
plus the modelled velocity curve for the found fault.
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Tectonics through GPS
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Look at your results shown in the output on the screen, giving you the inverted
locking depth D and the fault motion v0_1. The reduced Chi-square is a measure of fit
of the GPS observation to the fault model and should be around 1.
b) Reset the length and width of your box to test how sensitive the inversion for fault
location, locking depth D_1 and fault motion v0_1 is to your chosen box-size. You
can evaluate your results by the reduced Chi-square. Explain your observations.
3.2. Solve for the fault motion in the area of the San Andreas Fault, San Jacinto
fault (approximately -116°E to -117°E and 33°N to 34°N. Solve once for 1 fault
(“SAF1”), once for 2 faults (“SAF2”). By choosing the box center, box size and
projection azimuth, try to improve your results (~reduced Chi-square as close to 1 as
possible).
3.3. Solve now for three faults to take also in account for the Elsinore fault
(“SAF3”). Compare your results of all the three models and discuss them.
3.4. By introducing a third fault you’ve been increasing the number of free
parameters for fittin your data. Too many free parameters can give unreliable results.
We can reduce the number of free parameters again by fixing one of the variables. Fix
the locking depth D for all three faults to 12 km by creating a file “parameter” which
is basically set up in the same format as “parameter_SAF3” but with the lines of
D_1, D_2, and D_3 setted as:
D_1
= -12.0 # FIXED
Then uncomment line 148 in the code process_data and run the inversion, see your
results.
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Tectonics through GPS
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5. Try to answer the following questions:
a) What problems can occur when solving for the strain pattern across a single-fault?
b) What problem occurs when solving for multiple faults (3 or more) using the Savage
and Buford model?
c) Why is a locking depth of 60 km or more not anymore reasonable?
d) Which other geophysical observations can be used to estimate the locking depth?
For further information read Chapter 1.1. (ff)
COHEN, S.C., Numerical models of curstal deformation in seismic zones. Advances
in Geophjysics, Vol. 41.
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