23.9 FOC: Plot many FPS, stress inversion and Rose diagram

The SLICK program

This program is part of the Slick package doing the following quoting the author Michael (1984) "The slick package uses fault slip data (either field observations or from focal mechanism) to find the stress tensor that best explains the observations. Inputs are the orientation and slip direction of a set of fault planes. Outputs are the orientation and shape of the stress ellipsoid, including confidence regions, and statistics used to judge the success of the inversion. This method uses the linear inversion algorithm and non-parametric bootstrap statistics". The software is available at http://earthquake.usgs.gov/research/software/index.php.

In SEISAN, only the inversion part has been implemented so the error analysis is missing. Program SLICK can be run as a separate program, but is normally run as part of FOC which prepares the input for SLICK and plots the output. The method is explained in Michael (1984) where also examples are given with data available at the above web site. Running SLICK: slick "file", where "file" is a file with strike of dip, dip and rake. An example input file is:

Strik dp     Dip    Rake
   203.0    51.0   137.0
   280.0    85.0  -161.0
    ...

Note that in SEISAN, strike of fault plane is used so the strike of the dip is strike of the fault plane+90 degrees. The output is "file.oput" which gives the found stress tensor and the fit to the data, for details see Michael (1984). The stress tensor has a corresponding slip angle, (average slip) and for each event the difference in slip angle for the individual event and the average slip is calculated as well as the average difference and standard deviation. When running SLICK with FOC, an input file foc.slick is made for selected events (making the corrections to strike of slip) and the output file is foc.slick.oput. FOC also plots the direction of maximum compressive stress s1, minimum compress stress s3 and null axis s2. In the example below s1 has max value of 0.68 and strike and dip are 19 and 34 respectively. S3 has strike and dip of (113, 5) and s2 (-149, 56) respectively. The average fit angle is 59 with a standard deviation of 51, a bad fit.

stress tensor is:
-0.290526  0.236582  -0.146602  
0.236582  0.293028  -0.438347  
-0.146602  -0.438347  -0.00250278  
eigenvalue   vector: E,N,UP,direction,plunge
0.686771  -0.273399  -0.784281  0.556917  19.205739  33.820430
-0.37516  -0.917882  0.385856  0.0927811  112.725966  5.320093
-0.31161  0.287656  0.485818  0.82537  -149.270892  55.589101
variance= 0.283314
phi value= 0.940156

dip direction, dip, rake, fit angle, mag tau
  203.0     51.0    137.0    166.4    0.11
  280.0     85.0   -161.0    167.9    0.19
   ...
   13.9     68.1    -85.7     11.0    0.46
   14.0     70.0   -130.0     33.3    0.48
fit angle mean= 59.156784 standard deviation= 51.527176
for f=0.8 I= -2.242677 , std. dev.= 1.609795 D norm= 0.248640
avg tau=xx , std. dev.= xx

For a complete stress analysis it is recommended to also do the error analysis using the complete slick package or e.g. the program ZMAP (not a SEISAN program, uses MATLAB, found at http://www.earthquake.ethz.ch/software/zmap/ftp). FOC writes a file which is formatted for input to ZMAP. However doing stress analysis as implemented in SEISAN gives a good impression of the consistency of the fault plane solutions in a particular area. It is recommended that at least 10 events are used for inversion.

FOC program

FOC is a program doing different things with fault plane solutions given in a CAT-file: Converting data to other formats, plotting many solutions, running the SLICK program and displaying the results, plot P and T axis for many events and make statistics of polarities. The input is:

foc
 Give input file
collect.out
 Quality, ABC.., up to 5 chars, enter for all
AB                                            Comment: Different qualities can be selected
 Cumulative(c) or individual misfit(def)      Comment: See later

 Plot all solutions selected (Y=enter/n)      Comment: Analysis can be done without plotting all
N

The plot of the many fault plane solutions is seen in Figure 23.4. After plotting the fault plane solutions, a plot comes up plotting the location of the P and T axis and the results from SLICK, see Figure 23.6.

**Figure 23.6:** Left: The position of the T-axis given by the event numbers. The triangle is the SLICK minimum compressive stress direction and the circle is the null axis. Right: Corresponding for P-axis and the triangle is now the maximum compressive stress direction. Top: The misfit for each event as a function of event number. This figure can also show the cumulative misfit, see example run of FOC.
$\begin{figure}\centerline{\includegraphics[width=0.9\linewidth]{fig/fps-slick}}\end{figure}$

Output files:
Foc.out: P and T axis for all events, can be used as input to make rose diagrams.
Foc_events.out: The events used based on quality selection
Foc_pol.out: Statistics of polarities:

Stat     C    D
AZ05     3    2
MESC    18   60
VIF0     5    2
MIRA    10   32
VIF     44   19
LFA     52   18
PRCH    36    6
PVER    26    3
FRA0     0    2
AZ07     1    1
.
.
SET2     3    0
PSAN     1    3
 Sum of maximum number of polarities         570
 Sum of minimum number of polarities         158

For each station the different polarities are counted and a sum of the consistent polarities are given at the end. Foc.zmap: Input file in format used by ZMAP, notice direction of slip is used instead of strike of fault, see SLICK.
Foc.slick and foc.slick.oput: See SLICK.

NOTE: FOC uses the first instance of the fault plane solution found in file for a particular event.