40. FK Analysis

The FK routines were provided by Tormod Kværna from NORSAR and implemented into SEISAN by Andrius Pacesa.

Some basics

The FK-analysis, more strictly slowness analysis, is a standard tool in seismic array processing. It is used to find the apparent velocity and back azimuth of an incoming wavefront. Apparent velocity can be used to identify the type of wave (P, S, Lg and etc.) and the approximate distance to the source can be determined for teleseimic events. Utilizing azimuth and distance to the source, one can define the approximate location of the signal source.

A description of frequency-wavenumber analysis - f̈-k analysis-̈ may be found in Capon (1969). This method has been further developed to include wide-band analysis and maximum-likelihood estimation techniques - see Kvaerna and Doornbos (1986).

The principle of slowness analysis is beamforming in the frequency domain for a number of different slowness values and calculating the power for each beam. The beam power will be a maximum in case the slowness of the beam coincides with the slowness of the wavefront crossing an array. So the beam having the maximum power will indicate the slowness of the incoming signal.

Running the program

The FK program can be started directly with command fk or from MULPLT. The program expects that the file waveform.out with the seismic traces as input data, is available in the current directory. If the program is invoked directly, this file has to be created before using mulplt, selecting a window and creating the `waveform.out' file.

In general it is more useful, to start the FK program from MULPLT since the input file needs to be created by mulplt. The result of the fk analysis can be saved to the S-file.

The steps are:

-	start MULPLT
-	select channels and a time window
-	use option fk to start FK program (this option creates file `waveform.out' and starts FK program), accept maximum or pick value with mouse The options in FK are: R-Redo: Repeat fk analysis with different parameters M-Mouse: `m' or mouse click to pick values different from maximum S-Save and quit: save picked value to file and quit Q-Quit: quit
-	use option `save and quit' to save your result, so that it can be used by MULPLT
-	back in MULPLT: pick phase on the first trace used, to store back azimuth and apparent velocity in the S-file
-	in case of teleseismic events, the apparent velocity can be used for location, the fk analysis has to be done on the P phase

Note: The FK program only works by default with station file `STATION0.HYP'. If coordinates are in e.g. STATIONt.HYP, the user will be asked to specify another station file letter, in this case `t'.

Example

Input:

 
 Enter lower frequency,<ENTER> for default value 1 Hz

 Enter higher frequency,<ENTER> for default value 5 Hz

 Enter max slowness, <ENTER> for default value 0.4 s/km

 Enter No of grid points, <ENTER> for default value 51

 Do you want to plot level numbers, N/Y, <ENTER>=Y

 It will take some time ...
 APPARENT VELOCITY  10.26   AZIMUTH          140
 NORM. POWER MAX     0.99   POWER MAX IN dB  72.44
 MAX X SLOWNESS      0.06   MAX Y SLOWNESS   -0.07
 LOW FREQUENCY       0.94   HIGH FREQUENCY    5.00
 QUALITY (1=best, 4=worst)  1
  Plot file is fk.eps

Example of output file fk.out:

 DATE, TIME AND WINDOW LENGTH     99 256  9 13 12  0 33.843     7.62
 APPARENT VELOCITY  10.26   AZIMUTH          140
 NORM. POWER MAX     0.99   POWER MAX IN dB  72.44
 MAX X SLOWNESS      0.06   MAX Y SLOWNESS   -0.07
 LOW FREQUENCY       0.94   HIGH FREQUENCY    5.00
 QUALITY (1=best, 4=worst)  1
 VALUES TO SAVE
 APPARENT VELOCITY  10.26   AZIMUTH          140
 Station     Long      Lat         Elev   Xcoord    Ycoord Zcoord
 NRA0 S  Z   11.54150  60.73533    300         0         0    300
 NRA1 S  Z   11.54233  60.73650    291        45       129    291
 NRA2 S  Z   11.54333  60.73433    311        99      -111    311
 NRD4 S  Z   11.56333  60.72717    379      1186      -907    379
 NRD5 S  Z   11.54750  60.72217    348       326     -1463    348
 NRD6 S  Z   11.52883  60.72334    352      -688     -1334    352
 NRD7 S  Z   11.51617  60.73017    337     -1377      -574    337
 NRD8 S  Z   11.51667  60.73900    301     -1349       407    301
 XSLOW   YSLOW  POWER
  0.40    0.40   0.05
  0.38    0.40   0.05
  0.37    0.40   0.05
  0.35    0.40   0.05
...

**Figure:** The FK program can be started from MULPLT. The traces shown were selected and used as input to the FK program. The result of the FK analysis is shown in Figure 40.2. The event shown here is part of the testdata set.
$\begin{figure}\centerline{\includegraphics[width=0.9\linewidth]{fig/fig47}}\end{figure}$

**Figure 40.2:** Output from the FK program. Contours and values are the normalized maximum power.
$\begin{figure}\centerline{\includegraphics[width=0.9\linewidth]{fig/fig48}}\end{figure}$