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