# 32.2 Calculating kappa, KAPPA

This program calculates kappa from displacement or acceleration spectra. The program is a simplification and improvement of the kappa option in program SPEC. There is no option for graphics and no options for output file of the spectra, however the results are the same as in SPEC. Kappa is calculated from the P or S spectra and both displacement and acceleration can be used, but displacement is the most useful option. Kappa is calculated from the slope of the flat part of the displacement or acceleration spectrum. The effect of attenuation on the flat part of the spectrum can be described as

ln(A(f,t)) = ln(A0) + -pi*f(kappa+t/Q)

where A0 is the initial amplitude, A(f,t) the amplitude after the waves have traveled the time t, f is the frequency and Q(f) is the general frequency dependent Q.

It is generally assumed the distance is short enough (< 50km) so that the spectrum is not affected by Q so kappa simply can be calculated from the slope of the spectrum. However if Q is accurately known, the spectrum can be corrected for Q and larger distances might be used. When using displacement spectra, small events should be used in order to get a high corner frequency, Ml < 1.5 will give a corner frequency generally above 20 Hz. The frequency range for analysis could then be 3-16 Hz. A lower frequency than 3 Hz is not recommended since the macroseismic noise will affect the signal to noise ratio.

When using acceleration spectra, there is the same restriction on distance if no Q-correction, however now larger events should be used to get a large enough s/n for the frequency range above the corner frequency. If larger distances are used, a Q correction can be applied or kappa values can be plotted as a function of distance to get kappa at zero distance. This what is done in many other studies but is not part of the program. Using program KAPP_SORT and the output file kappa_chan.all an output file of kappa vs hypocentral distance can be made and kappa at zero distance can be determined by a standard least squares program, like LSQ.

Input files: Parameter file: The parameter file (default kappa.par) gives the processing parameters and the channels to process. Events file: The events are given in an CAT S-file (default kappa.inp) and the file must have been updated to have distances. The waveform files listed in the Nordic file must be available in the directory where KAPPA is executed. The files can be in the working directory, WAV or default WAV data base. The program can also use the ARC references in the S-file but for a large archive this can be very slow. The solution can then be to extract relevant data (particular stations or stations less than a given distance) from the archive with program GET_ARC and use file get_arc.out as input file.

```
Example of a parameter file:

selection criteria 1: P, 2: S, 3: S from P
2
window length, pre window
7.0 1.0
number of times to smooth
0
frequency band to use
3.0 16.0
maximum hypocentral distance
50.0
response removal: 1: displ., 3: accel.
1
rotate: 0: no, 1: yes
0
q0, qalpha
0.0,0,0
minimum corr, min s/n ratio
0.0, 2.0
stations and components, format a5,1x,a4,1x,a5,1x,a4
KTK1     Z
KTK1     N
KTK1     E
ARA0     Z
ARA0     N
ARA0     E
LOF      Z
LOF      N
LOF      E

The parameters are:

Selection criteria: The phase to use. If no S, the time of S can be calculated
from the P-time assuming a Vp/Vs ratio of 1.78.

Window length, pre window: The window (s) for the signal starting with P or S
and the start of the time window before the phase. The total time window
is then the sum of the two.

Number of times to smooth: The spectrum can be smoothed before calculating kappa,
often it is not so no to change the slope.

Maximum hypocentral distance: maximum hypocentral distance (km).

Response removal: Displacement or acceleration.

Rotate: If rotate is selected, component N will be R and component E will be T.
The output will still show Z, N and E.

q0, qalpha: Q0 and the exponent of the frequency dependence for spectral
Q correction. Note that if qalpha is 1.0, kappa is not affected.

Minimum corr, min s/n ratio: The minimum absolute correlation coefficient
for accepting the calculated kappa value. The minimum signal to nose ratio
for accepting the kappa value. The s/n ratio is calculated using a 5 times
smoothed signal and noise spectra and the ratio is checked for each
spectral point. This comes in addition to the smoothing above.

Stations and components: For component at least the orientation must be
given. The number of channels has no limits but the number of
good kappa values is limited to 100000.
```

Output files:

Kappa.out: detailed output, also shown on screen. At the end is the overall average of all data for each channel.

Kappa_average.out: for each channel, average, sd and number of values. Example:

```
KTK1    Z   0.031  0.012   33
KTK1    N   0.037  0.013   39
KTK1    E   0.026  0.013   45
ARA0    Z  -0.001  0.014   17
ARA0    N   0.006  0.022   18
ARA0    E   0.011  0.017   17
LOF     Z   0.039  0.016   19
LOF     N   0.037  0.021   23
LOF     E   0.034  0.018   23
```

Kappa_chan.all: all individual kappa values with some extra information. Can be used as input for more analysis, see program KAPPA_SORT. Example:

```
KTK1     Z k=  0.020 h=    9.6 hd=  17.5 ed=  14.6 lt= 68.895 lo=  23.403 baz= 152.7 2013 1026 1722 51.7
KTK1     Z k=  0.007 h=    3.0 hd=   8.0 ed=   7.4 lt= 69.076 lo=  23.279 baz=  11.3 2015 0214 0145 22.6
KTK1     Z k=  0.044 h=    7.4 hd=  14.3 ed=  12.2 lt= 69.084 lo=  23.467 baz=  48.8 2015 0405 1120 55.9
KTK1     Z k=  0.027 h=    6.1 hd=  21.0 ed=  20.1 lt= 68.833 lo=  23.308 baz= 170.2 2015 0501 1207 16.4
KTK1     N k=  0.024 h=    9.6 hd=  17.5 ed=  14.6 lt= 68.895 lo=  23.403 baz= 152.7 2013 1026 1722 51.7
KTK1     N k=  0.047 h=    3.0 hd=   8.0 ed=   7.4 lt= 69.076 lo=  23.279 baz=  11.3 2015 0214 0145 22.6
KTK1     N k=  0.048 h=    7.4 hd=  14.3 ed=  12.2 lt= 69.084 lo=  23.467 baz=  48.8 2015 0405 1120 55.9
KTK1     N k=  0.028 h=    6.1 hd=  21.0 ed=  20.1 lt= 68.833 lo=  23.308 baz= 170.2 2015 0501 1207 16.4
KTK1     E k=  0.016 h=    9.6 hd=  17.5 ed=  14.6 lt= 68.895 lo=  23.403 baz= 152.7 2013 1026 1722 51.7
```

The data are: station, component, kappa, depth, epicentral distance, hypocentral distance, latitude, longitude, back azimuth and origin time.

Kappa_event.z n e: Compact S-file with the events with ok kappa value for respective channel. It can be used to plot ok events for a particular component.

Kappa.z n e: Nordic format file with average kappa at a particular station. The epicenter is the station coordinate and the magnitude is proportional with kappa. The file can be plotted with MAP or MAPG and can also be used for further analysis, see example next section. Example:

2000 0101 0101 0.0 L 69.012 23.237 33 3.1 1

KTK1 Z 0.031 0.012 3

2000 0101 0101 0.0 L 69.535 25.506 17 -0.1 1

ARA0 Z -0.001 0.014 3

2000 0101 0101 0.0 L 68.132 13.540 19 3.9 1

LOF Z 0.039 0.016 3

In the header line is the number of kappa values in number of stations field (33), kappa multiplied by 100 (3.1) in magnitude field. The second line gives station, component, average kappa and sd. If plot with e.g. MAP, the stations are shown with magnitude symbol proportional with kappa.

Run the program:

Parameter file, kappa.par is default (return)

CAT File file with events, name kappa.inp is default (return)

Both parameter file and CAT file can have different names. The program has 3 optional arguments: - batch: no questions asked and it is assumed that input file names are kappa.par and kappa.inp.

-par: give parameter file

-cat: give CAT file