GGP DECIMATION FILTERS
Decimation filters are used to convert the GGP raw data  sampled at 1, 2, 5, or 10 s  to the 1 minute GGP files (*.ggp) for uploading to ICET/ISDC. Many stations have constructed their own filters to do this, based on the following general requirements:
Requirement 1: The filter should adequately cutoff all frequencies higher than the Nyquist frequency for 1 minute data. This Nyquist frequency is by definition f_{N }= 1 /(2 Dt). For Dt = 1 min, f_{N} = 0.00833 Hz, or log_{10} (f_{N}) =  2.08. The quality of the filter is measured by the attenuation at the Nyquist. Values of 10^{7} or smaller are excellent  there is not a lot of room for debate here.
Requirement 2: The filter should be flat in its passband. This means that frequencies up to the stopband cutoff (e.g. long period normal modes) should be passed with little amplitude attenuation as possible. Filters that roll off too slowly may cause difficulties due to amplitude attenuation. A 1% attenuation at 510 min period is reasonable (but this is subject to debate).
Requirement 3: The filter should not be too long in the time domain. The above two requirements can be met simultaneously by lengthening the filter, but a long filter will corrupt data by spreading spikes and data disturbances with the filter response. The filters shown below have lengths between 20 and 30 min, and the number of coefficients depends on the different sampling intervals.
The table shows the filters for 5 stations and their details; note that stations MO and SU have the same filter. This work was done in 2001, and the filters for other stations were not available.
Table 1. Performance of some GGP FILTERS
Station 
File 
Amplitude response 
Sampling^{1} (sec) 
Length^{2} (# points) 
Length^{2} (min) 
1% down^{3} (min) 
attenuation at Nyquist^{4} (0.00833 Hz) or 2.08 in log_{10} 
MO/SU 
1 
1799 
30 
8.6 
2.2 x 10^{8} 

ST 
2 
599 
20 
5.1 
1.1 x 10^{4} 

VI 
1 
1225 
20 
4.9 
1.1 x 10^{5} 

BO 
5 
301 
25 
4.9 
5.0 x 10^{8} 
Notes:
Sampling is original sample interval.
Length is given both by the number of points and filter length. A single large value will contaminate up to this length of the data.
The 1% down point is the period at which the amplitude response is down by 1% of the nominal pass band value (1.0). The smaller this number is, the better, so that data with all periods longer than this will have correct amplitudes (e.g. free oscillations).
The attenuation at Nyquist shows how well the filter rejects noise at a frequency corresponding to a 1 minute sampling. The smaller this number is, the better.
Plots of the time domain and frequency domain responses of the filters in Table 1 can be found here:
Fig 1. filters in the time domain
Fig 2a. filters in the frequency domain  response 10^{3} to 0 Hz
Fig 2b. filters in the frequency domain  response 10^{3} to 10^{1.5} Hz
Chebyshev filters for all sampling intervals
From Table 1. it can be seen that filter bo2.dat performs well in the above categories. It is a Chebyshev filter in which a compromise between the passband and stopband ripples is achieved through a least squares adjustment procedure. The source code to produce this filter is given here lpfiltd.f, and an input file lpfiltd.in is also required. We have constructed similar filters for decimation at 1s, 2s, and 10s as used in GGP data acquisition systems. Their properties are shown in Table 2.
Table 2. Performance of some Chebyshev filters
File 
Amplitude response 
Sampling (sec) 
Length (# points) 
Length (min) 
1% down (min) 
attenuation at Nyquist (0.00833 Hz) or 2.08 in log_{10} 
1 
1009 
17 
7.8 
1.8 x 10^{7} 

2 
571 
19 
6.5 
1.1 x 10^{7} 

5 
301 
25 
4.9 
5.0 x 10^{8} 

10 
151 
25 
6.1 
2.0 x 10^{8} 
#this filter was used for the Cantley station between 1989 and 1995
*same as bo2.dat in Table 1.
Plots of the frequency domain responses of the filters in Table 2 can be found here:
Fig 3a. filters in the frequency domain  response 10^{3} to 0 Hz
Fig 3b. filters in the frequency domain  response 10^{3} to 10^{1.5} Hz
Similar filters for decimation at 1s, 2s, and 10s with higher precision are shown in Table 3.
Table 3. Double precision Chebyshev filters
File 
GWR format  Amplitude response 
Sampling (sec) 
Length (# points) 
Length (min) 
Nominal Passband (min) 
1% down (min) 
attenuation at Nyquist

g1s1md.gwr 
1 
1009 
17 
30 
7.8 
2.3 x 10^{7} 

g2s1md.gwr 
2 
571 
19 
20 
6.6 
1.1 x 10^{7} 

g5s1md.gwr 
5 
301 
25 
10 
4.9 
7.2 x 10^{8} 

g10s1md.gwr 
10 
151 
25 
10 
5.8 
6.7 x 10^{8} 
Plots of the frequency domain responses of the filters in Table 3 can be found here:
Fig 4a. filters in the frequency domain  response 10^{3} to 0 Hz
Fig 4b. filters in the frequency domain  response 10^{3} to 10^{1.5} Hz
Comment
Chebyshev filters are only one type that can be considered for decimation; they are characterized by a flat stopband. Several others types are possible (see Figs 2a, 2b). For 1 s to 1 min, the filter for MO/SU (Table 1) has the best rejection, but cuts off earlier in the passband than g1s1m.dat.
D. Crossley, St. Louis 27 March 2007, updated 19 April 2010
crossley@eas.slu.edu