[irised] Filters

[ChrisAtUpw at aol.com]

In a message dated 31/12/2006, jerdell at cox.net writes:

Greetings,  
I am trying to understand the band pass filters and  have a few questions. 
1. John Lahr stated that; 
“Since the AS-1 samples the amplitude of the  seismic signal about 6 times 
per second, clearly high frequencies will not be  well represented.  The highest 
frequency that it's theoretically possible  to record faithfully is one half 
of the sample  rate.”
    You interpret this as six/2 = max  frequency = 3Hz You tend not to get 
waveforms accurately represented until you  get several samples over the cycle, 
say five.
So if a sample is taken every .17 seconds  (6 times per second) and you 
divide that in half you get .33seconds.  
0.17 x  2 sec = 0.34 sec ~= 3  Hz 
Does this mean that if the period is less than 3 seconds the AS-1 will  not 
record it?  
The AS-1 response is from about 0.34 sec up to  about 15 secs 
I am used to thinking about sound and light and find it hard to believe  that 
it could take so long for one complete cycle. Does .33 Hz mean that only  
33/100 of a wave passes a fixed point per second? I find all this amazing. I  
just never thought about seismic waves like this before. I find it much easier  
to think about period than Hz.  
Seismic waves have high velocities compared  to sound in air, but they have 
long periods. The quake generates a wide spectrum  of  P and S waves, but waves 
with frequencies above about 2 Hz  are selectively abosrbed as they pass 
through the earth. When the P and S waves  reach the Earth's surface, they 
generate Rayleigh and Love surface waves, which  spread out radially, but have much 
longer  periods. 
Are the following two statements  true? 
A "high-pass filter" allows waves with  periods lower than a set corner 
period to pass unchanged, while attenuating  higher periods.
    Correct.

A "low-pass filter" allows waves with  periods that are higher than a set 
corner period to pass unchanged, while  attenuating lower periods
    Correct.

2. What are the normal periods for P  waves? S waves? L waves?
    1 sec downwards, 2 sec downwards and  typically 10 to 30 secs for very 
distant events. Local events may have P & S  frequency components over 10 Hz 
(0.1Sec). I suggest that you download and read  
_http://psn.quake.net/info/analysis.pdf_ (http://psn.quake.net/info/analysis.pdf)  for  more information
3. Is it best to just not use filters at  all till you want to study a 
recording in more detail? 
With Amaseis, the waveform should all  be recorded. The filter settings just 
determine how you process the data  for display. If you set the lowpass less 
than 2 to 3 Hz, your are likely to miss  some local P waves.

4. Considering my location in Arizona, how do you  think I set my filters? 
Just after the earthquake on 12/26/2004 a  “sound” recording of the 
earthquake was released. The recording was made by a  recording device located on the 
bottom of the Indian  Ocean. The lowest sound we can hear is about 20 Hz. Does 
that mean  that the recording wasn’t real time? It must have been speeded  up.

    The quake would have been greatly 'speeded up',  possibly over 1000 
times. You simply convert the data file into a .wav file. You  have several 
playback speed options.
 
    Hope that this helps,
 
    Chris Chapman
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