Thread: (no subject)

Jerry,

I'll try to answer your questions below.

Bob H.

At 09:22 PM 12/30/2006, Jerry Cook and Dell Taylor wrote:

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."

This statement means that the highest frequency possible to record when
sampled at 6 samples per second is 3 Hz, or 3 cycles per second. Period
(T) is 1/f, so the corresponding period is 0.33 seconds.

So if a sample is taken every .17 seconds (6 times per second) and you
divide that in half you get .33seconds.

If you were to divide the period by 2, you would get 0.17/2 = 0.085
seconds, not 0.33 seconds. It's the frequency (6 Hz) that we are dividing
by 2, not the period. In the following discussion, it's better to stick
with frequency for everything, not period, until we're all done. So I will
make some changes to and comments about your paragraph so that it hopefully
makes more sense, keeping everything in terms of frequency where it makes
sense to do so (see below the following paragraph):

Therefore seismic waves with a frequency higher than .33 seconds will not
be well recorded. The period for .33Hz is then calculated by dividing
1/.33 = 3sec. Does this mean that the time for one complete cycle is 3
seconds? Is this true? I find it hard to believe that the time from "crest
to crest" is so long. This just seems fantastic to me. Does this mean that
if the period is less than 3 seconds the AS-1 will not record it? 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.

Your first few sentences should read as follows: Therefore seismic waves
with a frequency higher than 3 Hz (3 cycles/sec) will not be well
recorded. The period for 3 Hz is calculated by: 1/3 = 0.33 seconds. The
time for one complete cycle is therefore 0.33 seconds.

Discussion: Note that, since we are sampling at 6 samples per second (6
Hz) and can therefore only faithfully record a maximum frequency of 3 Hz (3
cycles per second), we can also faithfully record all frequencies lower
than that (down to the lowest frequency capable of being detected by the
AS-1 and the filter in the black box). The AS-1/filter combination easily
detects frequencies as low as 0.05 Hz, representing surface waves from
magnitude 6 and larger earthquakes at great distance. Normally, the larger
the quake, the lower frequency is the energy produced. Quakes like the
2004 Sumatra quake (greater than magnitude 9) produce extremely low
frequency surface waves of very large amplitude. These very large surface
waves can have frequencies as low as 0.01 Hz or even lower.

Now, translate these very low frequencies into period (T = 1/f):

1/(0.05 Hz) = 20 seconds (hence the common reference to "20-second surface
waves")

1/(0.01 Hz) = 100 seconds

Yes, this means that it is really 100 seconds from crest to crest (or
trough to trough). Most seismic waves are in the "infrasound" region
(below the range of normal sound that can be heard by a human), just as
infrared light is below the range of normal human sight.

The normal range of frequencies recorded reasonably well by the
AS-1/filter/digitizer combination (with the digitizer sampling at 6 samples
per second) is 0.05 Hz to 3 Hz. In terms of period, the range is then 0.33
seconds to 20 seconds period. While the AS-1 can detect larger, lower
frequency surface waves when they are produced by very large quakes, this
is fairly rare (because of the rarity of such large quakes).

Are the following two statements true?

A "high-pass filter" allows periods lower than a set corner period to pass
unchanged, while attenuating higher periods.

True. It's called a high-pass filter because it passes high frequencies
(short periods) while attenuating lower frequencies (longer periods).

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

True. It's called low-pass filter because it passes low frequencies (long
periods) while attenuating higher frequencies (shorter periods).

2. What are the normal periods for P waves? S waves? L waves?

To avoid confusion, let me state these in terms of both frequency (and period):
P waves: Usually around 1 Hz (1 sec) for teleseisms, higher frequency
(shorter period) for local quakes.
S waves: Usually around 0.3 to 1 Hz (3.3 sec to 1 sec)
L waves and other surface waves: Usually around 0.05 Hz (20 sec)

3. Is it best to just not use filters at all till you want to study a
recording in more detail?

With the AS-1 seismometer, which has a natural frequency of about 1 Hz, if
there were no filter at all in the black box, you would see mostly just P
waves and S waves. The surface waves would be attenuated so much that you
would seldom see them except in the case of very large quakes. You may not
have known this before, but the black box has a hardware low pass filter in
it (before the digitizer) that helps to accentuate low frequencies, making
it possible to also see surface waves from smaller events ( approx. mag 6
and up).

I believe your questions 3 and 4 refer to the software filters available in
the Alan Jones display software. If you are in a quiet location (little
traffic or other nearby noise sources), you may not want to use any
filters, because the seismograph is already set up to show you a reasonable
range of frequencies (0.05 Hz to 3 Hz). However, if you see a lot of high
frequency noise from traffic, etc, then you might want to use a 1 Hz low
pass filter to help attenuate this high frequency noise, making it easier
to see the P waves and S 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.

I am not sure about this last question, but this recording may have been
made with a hydrophone. If that is the case, the recorded frequencies may
already have been in the range of human hearing (20 Hz and up) without
being speeded up.

J. Bob Cook




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