[irised] What do band pass filters do??? (Version 2)

[John or Jan Lahr]

I'm sending this again to correct the spelling of "sine" as in "sine 
wave."  "Sign waves" are what people do on the curb to generate 
business for a car wash! <http://www.mccullagh.org/db9/10/kids-car-wash.jpg>
A sine wave is a mathematical function. 
<http://www.devx.com/assets/intel/9052.jpg>


Recently someone asked, "Is there a place that I can read about the 
band pass filters and what they do? "

I'll take a stab at an answer and hope others will chime in as well.

Any seismic signal can be decomposed into an infinite set of sine 
waves, each with a specific
amplitude and frequency.  If all of the sine waves are added up, the 
original seismogram will be
produced.  Often the signal of interest has a low frequency and is 
recorded with a low amplitude.
When viewed on the original seismogram, this small signal is buried 
in higher-frequency, higher-
amplitude noise.  In this case, if just the high frequencies are 
reduced in amplitude by a "low-pass
filter," then the gain can be increased to boost the low frequencies 
enough to become visible.

AmaSeis has two filters, a high-pass filter and a low-pass filter.

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

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

When both filters are set, the filter is called a "band pass" filter.

The corner frequencies can be adjusted by specifying either the 
frequency or the period of the corner.  The period is just 1 divided 
by the frequency.  For low frequencies, such as 0.05 Hz, it's easier 
to think in terms of period -- in this case 1/0.05 = 20 seconds period.

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. (For more 
details on this, look up Nyquist Frequency, 
http://en.wikipedia.org/wiki/Nyquist_frequency )

Therefore, the low pass corner setting for AmaSeis should never be 
set to a frequency higher than 3 Hz.

In order to enhance the surface waves, which have a lot of energy in 
the range of .05 Hz (20 seconds period), I find it useful to set the 
helicorder filters to pass the band from 12s to 25s.  In other words, 
the low-pass filter corner is set to 12 seconds and the high-pass 
filter corner is set to 25 seconds.

Try these settings on today's record to see the effect on your 
station.  Keep in mind that the filter settings do not change the 
data that are stored on disk, but simply change the way they are displayed.

To see what a broad-band research station looks like unfiltered, 
low-pass filtered, and high-pass filtered, click on this image to 
toggle between the three views:
http://www.jclahr.com/science/psn/cor/index.html

There is a interactive applet that demonstrates filtering of a signal 
that consists primarily of just two frequencies.  The band-pass 
filter bands can be adjusted to "bring out" each of the frequencies 
by itself.  In the case of seismology, the lower frequency would be 
so small that it would be hard to see prior to filtering out the 
higher frequency and raising the 
gain.  See:  http://www.chem.uoa.gr/applets/AppletFourAnal/Appl_FourAnal2.html

Hope this helps.  Keep the questions coming!

John