Why I Filter My Helicorder Record


Unfiltered AmaSeis record of 3/24/2007


Same time interval with the band pass filter set to 10s to 25s and the gain increased by a factor of ten.

The high frequency P arrival is clear in both records, but the surface waves are emphasized by the filter and gain settings.  These records show a combination of the waves from two different earthquakes that took place within two minutes of each other.

 

   
Another example from Alan Jones comparing unfiltered (left) with filtered (right) helicorder images.

The events 6.0 or above in the time span above are:
 
04-APR-2007 11:00:27 -20.73 168.88 6.3 10.0 LOYALTY ISLANDS
04-APR-2007 06:34:34  -7.78 156.49 6.2 10.0 SOLOMON ISLANDS
04-APR-2007 00:39:44  -7.12 156.07 6.0 10.0 SOLOMON ISLANDS (Can't see this one)
03-APR-2007 20:26:14 -20.70 168.86 6.3 41.4 LOYALTY ISLANDS

 

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

Finally, here's an example in which a regional earthquake is not visible prior to applying a high-pass filter.

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