# Thread: What do band pass filters do???

Started: 2006-11-18 06:25:49
Last activity: 2006-11-18 14:12:05
Topics:
John or Jan Lahr
2006-11-18 06:25:49
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 sign
waves, each with a specific
amplitude and frequency. If all of the sign 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

• Larry Braile
2006-11-18 14:12:05
Attached is a sac file of the Nov. 15, 2006 M8.3 Kuril Islands
earthquake seismogram recorded at West Lafayette, Indiana on an AS-1
seismograph. You can view the file using the AmaSeis software. The
distance from the epicenter to the station was 78.11 degrees or 8685 km
(78.11 deg. x 111.19 km/deg.).

The USGS reported magnitudes of M8.3, mb6.6, MS7.8 based on an average
of many stations. From the WLIN seismogram, I calculated magnitudes of
mb 6.4 and MS 7.8 using the online AS-1 Magnitude Calculator, and mb6.5
and MS 7.8 using the magnitude calculator in AmaSeis. These estimates
are in very good agreement with the official USGS magnitudes. If you
have an AS-1 seismograph, try calculating the magnitudes from your
seismogram. Or, use the attached seismogram to practice the calculation.

Following up on John Lahr's recent email on filtering, it's interesting
to filter the Kuril seismogram with a high pass filter. Try a cut-off
period of 2 s for the high pass filter. By emphasizing the high
frequencies, the P waves from the main shock earthquake and from several
aftershocks are enhanced. In the filtered record, one can identify the
first P arrivals from several aftershocks (at least 6 are visible). A
listing of the mainshock event and larger aftershocks is available at
http://earthquake.usgs.gov/eqcenter/recenteqsww/Quakes/quakes_big.php to
compare with the time differences between the main shock P arrival and
the aftershock P arrivals on the filtered seismogram.

-Larry Braile

--

Lawrence W. Braile, Professor and Head

Department of Earth and Atmospheric Sciences

550 Stadium Mall Drive

Purdue University

West Lafayette, IN 47907-2051

(765) 494-5979 (O), (765) 496-1210 (Fax)

E-mail: braile<at>purdue.edu <braile<at>purdue.edu>

Web page: http://web.ics.purdue.edu/~braile
http://web.ics.purdue.edu/%7Ebraile

Departmental web page: http://www.purdue.edu/eas/

SAGE web page: http://www.sage.lanl.gov/

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