PSN-L Email List Message

Subject: WinQuake RMS feature
From: BOB BARNS roybar@........
Date: Fri, 25 May 2001 15:26:38 -0400

Hi gang,
  The recent questions about noise measurement brought to mind a new
feature of WinQuake (Ver. 2.7 beta 6) which some of you may have
  This would not help for general noise measurements but is pretty neat
for any waveform you can display in WinQuake.  For example, you can
quantify the performance of your seismograph.
  There is an item in the "Calculate" menu "RMS/Max/Min".
Click this and you will see RMS, Max, Min, Mean and the number of sample
points.  This calcualtion is done on the currently displayed waveform,
i.e., either the whole record or the section you have zoomed in on.
  RMS is the root mean square value which is a good measure of the
average of a complex wave form.  Max and Min are what you would expect
and the mean is the average.  The mean tends toward zero when the DC
offset has been removed because the pos. waves cancel the neg. waves. 
This is why the RMS is a better measure.  The number of sample points is
also shown.
  How well your seismograph records weak signals from 'quakes does not
normally depend on "sensitivity".  "Sensitivity" is usually thought of
as the amount of output per unit of ground motion.  With modern op amps,
this can be made very high.
  What REALLY matters is the signal to noise ratio (S/N).  This is
useful in observing the performance of your seismograph over a period of
time or after making changes (e.g., changes in the period of a Lehman)
and/or comparing different seismographs.
  A useful measure of S/N can be obtained by finding the RMS value of a
section of a seismogram before 'quake waves arrive (the N value) and
comparing that to some measure of the size of the 'quake waves, e.g.,
peak-to-peak of the largest waves (the S) [Note 1].  For example, my S/N
for the recent Jalisco Mexico 6.3 'quake was about 400 on a rather quiet
day (RMS noise of 10 and max. peak-to-peak surface waves of 4,000.)
  Of course, the noise (N) is a combination of several things but the
two principal sources are:1.  Amplifier and filter noise, 2. Local
seismic noise (LSN).  The LSN varies a lot here but wind is a big
contributer.  The so-called microseisms (which peak around 0.16Hz) also
contribute but are usually reduced by filtering.  These may be due
principally to waves breaking on a shore.
Bob Barns

Quantum Mechanics: The dreams stuff is made of.
Note 1.  The peak-to-peak amplitude of the surface waves at your
location can be approximated by the formula
   A = (T * log(dist) + 0.18))/1000
where A is the amplitude of ground motion in microns, T is the period of
the waves (often about 20 secs. for teleseismic 'quakes), dist is the
angular distance to the 'quake (get this from WinQuake, Calculate menu
-> Great Circle Dist. -> Great circle dist.).
  The response of horizontal seismometers depends on the angle between
the direction of arrival of the waves and the direction of max. response
of the seismometers (which is perpendicular to the boom in a Lehman). 
This angle to the 'quake can be seen in WinQuake at Calculate menu ->
Great circle dist. -> Station to event azimuth.  The response is
proportional to the cosine of the angle.
   There are many caveates to calculating the ground motion.  There is a
lot of good info about this in Sean-Thomas' letters in the psn
Archives:9 Apr. 2000, 15 Nov. 2000 and 1 Dec. 2000.

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Larry Cochrane <cochrane@..............>