On Fri, 21 Apr 2000, Tom Schmitt wrote:
> > >  In exploration seismic work geophone arrays were used to filter local
> > noise.
> > >  The signals from several geophones would be summed.  The noise would be
> out
> > >  of phase at the geophones but the signal would be in phase. In
> reflection
> > >  work that assumption is more justified than in earthquake or refraction
> > >  seismology as in reflection the signal is coming more or less straight
> up.
> > >  Has this ever been used in earthquake seismology?

This technique is used in many variations.  The buzz word for these types of
techniques is "stacking" the data.  For data on a single phase for many
records you can average them, and because the noise is random it will be
reduced.  According to the mean value theorem of statistics, the noise should
totally disappear as you average an infinite number of records.  This is not,
of course, possible, but the more the better.

One of the cool things being done with stacking these days is to measure PP
and SS precursors.  These are the small reflections off the discontinuities in
the Earth occurring at 670, 500 and 410 km depths which are interesting to
study in terms of mineral phase transitions.  A small part of the energy of
the waves is reflected off these before the PP hits the surface, which is
almost precisely between the quake location and the seismograph station.
The result is a little wiggle one the seismogram just before the arrival of
the main SS or PP phase.  These are often too small to be seen for an
individual event.  By stacking enough seismograms for given "bounce points"
the topography of these features can be mapped out really well.  Also, the
amplitude of the bumps tells you about the impedance of the boundary, which is
useful in finding out what material change is occurring to produce it.

> >     Your letter raises several questions. How many and how widely spaced
> > locations were you proposing for your recording stations? The wavelength
> of
> > earthquake waves is likely to be VERY long when compared to explosive
> > sounding signals / environmental noise and what you actually record at a
> > particular site is effected by the wave path, which may have different
> > properties from different directions.
> 
> Well first I was hoping that one of the academic seismologists would answer
> with (1) that's impossable
> or (2) here is how to do it.  Lacking that clear guidance :-) I will attempt
> some speculations.
> 
> The period of the earthuakes is very long but the period of local noise is
> very short.  If I remember Sean-Thomas was talking about 100 HZ notch
> filters to remove the local noise.   At 5 km/sec for surface material and a
> frequency of 100hz the wavelength is 50 meters.   Considering a wave
> propigating only in the x-z plane, and a seismometer located at 0,0 a second
> seismometer located at 25,0  would be 180 degrees out of phase for a 100 hz
> signal.  Summing the two signals would result in zero ( minus the
> attenuation over 25 meters and local effects).

Correct, but you have many different frequencies to deal with.  If the
stations get too far apart, then the seismic waves will hit each one at a
generally different time and phase.  This can be dealt with using some fairly
simple mathematics...  The bottom line is that the detail of an object or
structure you want to look at is never greater than the station spacing for a
single teleseismic earthquake.  Many earthquakes increase the resolution with
all of the paths, but the rays that hit the seismometer are still travelling
at a nearly vertical angle and the stations are far apart.

Recent work has begun to develop using noise more creatively.  For instance,
atmospheric noise excites some of the Earth's free modes, and this can be very
useful for some types of work.  There are all kinds of cool numerical tricks
for playing with this stuff.  But if you just want a decent-looking seismogram
for a teleseismic event then simply low-pass it...

> > >  The usual answer to noise is a quiet location but with
> > > educational seismometers rather than research
> > >  seismometers, location near the classroom is important.
> >
> >     If you can use your many observers to identify the various man made
> noise
> > sources, there is no reason in principle why you should not place an
> > auxiliary sensor(s) closer to sources and feed the relatively strong
> > interfering signals back to provide compensation, but don't expect a
> perfect
> > match. It is easier to do this using digital delays, rather than analogue
> > delay lines. Can you record an environmental noise channel to help in
> > identification and the seismograph channel? Could the identification /
> > characterisation / avoidance of local sources be a worthwhile project? If
> the
> > local noise is terrible, could you get on line data from some quiet
> location
> > for your 'real earthquakes' and use your local set-up as a teaching /
> backup
> > aid?
> >
> 
> The noise is usually diffuse in origin, thus having sensor near the noise
> probably will not work.    The idea is to have enough sesors out there that
> the sum of them at any given time covers an intergal number of  wave lengths
> of the noise.  The sum is then zero.  Since the signal is a much longer wave
> length it is not reduced by the summing.

No it is more complicated than that.  One of the theories for dealing with
noise uses the definition that noise is not correlated with itself.  By
removing the uncorrelated part of the seismogram, I think you can reduce some
of the noise by up to a maximum estimate of 1/sqrt(2) (don't quote me on this
value).

Anyways, you can use a large array, and see the phase move across it.  This is
similar in principle to the new binocular telescopes being implemented
around the world.  In this scenario you assume that the noise at each location
is completely random and different from the others.  Then you can easily
remove it.  It is not about averaging necessarily, it is more about finding
phases that cross the array which can be easily correlated.

> It would be prohibitively expensive to do this with long periond
> seismometers but your idea of noise monitors is good.  One might be able to
> use exploration geopones to get the "noise",  high pass those signals and
> sum them with the seismometer and reduce the noise.  The news broadcsasters
> often use a second noise canceling microphone in noisey environments.
> 
> The only reason for this is cosmetic or to look at local events.   Also
> exploration work is much simpler in that one knows the source and noise
> characteristics better.   Also that was an old technique in exploration,
> with vibroseis@ they may not have to do it any more.   Also a quiet beats
> filtering any day.

Yikes, I think it is difficult and nearly impossible to extrapolate records
over from a high frequency geophone to a low frequency instrument...better to
just low pass and focus on distant events whose frequencies are lower than the
poles on you filter.  I don't think anybody learns much about the earth by
putting a sophisticated broad band instrument right next to the earthquake
source; this is where strong motion instruments are used instead.  And when it
is strong motion you are recording, the local noise is going to be small
compared to recording distant events.

> > >  Second.  There is a new chip that is up to a 6 pole analogue filter.
> The
> > >  configuration of the filter is set in a device similar  to an EPROM
> burner.
> > >  The software that comes with it has full design features such as
> simulation
> > >  of amplitude and phase.
> >
> >     Filters of this type are produced for use in hearing aids, to vary the
> > audio characteristics over a wide band. In your application, it is
> probably
> > better to use four pole Bessel filters, which are relatively easy and
> cheap
> > to make with a couple of OPAs. When you go to six pole filters, the delay
> can
> > get rather long. You may find that shifting the corner frequency downwards
> > just a bit is actually preferable to adding more filter stages. If you
> have a
> > two channel recording system, could you use it to compare the simultaneous
> > results of various filter choices? If you initially use 'plug in'
> breadboard
> > (with silver plated contacts), you can easily change the filter
> > characteristics.
> I am going to send this whole thing to one of my academic friends to see
> what he says.
> 
> I suspect some of these tricks might have been used in the good old days
> when we were monitoring the nuclear detonations of the former Soviet Union.
> There were some very long dedicated arrays focused to specific points in
> Asia.
> 
> I do not have a machine right now, I hope to have one by the end of the
> Summer as I want that as a Summer science project for my daughters.  I am
> working on a computer interface now.  We live in a noisy environment which
> is why Sean Thomas' comments hit home.
> Thank you
> Tom Schmitt
> tschmitt@..............

Tom,
   One sure way to test if something is noise or not, like a nuclear explosion
is to forward model it.  You then predict the groundmotion at each station
where you can get records.  This can be done fairly accurately by using either
the travel-time tables or some mathematical model.  You can either look
directly at the seismograms or you can try and do a convolution of your
predicted data with the actual records for each station.  If the correlation
is high for most of the records, then you can test it by using a given
confidence interval (e.g. 95%).  The more records you have, of course, the
better you can decide.  Many times, you add records and can correspondingly
increase your confidence level.  Also, you may want to statistically weight
stations closer to the event more than ones further if it is a weak source.

John Hernlund
E-mail: hernlund@.......
WWW: http://www.public.asu.edu/~hernlund/

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