In a message dated 15/06/2009, bobmcclure90@......... writes:

MY  THOUGHTS ON SEISMIC DATA FILTERING.

On most seismic events, it  is necessary to filter the raw data in order=
 to 
suppress cultural noise   to get a better view of the ground motions of th=
e 
event. First off, the sensor  itself filters the data,
and the amplifier filters the sensor output. The  digitization process can=
 
also filter (and distort) the data. We can never  truly sense ground motio=
n, 
but we can hope to reproduce accurately enough the  data of interest.

Sensors of the force-feedback type are best  for high fidelity detection=
 of 
ground motion. Most amateurs are limited to the  use of open loop pendulum=
 
types, such as the horizontal Lehman sensor and  vertical sensors of the=
 
spring supported pendulum type. Open loop sensors can  only accurately 
reproduce signals appreciably higher than the natural resonant  frequency=
 of the 
pendulum.
Hi Bob,
 
    Are you forgetting period extending amplifiers,  which can extend the=
 
response period by x10, fairly easily? I have extended the  period of an=
 AS1 
from 1.5 to 20 seconds quite OK this way. And it is a very  considerable=
 
improvement! The Roberts circuit can be used, provided that you  couple th=
e two 
stages with a two pole high pass filter to remove the long period  1/f 
noise. See _http://jclahr.com/science/psn/roberts/index.html_ 
(http://jclahr.com/science/psn/roberts/index.html) 

A signal  at the resonant frequency of the pendulum is shifted 90 degrees=
 
leading in  phase, and its amplitude is proportional to the Q of the syste=
m. 
Q is  inversely proportional to the damping factor, D. The relationship is=
 Q 
=3D  0.5/D. Critical damping occurs when D=3D1 or Q=3D0.5. Usual practice=
 is to 
adjust  damping to a value of about 0.6, just low enough to sense a little=
 
overshoot  on the return of a displaced pendulum to equilibrium. If you us=
e 
more damping,  you have little idea of how much it is, and if you use less=
 
damping, you may  get ringing on seismic signals. At frequencies below 
resonance, the response  falls off rapidly at a rate of 12 decibels per oc=
tave, and 
the phase shift  heads toward 180 degrees leading.
    With say a 3 cycle P wave, you are driving the  previously stationary=
 
inertial mass with a force a bit below that required to  produce critical=
 
damping eg 0.7, so any overshoot should be quite low.

One can infer from the above that one should strive for a pendulum period=
  
longer than the longest period one wishes to reproduce. However, the  
difficulty of achieving this goal goes up as the square
of the period.  Horizontal sensors cannot distinguish the difference 
between horizontal ground  acceleration and ground tilt, and the response=
 to tilt 
goes up as the square  of the period. Most amateurs do not have a site 
really stable in tilt. 
    WWSSN horizontal seismometers were designed for  periods of 30 seconds=
, 
but were usually run at periods of 15 seconds to ensure  that they did not=
 
drift out of the linear sense range between annual servicing.  I find it=
 
quite satisfactory to run my Lehman at 20 seconds. They still pick up  the=
 
occasional 40 second wave.

The same  can be said for temperature stability. Temperature fluctuations=
 
can cause the  sensor to change its alignment, producing the same problems=
 as 
ground tilt  changes.
    This depends on how well you design your  sensor. I have not found any=
 
significant thermal drift variations on my  Lehman. 

All this said, we amateurs just have to do the best we can with what we 
have,  but my signal processing utilities can make a lot of improvement in=
 the  
recorded data.

After the sensor comes the amplifier, which must  also attenuate high 
frequency signal components to avoid aliasing at the  subsequent sampling=
 and 
digitization steps. Less low pass filtering is needed  the higher the samp=
ling 
rate. It is best to sample at a high rate, and then  sample average n data=
 
points taken at the high rate to get a final sample rate  1/n times the in=
put 
sample rate. My Dataq acquisition system does that  automatically for me.=
 
Its A/D samples at 240 samples per second overall. If I  record three 
channels, each is being sampled at a rate of 80 samples per  second. I usu=
ally set 
my recorded rate at 5 samples per second per channel, so  the Dataq record=
er 
averages 16 data samples for each data point recorded. This  process 
largely avoids any aliasing, effectively suppresses high frequency  noise,=
 and 
gives me 14 bit resolution out my 12-bit A/D.
    I don't quite follow this. With a high sample rate  you will still hav=
e 
higher frequency components which you don't want in your  final data. This=
 
also rather depends on how the noise level in your ADC  responds to sampli=
ng 
rate changes. The 20 micro second ADCs typically had 3 bits  of noise. 16=
 
data samples would remove two bits of ADC noise. Some of the  sigma-delta=
 
types have only +/-1/2 LSB noise at the slower speeds.

Once we have logged data, we still must usually digitally filter it to  
suppress unwanted frequency components, both low frequencies and high  
frequencies. However, filtering done inappropriately can really mess up th=
e  
waveform of the signal we want to preserve. WinQuake is a marvellous progr=
am,  
grateful thanks to Larry Cochrane, and we would be in the Dark Ages withou=
t  it. 
However, it offers so many choices on filtering that the na=EFve user has=
  
ample opportunity to do bad things.
I do not  believe in ever using more than 4 poles in the filters, for 
example. The more  poles you use, the sharper the cut-off, the more the si=
gnal is 
time delayed  and distorted, and more ringing may occur.
    This mostly happens if you use Butterworth or  elliptic filters. Besse=
l 
filters seem to be OK, but I agree that you rarely need  more than 4th 
order filters. If you have been using a 10 Hz Butterworth filter,  you can=
 get 
roughly the same HF roll off by designing a Bessel filter for 7  Hz. It 
doesn't ring and there are no spiky signal delays at the band  edge! 

I also prefer not to use WinQuake's causal  Butterworth filter, which is=
 
the only IIR choice offered. I prefer to use only  the filters implemented=
 in 
my "WQFilter.exe" application. My filters are not  causal (i.e., operating=
 
only on present and past data, as analog filters do),  but operate on past=
, 
present, and future data to yield the present filtered  data point. What=
 I do 
to achieve this is to filter the data series forward in  time in the usual=
 
manner, and then apply the filter to that result again, but  backward in=
 
time. This results in output data that is undistorted in time and  phase.=
 To 
use a photographic analogy, it softens the noise in a grainy picture  by=
 
defocusing it rather than smearing it. Most often, I use a 2nd order  Butt=
erworth 
run forward and backward through the recorded time series to yield  a 
4-pole zero lag filter. Its response is 6 dB down at the corner frequency,=
  and 
falls at the rate of 24 dB per octave for frequencies outside the  passban=
d. 
It suppresses unwanted frequencies, without much  ringing.
    Very interesting.

WinQuake also features FFT filtering, which is also non-causal and yields=
 
zero  lag and no phase distortion. I have tested its spectral response, an=
d 
it  matches the classical Butterworth response. If you use FFT filtering,=
 I  
recommend no more than 2 or 4 poles.

I have also developed a  special digital filter for extending the useful=
 
bandwidth of an open loop  sensor to lower frequencies. It is essentially=
 a 
mathematically correct "bass  boost" amplifier that
corrects for the fall off of response of the sensor  to frequencies below=
 
the natural period, and can even correct for the gain  error caused by 
damping. To get the correct output, the sensor's  natural
period must be accurately known. The damping factor must also be  known,=
 
but it is not so critical. My vertical sensor has a period of 4.4  seconds=
.. I 
routinely apply this filter to its data, to emulate the
output  of a 32-second sensor. 
    This requires an additional maximum gain of x53, so  if your backgroun=
d 
levels are say 200 counts, you will likely be OK.

My  horizontal sensors are adjusted to 8 and 13 seconds, respectively, and=
 
I  routinely extend their period to 32 seconds. I get heliplots that close=
ly 
 resemble those displayed at the nearby LDEO Palisades web site, which use=
s 
the  expensive STS-2 force feedback sensor, but of course I show reduced=
 
amplitude  on very long period waves, and a lot more cultural noise. I use=
  
DC-coupled
amplifiers in order not to attenuate further the low amplitude  low 
frequency signal components. Along with the longer period performance  com=
es 
greater sensitivity to tilt from moving around my site and from wind. I =
 can't get 
away from that. What is very bad and troublesome at times is that  any 
spurious spikes in the data show up in the filtered output as large  trans=
ients, 
like someone tapped a long period pendulum.
    There is really no problem in making horizontal  sensors with periods=
 
of up to 30 seconds. I get about 2 mm cyclic tilt  drift in a linear outpu=
t 
range of +/-10mm.  If you use a position  sensor as opposed to magnet  +=
 coil 
induction, you can use the integrated  output to keep the mass centralised=
.. 
Adding a couple of photocells, a long  integration period amplifier and a=
 
small coil can also do this job.

I  have developed a utility program called "WQFilter.exe" which can be use=
d 
to  apply all my filters to WinQuake event files. Should you want to 
experiment,  you can get the latest version from page "WinQuake and SAC Ut=
ility 
Programs".  You should use the "LONG PERIOD Plus HPF" option. It applies=
 the 
period  extending filter, followed by a backward Butterworth high pass fil=
ter 
set to  the same period as the period extending filter. This results in 
better  rejection of low frequency noise, and very importantly, it elimina=
tes 
all  phase and time distortion from the filtered record. To preserve time=
 and 
phase  on the high frequency end of the spectrum, the low-pass filter 
should filter  in both time directions.
    I certainly appreciate the great value of what you  have achieved with=
 
digital filters.

Since it is very difficult to build open loop vertical sensors having more=
  
than a few seconds natural period, my period extending filter is 
practically a  must for amateur vertical sensors. I would encourage amateu=
rs to 
acquire or  build vertical sensors. They are much better than horizontal=
 sensors 
for  detecting P waves. They do not respond to ground tilt, so their signa=
ls 
are  ideal for digital period extension filtering.
    You have a free choice with 24 bit ADC systems.  With 16 bit systems,=
 
the long period response can be comparable to, or below the  digital step=
 
amplitude for small amplitude quakes. 1/f^2 analog  period extension is a=
 
viable alternative out to x10 with no restriction on  signal amplitude. 
 
    Unless you use either a hermetic container, or  pressure compensation,=
 
atmospheric noise should be the principal  source with a vertical sensor.=
 
Have you tried compensating this?

 
    Best Regards,
 
    Chris





In a message dated 15/06/2009, bobmcclure90@......... writes:
MY 
  THOUGHTS ON SEISMIC DATA FILTERING.

  On most seismic events=
, it 
  is necessary to filter the raw data in order to suppress cultural noise&=
nbsp; 
  to get a better view of the ground motions of the event. First off, the=
 sensor 
  itself filters the data,
and the amplifier filters the sensor output.=
 The 
  digitization process can also filter (and distort) the data. We can neve=
r 
  truly sense ground motion, but we can hope to reproduce accurately enoug=
h the 
  data of interest.

  Sensors of the force-feedback type are=
 best 
  for high fidelity detection of ground motion. Most amateurs are limited=
 to the 
  use of open loop pendulum types, such as the horizontal Lehman sensor an=
d 
  vertical sensors of the spring supported pendulum type. Open loop sensor=
s can 
  only accurately reproduce signals appreciably higher than the natural re=
sonant 
  frequency of the pendulum.
Hi Bob,
 
    Are you forgetting period extending amplifier=
s, 
which can extend the response period by x10, fairly easily? I have extende=
d the 
period of an AS1 from 1.5 to 20 seconds quite OK this way. And it is=
 a very 
considerable improvement! The Roberts circuit can be used, provided that=
 you 
couple the two stages with a two pole high pass filter to remove the long=
 period 
1/f noise. See http://jclahr.co=
m/science/psn/roberts/index.html
A signal 
  at the resonant frequency of the pendulum is shifted 90 degrees leading=
 in 
  phase, and its amplitude is proportional to the Q of the system. Q is 
  inversely proportional to the damping factor, D. The relationship is Q=
 =3D 
  0.5/D. Critical damping occurs when D=3D1 or Q=3D0.5. Usual practice is=
 to adjust 
  damping to a value of about 0.6, just low enough to sense a little overs=
hoot 
  on the return of a displaced pendulum to equilibrium. If you use more da=
mping, 
  you have little idea of how much it is, and if you use less damping, you=
 may 
  get ringing on seismic signals. At frequencies below resonance, the resp=
onse 
  falls off rapidly at a rate of 12 decibels per octave, and the phase shi=
ft 
  heads toward 180 degrees leading.
    With say a 3 cycle P wave, you are driving th=
e 
previously stationary inertial mass with a force a bit below that required=
 to 
produce critical damping eg 0.7, so any overshoot should be quite low.
  
  One can infer from the above that one should strive for a pendulum perio=
d 
  longer than the longest period one wishes to reproduce. However, the 
  difficulty of achieving this goal goes up as the square
of the period=
.. 
  Horizontal sensors cannot distinguish the difference between horizontal=
 ground 
  acceleration and ground tilt, and the response to tilt goes up as the sq=
uare 
  of the period. Most amateurs do not have a site really stable in tilt.=
 

    WWSSN horizontal seismometers were designed=
 for 
periods of 30 seconds, but were usually run at periods of 15 seconds to en=
sure 
that they did not drift out of the linear sense range between annual servi=
cing. 
I find it quite satisfactory to run my Lehman at 20 seconds. They still pi=
ck up 
the occasional 40 second wave.
The same 
  can be said for temperature stability. Temperature fluctuations can caus=
e the 
  sensor to change its alignment, producing the same problems as ground ti=
lt 
  changes.
    This depends on how well you design your=
 
sensor. I have not found any significant thermal drift variations on=
 my 
Lehman. 
  
  All this said, we amateurs just have to do the best we can with what we=
 have, 
  but my signal processing utilities can make a lot of improvement in the=
 
  recorded data.

  After the sensor comes the amplifier, which=
 must 
  also attenuate high frequency signal components to avoid aliasing at the=
 
  subsequent sampling and digitization steps. Less low pass filtering is=
 needed 
  the higher the sampling rate. It is best to sample at a high rate, and=
 then 
  sample average n data points taken at the high rate to get a final sampl=
e rate 
  1/n times the input sample rate. My Dataq acquisition system does that=
 
  automatically for me. Its A/D samples at 240 samples per second overall.=
 If I 
  record three channels, each is being sampled at a rate of 80 samples per=
 
  second. I usually set my recorded rate at 5 samples per second per chann=
el, so 
  the Dataq recorder averages 16 data samples for each data point recorded=
.. This 
  process largely avoids any aliasing, effectively suppresses high frequen=
cy 
  noise, and gives me 14 bit resolution out my 12-bit A/D.
    I don't quite follow this. With a high sample=
 rate 
you will still have higher frequency components which you don't want in yo=
ur 
final data. This also rather depends on how the noise level in your=
 ADC 
responds to sampling rate changes. The 20 micro second ADCs typically had=
 3 bits 
of noise. 16 data samples would remove two bits of ADC noise. Some of the=
 
sigma-delta types have only +/-1/2 LSB noise at the slower speeds.
  
  Once we have logged data, we still must usually digitally filter it to=
 
  suppress unwanted frequency components, both low frequencies and high 
  frequencies. However, filtering done inappropriately can really mess up=
 the 
  waveform of the signal we want to preserve. WinQuake is a marvellous pro=
gram, 
  grateful thanks to Larry Cochrane, and we would be in the Dark Ages with=
out 
  it. However, it offers so many choices on filtering that the na=EFve use=
r has 
  ample opportunity to do bad things.
    I do not=
 
  believe in ever using more than 4 poles in the filters, for example. The=
 more 
  poles you use, the sharper the cut-off, the more the signal is time dela=
yed 
  and distorted, and more ringing may occur.
    This mostly happens if you use Butterwor=
th or 
elliptic filters. Bessel filters seem to be OK, but I agree that you rarel=
y need 
more than 4th order filters. If you have been using a 10 Hz Butterworth fi=
lter, 
you can get roughly the same HF roll off by designing a Bessel filter =
;for 7 
Hz. It doesn't ring and there are no spiky signal delays at the band 
edge! 
     I also prefer not to use WinQuake's ca=
usal 
  Butterworth filter, which is the only IIR choice offered. I prefer to us=
e only 
  the filters implemented in my "WQFilter.exe" application. My filters are=
 not 
  causal (i.e., operating only on present and past data, as analog filters=
 do), 
  but operate on past, present, and future data to yield the present filte=
red 
  data point. What I do to achieve this is to filter the data series forwa=
rd in 
  time in the usual manner, and then apply the filter to that result again=
, but 
  backward in time. This results in output data that is undistorted in tim=
e and 
  phase. To use a photographic analogy, it softens the noise in a grainy=
 picture 
  by defocusing it rather than smearing it. Most often, I use a 2nd order=
 
  Butterworth run forward and backward through the recorded time series to=
 yield 
  a 4-pole zero lag filter. Its response is 6 dB down at the corner freque=
ncy, 
  and falls at the rate of 24 dB per octave for frequencies outside the 
  passband. It suppresses unwanted frequencies, without much 
ringing.
    Very interesting.
  
  WinQuake also features FFT filtering, which is also non-causal and yield=
s zero 
  lag and no phase distortion. I have tested its spectral response, and it=
 
  matches the classical Butterworth response. If you use FFT filtering, I=
 
  recommend no more than 2 or 4 poles.

  I have also developed=
 a 
  special digital filter for extending the useful bandwidth of an open loo=
p 
  sensor to lower frequencies. It is essentially a mathematically correct=
 "bass 
  boost" amplifier that
corrects for the fall off of response of the se=
nsor 
  to frequencies below the natural period, and can even correct for the ga=
in 
  error caused by damping. To get the correct output, the sensor's 
  natural
period must be accurately known. The damping factor must also=
 be 
  known, but it is not so critical. My vertical sensor has a period of 4.4=
 
  seconds. I routinely apply this filter to its data, to emulate the
ou=
tput 
  of a 32-second sensor. 
    This requires an additional maximum gain of=
 x53, so 
if your background levels are say 200 counts, you will likely be OK.
My 
  horizontal sensors are adjusted to 8 and 13 seconds, respectively, and=
 I 
  routinely extend their period to 32 seconds. I get heliplots that closel=
y 
  resemble those displayed at the nearby LDEO Palisades web site, which us=
es the 
  expensive STS-2 force feedback sensor, but of course I show reduced ampl=
itude 
  on very long period waves, and a lot more cultural noise. I use 
  DC-coupled
amplifiers in order not to attenuate further the low ampli=
tude 
  low frequency signal components. Along with the longer period performanc=
e 
  comes greater sensitivity to tilt from moving around my site and from wi=
nd. I 
  can't get away from that. What is very bad and troublesome at times is=
 that 
  any spurious spikes in the data show up in the filtered output as large=
 
  transients, like someone tapped a long period pendulum.
    There is really no problem in making horizont=
al 
sensors with periods of up to 30 seconds. I get about 2 mm cyclic til=
t 
drift in a linear output range of +/-10mm.  If you use a positio=
n 
sensor as opposed to magnet  + coil induction, you can use the integr=
ated 
output to keep the mass centralised. Adding a couple of photocells, a long=
 
integration period amplifier and a small coil can also do this job.
  I 
  have developed a utility program called "WQFilter.exe" which can be used=
 to 
  apply all my filters to WinQuake event files. Should you want to experim=
ent, 
  you can get the latest version from page "WinQuake and SAC Utility Progr=
ams". 
  You should use the "LONG PERIOD Plus HPF" option. It applies the period=
 
  extending filter, followed by a backward Butterworth high pass filter se=
t to 
  the same period as the period extending filter. This results in better=
 
  rejection of low frequency noise, and very importantly, it eliminates al=
l 
  phase and time distortion from the filtered record. To preserve time and=
 phase 
  on the high frequency end of the spectrum, the low-pass filter should fi=
lter 
  in both time directions.
    I certainly appreciate the great value of wha=
t you 
have achieved with digital filters.
  
  Since it is very difficult to build open loop vertical sensors having mo=
re 
  than a few seconds natural period, my period extending filter is practic=
ally a 
  must for amateur vertical sensors. I would encourage amateurs to acquire=
 or 
  build vertical sensors. They are much better than horizontal sensors for=
 
  detecting P waves. They do not respond to ground tilt, so their signals=
 are 
  ideal for digital period extension filtering.
    You have a free choice with 24 bit ADC system=
s. 
With 16 bit systems, the long period response can be comparable to, or bel=
ow the 
digital step amplitude for small amplitude quakes. 1/f^2 analog 
period extension is a viable alternative out to x10 with no restricti=
on on 
signal amplitude. 
 
    Unless you use either a hermetic container,&n=
bsp;or 
pressure compensation, atmospheric noise should be the prin=
cipal 
source with a vertical sensor. Have you tried compensating this?

 
    Best Regards,
 
    Chris