PSN-L Email List Message

Subject: dynamic range of the tiltmeter
From: Randall Peters PETERS_RD@..........
Date: Tue, 31 Jul 2012 12:12:10 -0400


Brett,
     Assuming my rough estimate for the calibration constant of 10^8 cts/ra=
d, your max count value of 1.3e6 corresponds to an equivalent pendulum angu=
lar deflection of 13 mrad.   Assuming (only a rough) estimate for the dynam=
ic range of 70 dB (minimum measurable PG plate displacement of 60 nm), my g=
uess is that this corresponds also to something close to the largest angle =
that could be measured without clipping.
     A minimum measurable displacement of 60 nm corresponds to a smallest a=
cceleration that could be measured of 6 e -7 m/s^2, independent of drive fr=
equency (assuming no electronics drift), for excitation frequencies below 0=
..5 Hz.  This amounts to -120 dB per one-7th decade noise equivalent instrum=
ent power (flat below =BD Hz).  Your feedback instrument is no doubt signif=
icantly better than this for frequencies down to somewhere near the telesei=
smic Rayleigh wave frequency of 1/20th Hz.  On the other hand, it would be =
interesting to see how the two might compare in the range from 1/20th Hz do=
wn to eigenmode frequencies (less than 1 mHz).
      Eric and I need a good helicord-type data processing/display software=
 package before such comparisons with long-time records should become strai=
ghtforward.  Larry has already made this happen with WinSDR/WinQuake for th=
e VolksMeter (which also uses the AD7745).
    The thinking that my instrument and yours might compare more favorably =
at the lowest detectable frequencies relates to the following.   As previou=
sly mentioned (posting about instrument sensitivity)-- the ultimate sensiti=
vity of every seismometer depends overwhelmingly on one thing-the reciproca=
l of the product of [ (i)the square of the characteristic frequency of the =
mechanical system and (ii) the smallest displacement of the inertial mass o=
f that system that can be measured].  One can only do so much with electron=
ics to overcome the influence of this quadratic dependence on period of the=
 oscillator, independent of the electronics.   And when the derivative of m=
ass displacement is performed (to produce a velocity detector for accelerat=
ions having frequency above the instrument's characteristic-typical of all =
the feedback instruments that I know about)-there is an unavoidable falloff=
 in sensitivity as the frequency goes toward zero.  Your instrument (if I u=
nderstand how it works) cannot avoid going toward zero as f goes toward zer=
o.  But our tiltmeter response does not fall-off as f goes toward zero (as =
a property of its displacement sensor). The only limit to its so-called d.c=
.. response is the stability of the electronics.
    What too few appreciate is also the following:  When the period of an i=
nstrument gets very long, it is not only very sensitive to external acceler=
ation.  It is also increasingly very, very sensitive to the internal struct=
ural changes that are an unavoidable characteristic of the mechanical compo=
nents, primarily the spring in a vertical seismometer.  To change their thi=
nking, anybody who questions the physics of this statement needs only to lo=
ok at the herculean challenges of trying to detect gravitational waves.  Th=
e researchers at LIGO  have time and again bumped up against this curse-wor=
thy feature of the real world.   It was a cause for me meeting some of the =
LIGO personnel at the 2004 IRIS broadband conference.  They began to increa=
singly interact with the seismology world through the discovery that they w=
ere being impacted by similar material property challenges.  Such limitatio=
ns become almost (maybe 'almost' is  not applicable) insurmountable when tr=
ying to measure displacements at the level of 10^(-17) m.

   Randall

Brett,

=A0=A0=A0=A0 Assuming my rough estimate for the c= alibration constant of 10^8 cts/rad, your max count value of 1.3e6 correspo= nds to an equivalent pendulum angular deflection of 13 mrad.=A0 =A0Assuming= (only a rough) estimate for the dynamic range of 70 dB (minimum measurable= PG plate displacement of 60 nm), my guess is that this corresponds also to= something close to the largest angle that could be measured without clippi= ng.

=A0=A0=A0=A0=A0A minimum measurable= displacement of 60 nm corresponds to a smallest acceleration that could be= measured of 6 e -7 m/s^2, independent of drive frequency (assuming no elec= tronics drift), for excitation frequencies below 0.5 Hz.=A0 This amounts to= -120 dB per one-7th decade noise equivalent instrument power (f= lat below =BD Hz).=A0 Your feedback instrument is no doubt significantly be= tter than this for frequencies down to somewhere near the teleseismic Rayle= igh wave frequency of 1/20th Hz.=A0 On the other hand, it would = be interesting to see how the two might compare in the range from 1/20= th Hz down to eigenmode frequencies (less than 1 mHz).=A0 =

=A0=A0=A0=A0=A0=A0Eric and I need a good helicord-= type data processing/display software package before such comparisons with = long-time records should become straightforward.=A0 Larry has already made = this happen with WinSDR/WinQuake for the VolksMeter (which also uses the AD= 7745).=A0

=A0=A0=A0=A0The thinking that= my instrument and yours might compare more favorably at the lowest detecta= ble frequencies relates to the following. =A0=A0As previously mentioned (po= sting about instrument sensitivity)-- the ultimate sensitivity of every sei= smometer depends overwhelmingly on one thing—the reciprocal of the pr= oduct of [ (i)the square of the characteristic frequency of the mechanical = system and (ii) the smallest displacement of the inertial mass of that syst= em that can be measured].=A0 One can only do so much with electronics to ov= ercome the influence of this quadratic dependence on period of the oscillat= or, independent of the electronics.=A0 =A0And when the derivative of mass d= isplacement is performed (to produce a velocity detector for accelerations = having frequency above the instrument’s characteristic—typical = of all the feedback instruments that I know about)—there is an unavoi= dable falloff in sensitivity as the frequency goes toward zero.=A0 Your ins= trument (if I understand how it works) cannot avoid going toward zero as f = goes toward zero.=A0 But our tiltmeter response does not fall-off as f goes= toward zero (as a property of its displacement sensor). The only limit to = its so-called d.c. response is the stability of the electronics.

=A0=A0=A0=A0What too few appreciate is also the f= ollowing:=A0 When the period of an instrument gets very long, it is not onl= y very sensitive to external acceleration.=A0 It is also increasingly very,= very sensitive to the internal structural changes that are an unavoidable = characteristic of the mechanical components, primarily the spring in a vert= ical seismometer.=A0 To change their thinking, anybody who questions the ph= ysics of this statement needs only to look at the herculean challenges of t= rying to detect gravitational waves.=A0 The researchers at LIGO =A0have tim= e and again bumped up against this curse-worthy feature of the real world. = =A0=A0It was a cause for me meeting some of the LIGO personnel at the 2004 = IRIS broadband conference.=A0 They began to increasingly interact with the = seismology world through the discovery that they were being impacted by sim= ilar material property challenges.=A0 Such limitations become almost (maybe= ‘almost’ is =A0not applicable) insurmountable when trying to m= easure displacements at the level of 10^(-17) m.=A0

 

=A0=A0 Randall<= /o:p>

=

[ Top ] [ Back ] [ Home Page ]