Mauro,
    I am not familiar with Seismowin but am interested in what it does; if =
you will educate me concerning the algorithm. (I am interested in your thou=
ghts on this matter, since Chris Chapman thinks highly of you.)  If Seismow=
in works with pole/zero manipulations, as is customary in the professional =
world; then it is an 'overkill' with too much attention to issues that are =
unnecessary.  The correction of the FFT to accommodate the transfer functio=
n of an instrument is really quite straightforward.  There is no need to em=
ploy details of the Laplace Transform, which identifies the location of pol=
es and zeroes in the complex plane.  It is only necessary to make 'adjustme=
nts' of the frequency dependent terms of the modulus squared values of the =
FFT, using an f-multiplier or -divisor term (raised to the correct power), =
consistent with the information provided by Erhard Wielandt's webpage graph=
ics at http://www.geophys.uni-stuttgart.de/oldwww/seismometry/man_html/node=
12.html when you click on "transfer functions of mechanical .....".  These =
are consistent with an instrument's steady state response.  On the other ha=
nd pole/zero analysis is necessary if transient response were called for; h=
owever, the PSD is a plot corresponding to steady state response devoid of =
transients.  When your instrument is operating close to the ideal quality f=
actor of 0.707 (near critically damped at 0.5) the transients that derive f=
rom the convolution of the drive and the Green's function of the instrument=
 are of no concern.  =20
  =20
Randall
  =20


-----Original Message-----
From: Mauro Mariotti [mailto:mariottim@..............
Sent: Thursday, July 19, 2012 2:29 AM
To: psnlist@..............
Cc: Randall Peters; psnlist@..............
Subject: Re: PSD and 'velocity' output

may RESP module of Seismowin be helpful for this?

rgds
mauro

Il 19/07/2012 02:27, Randall Peters ha scritto:
> Randy,
>
> With your instrument, for frequencies of drive that are above its
> characteristic frequency (reciprocal of its period), the output is
> indeed proportional to the velocity of the ground on which the
> instrument sits; i.e., to the first time derivative of ground
> displacement. Thus by taking the derivative of the output voltage from
> your sensor in that regime you would obtain the acceleration that is
> used in calculating the PSD. On the other hand, for ground oscillation
> that is at lower frequencies than the instrument's natural frequency,
> the output is proportional to the third time derivative of the ground
> displacement. To get the acceleration in that regime requires an
> integration of the output voltage. This happens because the transfer
> function of the instrument rises as 1/f toward the characteristic
> frequency and then falls as 1/f in going away from it toward high f. A
> 'connection' with the calculus is realized by noting that a derivative
> corresponds to multiplying by f, whereas an integral to dividing by f.
>
> Conventional seismometers (even those with feedback) generally operate
> this way so as to mimic the old standard of voltage generated from
> relative motion of a coil and magnet in accord with Faraday's Law. As
> Chris Chapman has frequently pointed out to this list-serve-for
> sensitive instruments, always let the coil be the part that moves with
> the inertial mass of the instrument, not the magnet system; which should
> be placed at rest on the frame.
>
> To calculate a proper PSD one must correct the Fourier transform of a
> signal for this frequency dependence of the instrument's transfer
> function. One can at the same time this correction is applied, also
> 'adjust' the math for the difference between your sensor and the type of
> sensor I prefer (as in the VolksMeter - output voltage proportional to
> ground acceleration below the characteristic frequency).
>
> Much confusion exists because of the critical influence of the
> instrument transfer function. In your instrument, the voltage generated
> by the relative motion of coil and magnet is proportional to the time
> derivative of the displacement of your inertial mass relative to the
> case. On the other hand, with the VM, the voltage generated by its fully
> differential capacitive sensor is instead proportional to the
> displacement itself, of the mass relative to the case. For either case,
> the displacement of the mass relative to the case is proportional to
> ground acceleration, when the frequency of that acceleration is below
> the natural frequency of the instrument.
>
> So in answer to your question-because of its complicating influence, the
> best way to get to acceleration (valid for all frequencies) with your
> instrument (for purpose of PSD calculations) is to correct your FFT with
> a properly formed transfer function. I can help you (and others if they
> are interested) to master the method of doing this using Excel. I have a
> vested interested in doing so-since with a 'network' of instruments
> generating such records, we could hopefully have a better means for
> earthquake prediction based on the paper that I previously mentioned.
>
> Randall
>

--=20
Mauro Mariotti
SARA electronic instruments s.r.l.
Via A.Mercuri 4 - 06129 - Perugia
Tel. +39 075 5051014 Fax +39 075 5006315
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