From: Randall Peters PETERS_RD@..........

Date: Thu, 19 Jul 2012 08:11:23 -0400

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 __________________________________________________________ Public Seismic Network Mailing List (PSNLIST) To leave this list email PSNLIST-REQUEST@.............. with the body of the message (first line only): unsubscribe See http://www.seismicnet.com/maillist.html for more information.