PSN-L Email List Message

Subject: RE: specific power spectral density
From: Brett Nordgren brett3nt@.............
Date: Thu, 19 Jul 2012 09:06:28 -0400


Randy,

I have one additional thought on why instruments often are designed 
to have a midband response which is flat with respect to 
velocity.  The nature of earth noise, displayed in terms of velocity, 
tends to be more symmetrical over the frequency range.  It goes up at 
the lowest frequencies and also rises at the highest, being very 
roughly "flat" in the middle.   Also the long-period surface waves 
will generally be easier to see with a velocity-responding 
instrument, while the higher-frequency city noises will not be as 
large.  However if you are studying local events, accelerometers 
would more commonly be used.

Regarding the need to involve the instrument response in your noise 
measurements:
What you are recording is counts, which you can easily convert to 
Volts.  But you want to express your noise numbers in terms of ground 
motion, most commonly ground acceleration.  To get from Volts to 
ground velocity you need to divide your Voltage spectrum (Volts) by 
the instrument response at each frequency (Volts / m/s), thus giving 
m/s, ground velocity.  This process is frequently referred to as 
"deconvolving" the data.  Then if you want, you can go on to multiply 
by 2 Pi f in order to convert to ground acceleration.

Regards,
Brett

At 06:28 PM 7/18/2012, you wrote:
>Brett, Randall,
>
>Good discussion.  Challenging my long forgotten math abilities.
>
>Randall - Normalizing with division by N worked for my test program 
>and gave equal bin values as I had looked for.  Thank you.  Also, I 
>frequently see the "acceleration" term in the PSD graph labels that 
>appear to be computed from velocity records.  From your discussion 
>then we should also take the derivative of velocity data after all 
>instrument and calibration adjustments have been applied before 
>computing PSD if the desire is to compute a true power value.  Is 
>that correct?
>
>Randy
>


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