From: Brett Nordgren brett3nt@.............

Date: Fri, 13 Jul 2012 09:25:17 -0400

Randall, No challenge, just a suggestion as to the source=20 of the confusion regarding units. Power Spectral Density plots can be found which=20 are plotted both "per Hz" and "per 1/6 decade" or=20 "per octave", etc. There is a subtle distinction=20 regarding the units. Octaves and decades, being=20 ratios, are dimensionless. Hz, on the other hand, has units of 1/seconds. Considering an acceleration PSD, given as=20 m^2/sec^4 per Hz, and applying the units for Hz=20 we get just m^2/sec^3. On the other hand, the=20 units m^2/sec^3 per octave are also correct. I=20 believe these are consistent, both with what I=20 see in most published plots, and with what you were suggesting. When working with Hz, I tend to prefer the form=20 m^2/sec^4 per Hz as it is more obviously an=20 acceleration-power density with respect to=20 frequency, but that's mostly a matter of style. Regards, Brett At 01:35 PM 7/11/2012, you wrote: > I will probably meet with debate over this=20 > posting, since I have gone =91round and round=92=20 > for more than a decade with the professional=20 > seismologists about their need to start working=20 > with a better set of power spectral density=20 > units. To satisfy both Parseval=92s theorem and=20 > to also work with something that makes formal=20 > physics sense in terms of power=ADthere can be=20 > only one set of PSD units that are reasonable=20 > in terms of the whole world=92s recognition of the proper unit of power= (watts). >That set of units can only be W/kg/Hz which=20 >equals m^2/s^3/Hz and not the long-standing=20 >seismology and mechanical engineering tradition of m^2/s^4/Hz (or g^2/Hz). >Some of them more correctly label their graphs=20 >with the words acceleration spectral=20 >density. When one computes the FFT of the=20 >output from a seismometer (accelerometer in=20 >general) in the units corresponding to the only=20 >thing to which the instrument responds; i.e.,=20 >acceleration; then the ASD is simply=20 >m^2/s^4/Hz. In other words, the ASD is very=20 >close to the single sided Fourier transform=20 >spectrum discussed above, if properly normalized=20 >to satisfy Parseval=92s theorem. One must be=20 >very, very careful, however, to recognize=20 >another subtlety that most everybody=20 >ignores. The units as generated are really=20 >m^2/s^4/bin width. The bin width is never=20 >actually one Hz, and so a multiplicative factor=20 >must be considered if one is to actually use m^2/s^4/Hz, properly computed. __________________________________________________________ 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.