[SAC-HELP] Fwd: polezero option

George Helffrich george at gly.bris.ac.uk
Mon Apr 27 05:26:47 PDT 2009


Dear All -

	My rewrite will arrive in a separate posting anon.  Some comments on 
Arthur's:

On 26 Apr 2009, at 14:26, Arthur Snoke wrote:

> Thank you George and Kuang-He for comments.  Kuang-He picked up on a 
> typo in the equation I wrote.  I wrote him off list with a corrected 
> version that he said was okay:
>
> (s-z1)*(s-z2)*...*(s-zn)
> ________________________
>
> (s-p1)*(s-p2)*...*(s-pm)
>
> ...
>
>> %%%filters aren't causal, either!
>
> The polezero transfer functions are analog filters and in themselves 
> are causal.

The analog filter response that the pole-zero description represents is 
causal, but pole-zero descriptions are not necessarily causal.  That's 
the statement that I wanted to correct -- am I wrong?

>  The one I give as an example is an STS-2 response function, which is 
> mostly a damped harmonic oscillator.  (Aside: I have read that there 
> are three versions/generations of STS-2 seismometers, but so far as I 
> can tell the analog-stage response is always the same.  Can anyone 
> clarify?)
>
>> %%%Using TeX-style expressions isn't a good idea -- it assumes the 
>> reader %%%knows TeX, when many use nothing more than Word to typeset 
>> equations.
>> %%%Lay them out graphically in text, assuming a fixed-pitch font.
>
> As of now, SAC help files use 7-bit ASCII.  The minimal use I made of 
> TeX notation should be transparent to anyone who understands what a 
> Laplace transform is.

I don't see a connection between knowing mathematics and knowing TeX.  
I know mathematics but typeset them with eqn/troff.  See my own rewrite 
in a separate message.

> ...
>>
>>      u:  READ ABC.Z
>>
>>      u:  TRANSFER FROM POLEZERO SUBTYPE SRO.PZ TO NONE
>>
>
> I do not use SAC to do my instrument correction, but I do use polezero 
> files. The above example as written would probably get one in trouble 
> at very low frequencies, as all seismometers have zero response at 
> zero frequency.

SeisMac doesn't!  It is an accelerometer, but that can be a 
seismometer, too.

>  If I understand the notation correctly, "FROM" means a deconvolution, 
> which means it divides the input waveform by, in this case, the 
> polezero expression.  To avoid the output blowing up, this expression 
> should be amended to include the FREQLIMITS option.  Putting these in 
> definitely makes the total transfer function noncausal.
>
So are pole-zero responses acausal, or are only band-limited ones 
acausal?

                                     George Helffrich
                                     george at geology.bristol.ac.uk




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