[SAC-HELP] polezero option

[Arthur Snoke]

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)

I give some replies to George's comments below.  I welcome 
comments/suggestions/corrections from others as well.

> %%%Comments indicated flagged with this notation.
> %%%This paragraph is jumbled.  It confusingly combines information about
> %%%the concepts underlying a pole-zero representation with the way to specify
> %%%a response to SAC.  They should be separated.

I agree that the paragraph could be improved, and am looking for better 
ways to untangle SAC from RDSEED.  A couple of things came up as I was 
writing this:

1.  There is a question of units: the RDSEED "response in" units use m as 
a length measure, while SAC's IDEP uses nm.  I doubt that either are going 
to change, but I welcome suggestions to state this efficiently.

2.  As i note, the values given for the polezero transfer function in the 
RESP file is for velocity "response in" (with two zeros) but the polezero 
file returned by RDSEED is for displacement (three zeros).  Is there 
nothing within RDSEED that makes that clear?  Or am I missing something?

> %%%filters aren't causal, either!

The polezero transfer functions are analog filters and in themselves are 
causal.  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.  Note I resisted the temptation to use \cdots in the 
equation above.  Given that one cannot underline letters in 7-bit ASCII, I 
have not figured out a good way to show the subset of letters need (e.g., 
TRANS for TRANSFER).

>
> %%%The information about the input units and output units needs to be 
> %%%presented more clearly.  The description here jumbles what rdseed 
> %%%does with what SAC does.

See above comment.
>
>      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.  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.

Arthur Snoke