[SAC-HELP] remove instrument response

George Helffrich george at gly.bris.ac.uk
Wed Nov 14 01:09:24 PST 2007


Dear All -

	The CONSTANT value is calculated from your list of poles and zeros.  
It is a value that normalizes the transfer function product to be equal 
to 1 at your reference frequency.  It serves to numerically stabilize 
transfer function calculations because the numbers tend to get large.

	SAC calculates transfer functions in angular frequency omega = 2*pi*f. 
  Conventionally the reference frequency is 1 Hz, but this is a choice 
that depends on the frequency range over which the transfer function is 
used and the rest of your instrument response (the gain reference 
frequency, for example, if one is appropriate).  Thus the CONSTANT 
value should be the number that, when multiplying your transfer 
function expression at 1 Hz (or the reference frequency), gives it the 
value 1.  Here is an example.

ZEROS 1
1 0
POLES 1
2 0

Transfer function at 1 Hz is (1-2*pi)/(2-2*pi) = 1.233471.  Thus the 
CONSTANT is 1/1.233471 = 0.8107202.

	From your pole and zero values, I calculate your CONSTANT to be 
585717.5, but you should check yourself.

On 13 Nov 2007, at 10:11, FANG Lihua wrote:

>  Hi,
>
>  I use SAC to remove the instrument response,
>  SAC>transfer from polezoro subtype  response.pz to none freqlimits 
> 0.01 0.02 5.0 8.0
>  the following is the content of response.pz
>  *******************************
> POLES 5
>
> -0.03701
> +0.03701
>
>
> -0.03701
> -0.03701
>
>
> -1131.0
> 0.0000
>
>
> -1005.0
> 0.0000
>
>
> -502.7
> 0.0000
>  ZEROS 2
> 0.0000
> 0.0000
>
>
> 0.0000
> 0.0000
>  CONSTANT  ????
>  *******************************
>
>  But I don't know how to calculate the constant.
>
>  I got the calibration sheet from Gurapl. The normalization factor at 
> 1Hz is 2304000.
> The sensivity is 1500V/m/s.
>
>  I convert the unit from Hz to rad/s and re-calculate the 
> normalization factor:
>
>  1500*2304000*(2*pi)^(5-2)=8.5726e+011
>
>  I don't know whether I should multiply the AD convert factor of the 
> digitizer or not.
>  the digitizer is REFTEK 130, and the AD convert factor is 1.588e-06 
> v/conts.
>
>  If I multiply the AD convert factor, I got a new result.
>
> (1.588e-06)*1500*2304000*(2*pi)^(5-2)=1.3613e+006
>
>  I want to ask which CONSTANT I shoud use? 8.5726e+011 or 1.3613e+006?
>
>  Please help me!
>
>
>
>
>  
>  
>  
>
>
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>
								George Helffrich
								george at geology.bristol.ac.uk
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