Started: 2007-11-14 02:11:06
Last activity: 2007-11-14 17:09:24
Topics: aniso
2007-11-14 02:11:06
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

-1131.00.0000

-1005.00.0000

-502.70.0000
ZEROS 2
0.00000.0000

0.00000.0000

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?

• George Helffrich
2007-11-14 17:09:24
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?

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George Helffrich
george<at>geology.bristol.ac.uk

10:18:20 v.eb79165e