Poles and zeroes with positive normalization factors

Poles and Zeroes for all Guralp instruments are obtained by the frequency response of the instrument. They are measured using the HP spectrum analyzer and a curve is then fitted to this data. All poles and zeroes supplied with Guralp equipment are derived from actual measured data and not generated from examination of theoretical calculations.

The system that Guralp Systems uses produces the lowest order transfer function that fits the data. For the response of the instruments this function always has a negative normalization factor.

Whilst negative normalization factors are mathematically correct and give the correct results, Guralp Systems has been made aware that the SEED convention does not allow for them and that the standard RDSEED conversion program does not handle negative normalization factors properly.

By increasing the order of the transfer function, we have been able to provide an alternative fit to the data with a positive normalization factor.

All instruments that have their frequency responses measured at GSL have their frequency response data held on file here.

Because the instruments are true feedback instruments, their response is entirely defined by the parameters in the feedback path. The frequency response of instruments is within 0.1 % at the long period end and within 2 % at the high frequency end.

Values

360 Second CMG-3T & CMG-1T (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
0 −80.0 A = 2 304 000
0 −160.0
−180.0
−0.001964 + 0.001964j
−0.001964 – 0.001964j

120 Second CMG-3T, CMG-3ESP & CMG-1T (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
0 −80.0 A = 2 304 000
0 −160.0
−180.0
−0.00589 + 0.00589j
−0.00589 – 0.00589j

100 Second CMG-3T, CMG-3ESP & CMG-1T (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
0 −80.0 A = 2 304 000
0 −160.0
−180.0
−0.00707 + 0.00707j
−0.00707 – 0.00707j

60 Second CMG-3T, CMG-3ESP, & CMG-40T (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
0 −80.0 A = 2 304 000
0 −160.0
−180.0
−0.01178 + 0.01178j
−0.01178 – 0.01178j

30 Second CMG-3T, CMG-3ESP & CMG-40T (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
0 −80.0 A = 2 304 000
0 −160.0
−180.0
−0.02356 + 0.02356j
−0.02356 – 0.02356j

1 Second to 100 Hz, CMG-40T (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
0 −75.0 A = 585 800 000
0 −350.0
−0.707 + 0.707j
−0.707 – 0.707j
−62.3816 + 135.392j
−62.3816 – 135.392j

DC to 100 Hz, Fortis / CMG-5T / CMG-5TD / CMG-5TB (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
−755.9 A = 1 939 000 000
−209.7
−63.79 – 90.39j
−63.79 + 90.39j

DC to 200 Hz, CMG-5T / CMG-5TD / CMG-5TB (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
–174.0 – 177.1j A = 1.634 × 1010
–174.0 + 177.1j
–309.7
−855.9

DC to 200 Hz Fortis / CMG-5TC (in Hz)

Zeroes Poles Normalization Factor at 1 Hz
−60.8 – 155j A = 4.6839 × 109
−60.8 + 155j
−123
−1320

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Address

 

Guralp Systems Limited
Midas House
Calleva Park
Aldermaston
Reading
RG7 8EA, UK

Tel: +44 118 981 9056
Fax: +44 118 981 9943
E-Mail: sales@guralp.com

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