How to prepare a pole and zero file for ISOLA



How to prepare a pole and zero file (pzfile) for ISOLA.

Preparing a proper pz-file needs some training. That is why it may often cause some problems to the beginners. To facilitate the training, we give here a simple explanation (without formulas) and an example.

Instrumental correction in ISOLA code includes two steps. Symbol [] denotes units.

Step 1: Record in [counts] is multiplied by a conversion constant C [(m/s)/counts],

thus we get record in (m/s).

Step 2: Complex spectrum of record is divided by complex transfer function and back transformed into time domain. The transfer function is computed using poles, zeros and a constant, usually denoted A0. Modulus of the transfer function has a plateau, the hight of which must equal 1. This is achieved just by A0, thus A0 is called normalization constant.

ISOLA needs poles, zeros and A0 expressed in rad/sec. Some manuals (e.g. Guralp) give them in Hz, instead. To get poles and zeros in [rad/sec] we multiply their values in [Hz] by 2pi. To get A0 [rad/sec] we multiply A0 [Hz] by (2 pi)**(NP-NN)

where NP and NZ is the number of the (complex) poles and zeros.

ISOLA needs the so-called velocity, broad-band records. It means records of the instruments whose amplitude response (modulus of transfer function) to input velocity is flat in a broad frequency range.

When user has no velocity recorder, but an accelerograph instead, he has to apply an appropriate conversion constant C to get from counts to m/sec^2, and then there are two options what to do. (i) Apply instrumental correction using poles, zeros and A0 of the accelerograph with one modification – one complex zero must be added. This will be equivalent to integration of the acceleration record. Or, (ii) integrate the accelerograph record prior usage in ISOLA by his/her preferable software. If method (ii) is used, the instrumental correction must be by-passed. This can be achieved by formally prescribing A0=1 and just one pole and one zero, both with Re=1, Im=0.

Users working with data in SEED format get two files containing the intrumental information: the so-called RESP files, and the SAC-pz files (for each component separately, everything in rad/sec). The files may obtain the ‘history’ of the instrument, so the data corresponding to the appropriate recording period (say, from 2000 to 2002) must be selected. Use of RESP is complicated also by the fact that poles and zeros are not necessarily in one place (for example, this is the case of Lennartz/20sec data of the HL network, where user must combine values from different ‘stages’). Advantage of RESP files is that they explicitly provide the A0 value. The conversion constant C can be obtained from RESP files using the so-called sensitivity, available at the end of the files, in the B053F07 numerical field: we compute C [(m/s)/counts] = 1 / sensitivity. Advantage of the SAC-pz files is simplicity, but one must very cautious with the zeros; the SAC-pz files represent response for input displacement, so user of ISOLA must ignore one zero (e.g., if the SAC-pz file gives three zeros, ISOLA must have prescribed two zeros). SAC-files do not explicitly give A0 and C. Instead, they provide the value called CONSTANT which is A0 / C. In case like that, when ISOLA user does not know the values of A0 and C separately, he can formally prescribe in his pz-file A0=CONSTANT and C=1. (In that case, however, his plots of the modulus of the transfer function will formally have their plateau equal CONSTANT, not 1.)

Users working for example with Guralp manuals will proceed in a slightly different manner. First of all (as already mentioned above), they will have to pass poles, zeros and A0 expressed in Hz to the ISOLA units of rad/sec. As for C, the user will have to know two constants. One of them is sensitivity of the seismometer (e.g. 2*3000 V/(m/s)). Note a different usage of the same word here, compared to the RESP seed files ! One has also to be cautious whether factor 2 is to be used, or ignored (i.e. to take 6000 or 3000). This depends on the type of the connection between the seismometer and the digitizer. Guralp provided the following guide: They have two types of digitizers: MK2 ... factor 2 is NOT to be used, MK3 ... factor 2 is to be used. Most often they used single-ended connection [the 3T sensor with digitizer MK2 mounted on its top] and differential connection [digitizers MK3 separately from 3T]. But this is not necessarily the case. Guralp therefore recommended this: If the serial number of the digitizer begins with letter D (e.g. in the sensor T3123/D103,) you have a MK2 digitizer, while the MK3 digitizers have serial numbers beginning with A, B or C (e.g. T3434/AB91). This issue needs a consultation with a technician or the provider. The other important constant is related to the digitizer, i.e. the constant to convert Volts to counts. If, for example, we know that 1 count=10**(-6) Volt, and, from above, we have 1 m/sec=3000 Volt, we get 1 count = 300 * 10**(-12) m/sec. In other words, for the 4th row of the ISOLA pz-file we got then C= 300 * 10**(-12) [(m/sec)/count]

Example

We present the above using the example of a Trillium seismometer and a Trident (Nanometrics) digitizer. From the manuals we know the following: The Trident digitizer is set at 1 count per microvolt. The Trillium manual gives:

[pic]

Thus we have the following: A0 = 133310. Using the Trillium sensitivity (1500 V/m/sec) and digitizer’s sensitivity (1cont/microV) we get the value 6.66667e-10 as m/sec per 1 count. Finally we put the above values in a text file with the following format.

Example of Pole and Zero file for ISOLA (Trillium40 seismometer and Trident digitizer).

A0

133310

count-->m/sec

6.6667e-10

zeroes

3

0.0 0.0

0.0 0.0

51.5 0.0

poles

5

-272 218

-272 -218

56.5 0

-0.1111 0.1111

-0.1111 -0.1111

Before proceeding with instrument correction we can use option Plot Response (from Raw data Preparation GUI). At this plot we should always check if the flat part of the amplitude response (the so-called ‘plateau’) is equal to 1. That means that our A0 value is correct.

[pic]

Frequency Response for Trillium-40 seismometer (amplitude-top, phase-bottom).

Using accelerograph records in ISOLA

1) Since ISOLA always needs the instrument response for input velocity, you should use poles and zeros for input acceleration and add one more complex zero (0.,0.). This is a must when your accelerograph is of an old style and its response is not flat down to zero frequency.

2) If your accelerograph has its response flat down to zero frequency (as common for most modern instruments, e.g. Guralp CMG-5T), and because most ISOLA applications are for frequencies below the corner frequency of accelerograph (e.g. 50 Hz), you even do not need poles and zeros of the accelerograph. You can simply use one pole (1.,0.) and one zero (1.,0.), which formally cancel each other in order to simulate constant acceleration response, and simply add one more zero (0.,0.) as explained above. This is demonstrated below.

3) If your record is in counts, you need conversion factor C to pass from counts to m/s^2: units of C are (m/s^2)/count; it should appear on line 4 of the pzfile. If your record is not in counts, but directly in ground motion units, you should only distinguish whether it is in m/s^2, or cm/s^2, etc. The following example is for record in cm/s^2. Line 4 in this case (1.e-2) then makes conversion from cm/s^2 to m/s^2 as needed in ISOLA.

A0

1

count-->m/sec

1.000000e-002

zeroes

2

0.000000e+000 0.000000e+000

1.000000e+000 0.000000e+000

poles

1

1.000000e+000 0.000000e+000

How to create pzfile in the Create Pole Zero tool of the ISOLA main window.

The window is self-explanatory, but it needs a few comments. In particular, the tool has two boxes to enter the two ‘sensitivity’ parameters:

Digitizer Sensitivity ... D [count/Volt]

Seismometer Sensitivity ... S [V/(m/s)]

Code uses the product (D.S) [count/(m/s)]

If user does not know D and S, but only the value of the product (D.S) [count/(m/s)],

he formally puts the value of D.S into the D-box and the value 1 into the S-box, or, vice versa (D.S into S and 1 into D).

In both cases the created pzfile will have the value C=1./(D.S) [(m/s)/count] on its 4th line, as always needed in ISOLA.

When using RESP files form SEED, it provides explicitly A0 and poles and zeros in rad/s. The conversion constant C [4th line of pzfile] can be obtained from RESP files using the so-called sensitivity [counts/(m/s)], available at the end of the files, in the B053F07 numerical field: we compute C [(m/s)/counts] = 1 / sensitivity. In other words, similarly to the above case, using the pzfiles tool of ISOLA, user enters directly the value of sensitivity form B053F07, either into box D or S, filling the other box with value 1.

The SAC-pz files (also obtained from SEED files) represent response for input displacement; therefore ISOLA user must remove one zero (e.g., if the SAC-pz file gives three zeros, ISOLA pzfile must contain only two zeros). The SAC-pz files do not explicitly give A0 and C. Instead, they provide the value called CONSTANT which is A0 / C. In case like that, when ISOLA user does not know the values of A0 and C separately, he can formally prescribe in his pz-file A0=CONSTANT and C=1, i.e. user enters value 1 into box boxes D and S.

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