How we obtained the response

It was a long and painful process creating the correct response files and plots for the Danish network. Along the way we discovered, that we were not the only ones struggling to get it right. We have therefor assembled a description of the steps taken to create the files and plots available from this web-site. The "response cookbook" below emphasizes the practical issues involved, and it applies strictly to the types of instrumentation used in the Danish network. However, we hope it can serve as inspiration for users of other instruments. For an in-depth theoretical treatment of the subject, we recommend Frank Scherbaum's book Of Poles and Zeros - Fundamentals of Digital Seismology from Kluwer Academic Publishers (1996).

Our equipment

We use Nanometrics HRD24 digitizers, and Streckeisen STS-1 and STS-2 seismometers. The system response contains contributions from the digitizer and from the seismometer. The digitizer is by far the most complicated of the two with zillions of coefficients. Fortunately, Nanometrics supply the users with a small program that can generate a file containing the coefficients. Streckeisen does not supply the user with poles and zeros, but he provides the formulas necessary to obtain the numbers.

Step-by-step cookbook

Finding the coefficients for the digitizer

If you are using Nanometrics HRD24 or Orion, run the Nanometrics supplied program "response" to create a file in SEED-like format containing all of the coefficients. When you run the program, you have to answer questions regarding which seismomter you are using, your sample rate, and DC-filter setting. Warning: The Nanometrics factory setting for the DC-filter is a corner frequency of 100mHz. This is inappropriate for use with a broadband seismometer! If you are using the digitizer with a broadband seismometer, change the configuration so that your DC-filter corner frequency is 10 or 1mHz, otherwise the surface waves will suffer. If you have an old version of the response information from Nanometrics, the DC-filter may or may not be included (it is the last stage, IIR filter). If it isn't included in your response file, you have to ask Nanometrics for a new version of the "response" program.

When you run the "response" program, it asks you which seismometer you use. If your seismometer isn't included in the list, just pick one at random. You can edit the output file later. It is called seed.rsp, but it isn't in standard IRIS SEED format. You can see and example of the seed.rsp file here.

If you use a digitizer of a different brand, ask the company you bought it from to supply you with a file containing all of the poles and zeros. If you get a choice, it is very handy to have the information in SEED format (dataless SEED volume).

Finding the coefficients for the seismometer

The easiest way is to borrow this information from someone who already went through the calculation... You can find the poles and zeros for the STS-1 (VBB version) and STS-2 seismometer in the response files on this web-site. Station COP is equipped with an STS-1, and station MUD is equipped with an STS-2.

If you want more precise response information taking into account the actual sensitivity of your seismometer, or if you can't find the poles and zeros you need, you'll have to sharpen your pencil.

In the seismometer manual, your'll find a formula describing the transfer function of the seismometer (if the formula isn't there, complain!). It is a complex function consisting of a polynomial in the numerator and a polynomial in the denominator. The complex roots of the numerator are the "zeros", and the complex roots of the denominator are the "poles". These poles and zeros describe where your seismometer will and won't function properly. It is very possible to make a classical factor 2 pi mistake, so be aware of what you're doing.

When you have found the poles and zeros for the seismometer, you need to add this information to the file containing the poles and zeros for the digitizer. If your have a Nanometrics seed.rsp file, it is quite obvious where to fill in the information (Stage 1).

Converting the response information to real SEED

At this stage we have the complete response information in Nanometrics format and would like to convert it to IRIS SEED format. There may be several ways of doing it, but here is one way that works:

• Find a small datafile from an Orion in Nanometrics X-format. It doesn't matter what the file contains or which station it is from.
• Run the Nanometrics "makeseed" program on your seed.rsp file and the data file. This results in a SEED volume containing the response information and the data.
• Run the "rdseed" program on the SEED volume using option "R" to strip the response information from the data.

Checking the response

How do you know if your brandnew SEED response file is correct? Well, basically you have to trust what you have done, but you can generate plots of the amplitude and phase response and see if they make sense. The IRIS software library contains a program called "evalresp". If you run "evalresp" on your SEED response file, you can get out files containing the gain as function of frequency for amplitude response, and phase as function of frequency for phase response. Plot these files in your favorite plotting program, and see if they look the way you would expect.

Example figures coming soon!