DeNU LOGOpartment of Earth and Planetary Sciences
            Northwestern University

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I am - hopefully! - going to post more stuff here.

Record Gaps in the Global Seismic Stations

This is a video of daily "measured" record gaps in global instruments which were
operational during 2014.

The units are "gap samples". Having the sampling rate of the  instruments at hand,
one can easily convert the units to seconds -- which is not  difficult to do.
However, for all practical purposes, presenting these results in samples
is much more useful.

The day number is the corresponding Julian Day for each measurement.

Note: Provided that you can use IRIS services (e.g. MUSTANG, PDF/PSD, etc),
this is actually an easy video to make.

Interesting Idea: Add SNR to the video!

Here is another example for done for the USArray.

Instrument Response Estimation

Although a seismometer can be a great means to measure the apparent ground motion, we need to know the the instrument specifications to correctly interpret the recorded data. The list  of these specifications are crucial in utilizing the output data from any seismometer in scientific research. Such information are usually presented in the form of response of a seismometer to external motion and are documented in different formats which should ideally accompany the seismometer. The "instrument response can be obtained in two ways:

  1. Directly from the published instrument documentation in the form of response files.
  2. Parameter estimation by comparison to instruments with know responses.

In the absence of a legitimate response, we need to use the second method. If we represent the recorded signal as a time series, u(t),  and let s(t), g(t) and i(t) represent the source developments, effects of the medium along the path, and the instrument (i.e seismometer) effect on the signal (in time), respectively, we can write

u(t) = s(t) * g(t) * i(t)

where the asterisks represent convolution of the time series. Now, if we manage to isolate i(t) in this equation and find its relative value to some known number(s), then there are means to find its absolute value which is basically the response function of the seismometer.

If the two seismic stations are close enough so that we could ignore the difference in the path traveled by the seismic waves from a single earthquake source, we can then consider i(t) as the only reason for the observed difference  in the seismograms, u(t), recorded by the two seismometers, which will be due to their sensitivity in picking the seismic signal, their internal structure and the structure (i.e building) they are installed in. This assumption is done by considering the nature of seismic wave propagation patterns.

Having achieved the above, the final steps of preparing a response documentation file for a seismometer will be to calculate and plot amplitude and phase curves in the frequency domain, as seismometers' responses are different at different frequencies. Such curves, in order to be reproducable, are usually published in the form of poles and zeros and amplification factors. It is then rather easy to to find the best fit to the response spectra in the frequency domain, considering the standard format of the response function for a LTI system to approximate the numbers and values of its poles and zeros. An example of is shown below.