1.
How would you expect the amplitudes of the surface waves and the tremor to appear in the
raw seismogram (before removing the instrument response) relative to how they appear in
figure a?
Answer: Note that instrument response in e) amplifies the original signal at all frequencies.
However, the higher frequencies (0.2Hz and higher) are amplified by a significantly larger factor
than at lower frequencies. Over all, this implies that the original signal s(t) has significantly
smaller amplitudes across all frequencies. The lower frequency waves would have relatively
larger amplitudes relative to the high frequency waves in the original signal s(t) than as they
appear in the broad band signal in a).
2. The high pass filter used to unmask the tremor was selected trying to avoid the attenuation of
the tremor signal. Draw a graph of how the frequency response magnitude of the filter may
look like.
Answer: The high pass filter dampens lower frequencies and intensifies higher frequencies.
3.
Is the lower limit of the y-axis figure in c) actually zero? Explain
4.
Answer: No. Since this is a spectrogram of the graph in a), we should expect to see low
frequency high amplitude surface waves between time 800 and 1000. Since there are no red
colors at low frequencies in this time interval in the spectrogram, the lower limit on the y axis
cannot be zero.
5. Assuming that the answer to question 3 is yes, what is the relationship between figure c) and
figure d)
Answer: The spectrogram c) plots the spectrum (amplitude vs. frequency) over a short time
window of time. The frequency spectrum (d) plots the maximum amplitudes of each frequency
observed over the entire time domain.
6. What information can be obtained from c) that can’t be obtained from d) and vice versa.
Answer: The frequency spectrum (d) gives you a high resolution understanding of all maximum
amplitudes observed at all frequencies, but does not give you any information about when they
occurred. The spectrogram (c) gives you a better understanding of when certain frequency
waves were observed, but in the process having a short time analysis window we must
necessarily have less frequency resolution (i.e. we have less certainty about what frequencies
were actually observed).
7. Is it possible to identify the tremor from figure d) ?
Answer: No. The frequency takes the maximum amplitude at each frequency represented in
the spectrogram. We know that the tremor has high frequency and small amplitude, but the
frequency spectrum takes the maximum at each frequency over all time. Thus, we can’t tell if
the high frequency, low amplitudes in this graph are the result of tremors or not.
8.
How could you obtain d) from c)
Answer: You can look at each frequency over the entire interval in time (each horizontal line)
and pick the maximum amplitude, then plot the maximum amplitudes vs. each frequency.
9. Is it possible to obtain c) from d)?
Answer: No. The frequency spectrum reveals no information about when each frequency was
observed.
10. If you were to decimate a), what is the minimum sampling frequency that you would use in
order to retain the important information in the seismogram?
Answer: We would use the nyquist frequency = 2*the highest frequency wave anticipated
11. Is this instrument appropriate for this kind of analysis? Why?
Answer: Yes, although the broad band waves give you much more information than is
necessary. It would have been sufficient to have an instrument that recovers high frequency
waves only, since they are what we are really interested in (tremors).