1. Intro to Spectral Analysis and Matlab

2. Time domain Seismogram - particle position over time Time Amplitude

3. Frequency domain Why might frequency be as or more important than amplitude? –Filtering signal from noise –Understanding earthquake source, propagation effects –Ground shaking

4. Time domain Frequency domain Possible to mathematically transform from time to frequency domain Relative importance of the frequencies contained in the time series Can completely describe the system either way. Goal of today’s lab –Begin to become familiar with describing seismograms in either time or frequency domains –Will leave out most of the mathematics

5. Sine wave in time

6. Spectra of infinite sine wave

8. Two sine waves in time

9. Spectra of 2 infinite sine waves

10. Spectra of discrete, finite sine waves

11. To create arbitrary seismogram Becomes integral in the limit Fourier Transform –Computer: Fast Fourier Transform - FFT

12. Time domain, single spike in time

13. Spectra of a single spike in time

14. Sampling Frequency Digital signals aren’t continuous –Sampled at discrete times How often to sample? –Big effect on data volume

15. How many samples/second are needed?

16. Are red points enough?

17. Aliasing FFT will give wrong frequency

18. Nyquist frequency 1/2 sampling frequency

19. Nyquist frequency Can only accurately measure frequencies <1/2 of the sampling frequency –For example, if sampling frequency is 200 Hz, the highest theoretically measurable frequency is 100 Hz How to deal with higher frequencies? –Filter before taking spectra

20. Summary Infinite sine wave is spike in frequency domain Can create arbitrary seismogram by adding up enough sine waves of differing amplitude, frequency and phase Both time and frequency domains are complete representations –Can transform back and forth - FFT Must be careful about aliasing –Always sample at least 2X highest frequency of interest

21. Exercise plots

22. Sine_wave column 2

24. Sine_wave column 2 and 3

25. Sine_wave column 2 and 3 sum

26. Spectra, column 2

27. Spectra, columns 2, 3

28. Spectra, column 2, 3, 2 and 3 sum

29. Multi_sine, individual columns

31. Multi_sine spectra

32. Spike in time

33. Spike in time, frequency

34. Rock, sed, bog time series

35. Rock spectra

36. Rock (black), Sed (red), bog (blue)

37. Spectral ratio sed/rock

38. Basin Thickness 110 m/s /2.5 Hz = 44 m wavelength Basin thickness = 11 m 80 m/s /1 Hz = 80 m Basin thickness = 20 m

39. Station LKWY, Utah raw Filtered 2-19 Hz Filtered twice

40. Station LKWY, Utah raw Filtered 2-19 Hz Filtered twice

41. Zoomed in once

43. Zoomed in again

44. Triggered earthquakes