1. Intro to Spectral Analysis and Matlab Q: How Could you quantify how much lower the tone of a race car is after it passes you compared to as it is coming towards you? How would you set the experiment up?

2. Running the Experiment. Data is often recorded in the time domain. The stored dataset is called a timeseries. It is a set of time and amplitude pairs.

4. Frequency Domain (Do a Fourier Transform on Timeseries) We have converted to the Frequency Domain. This dataset is called a Spectra. It is a set of frequency and Amplitude pairs.

5. Time Domain What’s the Frequency? What’s the Period? What will this look like in the Frequency Domain?

7. What’s the new (red) period? How Does its amplitude Compare to the 1 s signal?

8. Power Spectral Densities Secondary Microseism (~8 s) Primary Microseism (~ 16 s)

9. QSPA PSD PDF

10. The Mysterious Case of HOWD

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

12. How many samples/second are needed?

13. Are red points enough?

14. Aliasing FFT will give wrong frequency

15. Nyquist frequency 1/2 sampling frequency

16. 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

17. 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 and iFFT Must be careful about aliasing –Always sample at least 2X highest frequency of interest

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

19. Exercise plots

20. Sine_wave column 2

22. Sine_wave column 2 and 3

23. Sine_wave column 2 and 3 sum

24. Spectra, column 2

25. Spectra, columns 2, 3

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

27. Multi_sine, individual columns

29. Multi_sine spectra

30. Spike in time

31. Spike in time, frequency

32. Rock, sed, bog time series

33. Rock spectra

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

35. Spectral ratio sed/rock

36. Basin Thickness Sediment site 110 m/s /2.5 Hz = 44 m wavelength Basin thickness = 11 m Peat Bog 80 m/s /1 Hz = 80 m Basin thickness = 20 m

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

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

39. Zoomed in once

41. Zoomed in again

42. Triggered earthquakes