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Intro to Spectral Analysis and Matlab

Intro to Spectral Analysis and Matlab. Time domain. Seismogram - particle position over time. Amplitude. Time. Frequency domain. Why might frequency be as or more important than amplitude? Filtering signal from noise Understanding earthquake source, propagation effects Ground shaking.

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Intro to Spectral Analysis and Matlab

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  1. Intro to Spectral Analysis and Matlab

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

  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

  7. 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 frequency1/2 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

  23. 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

  30. 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

  42. Zoomed in once

  43. Zoomed in again

  44. Triggered earthquakes

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