intro to spectral analysis and matlab
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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Intro to Spectral Analysis and Matlab
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Time domain
• Seismogram - particle position over time
Time
Amplitude
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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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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
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Sine wave in time
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Spectra of infinite sine wave
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Spectra of infinite sine wave
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Two sine waves in time
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Spectra of 2 infinite sine waves
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Spectra of discrete, finite sine waves
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To create arbitrary seismogram
• Becomes integral in the limit • Fourier Transform
– Computer: Fast Fourier Transform - FFT
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Time domain, single spike in time
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Spectra of a single spike in time
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Sampling Frequency
• Digital signals aren’t continuous– Sampled at discrete times
• How often to sample?– Big effect on data volume
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How many samples/second are needed?
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Are red points enough?
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AliasingFFT will give wrong frequency
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Nyquist frequency1/2 sampling frequency
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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
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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
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Exercise plots
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Sine_wave column 2
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Sine_wave column 2
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Sine_wave column 2 and 3
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Sine_wave column 2 and 3 sum
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Spectra, column 2
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Spectra, columns 2, 3
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Spectra, column 2, 3, 2 and 3 sum
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Multi_sine, individual columns
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Multi_sine, individual columns
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Multi_sine spectra
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Spike in time
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Spike in time, frequency
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Rock, sed, bog time series
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Rock spectra
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Rock (black), Sed (red), bog (blue)
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Spectral ratio sed/rock
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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
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Station LKWY, Utah
raw
Filtered2-19 Hz
Filtered twice
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Station LKWY, Utah
raw
Filtered2-19 Hz
Filtered twice
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Zoomed in once
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Triggered earthquakes