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GG313 Lecture 28 Dec 6, 2005

Learn how to analyze directional data using spectral analysis techniques and remove ambiguity using mathematical transformations. Review concepts of fitting lines to directional data and conversion to rectangular coordinates. Also, understand the importance of applying windows to data before taking the Fourier transform.

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GG313 Lecture 28 Dec 6, 2005

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  1. GG313 Lecture 28Dec 6, 2005 More Spectra Directional Data

  2. The Gaussian is its own Fourier transform %gausst.m %% Fourier transform of a Gaussian t=[-5.11:.01:5.12]; curve=exp(-pi*t.^2); plot(t,curve); Fcurve=fft(curve); P=Fcurve.*conj(Fcurve); plot(P(1:50))

  3. time frequency The half-power width in the time domain in this case is 94 time steps. In frequency, the half-power (half-width) is ~3 frequency estimates. Thus, MULTIPLYING in the time domain by a Gaussian window will SMOOTH in the frequency domain by convolution with a Gaussian.

  4. Before taking the Fourier transform of data that are offset from zero, it’s a VERY good idea to remove the mean first. This prevents many problems with high frequency junk caused by “windowing” the data. It’s then a good idea to apply a window to zero the data at the edges of the time series. Many windows are available - Gaussian, Hanning, Hamming, Lanczos, cosine taper, etc. Each has different properties in the frequency domain. Select the data desired for the fft remove the mean apply a window take the fft

  5. EARTHQUAKEANALYSIS Quake_files

  6. Directional Data (Chapter 6) Recall that we have already done some analysis of directional data when we talked about fitting a line to a set of points. Might be good to review that… We distinguish between truly directional data - like a compass heading - that can cover the whole range between 0° and 360°, and “oriented” data that has a 180° ambiguity - like the strike of a layer in an outcrop. Look at some of the Matlab functions that plot directional data: directional_html

  7. In reviewing Paul’s notes, I found one cool concept. If the data are oriented (180° ambiguity) there is a problem eliminating the ambiguity when working with collections of data. Some people choose 95°, others might choose 280° - but these are the same angle. To eliminate the ambiguity: double all angles if any double angles are > 360°, subtract 360° divide all angles by 2 again. Now all angles will be between 0 and 180° TRY IT in EXCEL

  8. Another problem with directional data is that the angles 0° and 359° (or 0° and 179° for oriented data) are only 1 degree apart. If we’re trying to statistically find an average direction, we need to fix this. If we’re given angles, we can convert them to rectangular coordinates using the following: (6.2) (6.3) (6.4) Dividing by two gives the average angle.

  9. THURSDAY CLASS: REVIEW BRING QUESTIONS!!

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