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Outline

Outline. Correlation. Crosscorrelation. Crosscorrelation describes the similarity between two time series. For us a trace consists of a series of amplitude values at regular intervals of time or a time series.

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Outline

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  1. Outline • Correlation

  2. Crosscorrelation • Crosscorrelation describes the similarity between two time series. For us a trace consists of a series of amplitude values at regular intervals of time or a time series. • Mathematically, crosscorrelation is like convolution, but where none of the traces are reversed prior to the steps involving shifting, multiplication and addition (See lecture PowerPoint Presentation entitled “CMP”)

  3. Correlation of two traces Wavelet 1 has the same shape as wavelet 2. Wavelet 2 is a “time-advanced” version of wavelet 1 by 2 units of time Wavelet 1: 2,1,-1,0,0 Wavelet 2: 0,0,2,1,-1

  4. Correlation of Wavelet 1 with 2 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=0 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  5. Correlation of Wavelet 1 with 2 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=1 -2 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  6. Correlation of Wavelet 1 with 2 6 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=2 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  7. Correlation of Wavelet 1 with 2 Wavelet 1: 2,1,-1,0,0 (FIXED) 1 TIME=3 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  8. Correlation of Wavelet 1 with 2 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=4 -2 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  9. Correlation of Wavelet 1 with 2 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=5 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  10. Correlation of Wavelet 1 with 2 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=6 Crosscorrelation Wavelet 2: 0,0,2,1,-1

  11. The maximum value of the correlation is 6 at time =2 Wavelet 1: 2,1,-1,0,0 (FIXED) TIME=7 Crosscorrelation Wavelet 2: 0,0,2,1,-1

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