Methods of Analysis

Lesson

Introduction
Trace Moments (TM)
- Introduction
- Theoretical estimation: 1
- Theoretical estimation: 2
- Empirical estimation: in time
- Empirical estimation: in space
Double Trace Moments (DTM)
Probability Distribution Multiple Scaling
Structure Function
Empirical Modal Decomposition (EMD)
Exercises
Conclusion

Theoretical estimation: 1

The spectral analysis introduced in the previous courses (see Spectral Analysis courses) corresponds to a second order statistics analysis, the Trace Moment analysis is performed on large range of moment . This allows to determine the statistical moment function of over wide range of scale (resolution ). As we have seen in the previous courses the statistical moments of can be expressed as :

$\langle \varepsilon_\lambda^{q} \rangle \approx \lambda^{K(q)}$

The field is aggregated at resolution increasingly small ( where is the highest resolution)

Estimation of the statistical moment function for different order q

Then, the function corresponds to the slope of the moments of order according to in log-log plot.

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