1. Correlations 1 Surface waves and correlations  Correlation of time series  Similarity  Time shifts  Applications  Correlation of rotations/strains and translations  Ambient noise correlations  Coda correlations Scope: Appreciate that the use of noise (and coda) plus correlation techniques is one of the most innovative direction in data analysis at the moment: passive imaging

2. Correlations 2 Discrete Correlation Correlation plays a central role in the study of time series. In general, correlation gives a quantitative estimate of the degree of similarity between two functions. The correlation of functions g and f both with N samples is defined as: Correlation plays a central role in the study of time series. In general, correlation gives a quantitative estimate of the degree of similarity between two functions. The correlation of functions g and f both with N samples is defined as:

3. Correlations 3 Auto-correlation

4. Correlations 4 Cross-correlation Lag between two functions Cross-correlation

5. Correlations 5 Cross-correlation: Random functions

6. Correlations 6 Auto-correlation: Random functions

7. Correlations 7 Auto-correlation: Seismic signal

8. Correlations 8 Basic theory

9. Correlations 9 Basic Theory

10. Correlations 10 Basic theory

11. Correlations 11 Basic theory

12. Correlations 12 Noise correlation - principle From Campillo et al.

13. Correlations 13 Uneven noise distribution

14. Correlations 14 Theory

15. Correlations 15 Green‘s function retrieval

16. Correlations 16 Noise on our planet Stutzmann et al. 2009

17. Correlations 17 Wavefield directions (winter-green, summer-red) Geographical map showing at the station location (black circles) the azimuths of the most abundant sources of secondary microseisms for months January and February in green and July and August in red.

18. Correlations 18 Surface waves and noise Cross-correlate noise observed over long time scales at different locations Vary frequency range, dispersion?

19. Correlations 19 Surface wave dispersion

20. Correlations 20 US Array stations

21. Correlations 21 Recovery of Green‘s function

22. Correlations 22 Dispersion curves All from Shapiro et al., 2004

23. Correlations 23 Tomography without earthquakes!

24. Correlations 24 Global scale! Nishida et al., Nature, 2009.

25. Correlations 25 Time dependent changes in seismic velocity

26. Correlations 26 Time dependent changes in seismic velocity

27. Correlations 27 Time-dependent changes

28. Correlations 28 Chinese network

29. Correlations 29 Changes due to earthquake Velocity changes in 1-3s period band Chen, Froment, Liu and Campillo 2010

30. Correlations 30 Virtual sources

31. Correlations 31 Industrial application

32. Correlations 32 Reflectivity from noise

33. Correlations 33 Reflectivity Wapenaar, Snieder, Physics Today, 2010

34. Correlations 34 Remote triggering of fault-strength changes on the San Andreas fault Key message: Connection between significant changes in scattering parameters and fault strength and dynamic stress Taka’aki Taira, Paul G. Silver, Fenglin Niu & Robert M. Nadeau Nature 461, 636-639 (1 October 2009) doi:10.1038/nature08395

35. Correlations 35 How to Method:  Compare waveforms of repeating earthquake sequences  Quantity: Decorrelation index D(t) = 1-C max (t)  Insensitive to variations in near-station environment (Snieder, Gret, Douma & Scales 2002)

36. Correlations 36 Hypothesis

37. Correlations 37 Changes in scatterer properties:  Increase in Decorrelation index after 1992 Landers earthquake (Mw=7.3, 65 kPa dyn. stress)  Strong increase in Decorrelation index after 2004 Parkfield earthquake (Mw=6.0, distance ~20 km)  Increase in Decorrelation index after 2004 Sumatra Earthquake (Mw=9.1, 10kPa dyn. stress)  But: No traces of 1999 Hector Mine, 2002 Denali and 2003 San Simeon (dyn. stresses all two times above 2004 Sumatra)

38. Correlations 38 Changes in scatterer properties: Increase in Decorrelation index after 1992 Landers earthquake (Mw=7.3, 65 kPa dyn. stress) Strong increase in Decorrelation index after 2004 Parkfield earthquake (Mw=6.0, distance ~20 km) Increase in Decorrelation index after 2004 Sumatra Earthquake (Mw=9.1, 10kPa dyn. stress) But: No traces of 1999 Hector Mine, 2002 Denali and 2003 San Simeon (dyn. stresses all two times above 2004 Sumatra)

39. Correlations 39 Summary  The simple correlation technique has turned into one of the most important processing tools for seismograms  Passive imaging is the process with which noise recordings can be used to infer information on structure  Correlation of noisy seismograms from two stations allows in principle the reconstruction of the Green‘s function between the two stations  A whole new family of tomographic tools emerged  CC techniques are ideal to identify time-dependent changes in the structure (scattering)  The ideal tool to quantify similarity (e.g., frequency dependent) between various signals (e.g., rotations, strains with translations)