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Surface waves and correlations

Surface waves and correlations. Correlation of time series Similarity Time shifts Applications Correlation of rotations/strains and translations Ambient noise correlations Coda correlations

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Surface waves and correlations

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  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. 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:

  3. Auto-correlation Auto-correlation

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

  5. Cross-correlation: Random functions

  6. Auto-correlation: Random functions

  7. Auto-correlation: Seismic signal

  8. Basic theory

  9. Basic Theory

  10. Basic theory

  11. Basic theory

  12. Noise correlation - principle From Campillo et al.

  13. Uneven noise distribution

  14. Theory

  15. Green‘s function retrieval

  16. Noise on our planet Stutzmann et al. 2009

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

  19. Surface wave dispersion

  20. US Array stations

  21. Recovery of Green‘s function

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

  23. Tomography without earthquakes!

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

  25. Time dependent changes in seismic velocity

  26. Time dependent changes in seismic velocity

  27. Time-dependent changes

  28. Chinese network

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

  30. Virtual sources

  31. Industrial application

  32. Reflectivity from noise

  33. Reflectivity Wapenaar, Snieder, Physics Today, 2010

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

  36. 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)

  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. 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)

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