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Correlations

Correlations. Correlation of time series Similarity Time shitfs Applications Correlation of rotations/strains and translations Ambient noise correlations Coda correlations Random media: correlation length

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Correlations

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  1. Correlations Correlation of time series Similarity Time shitfs Applications Correlation of rotations/strains and translations Ambient noise correlations Coda correlations Random media: correlation length 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 Computational Geophysics and Data Analysis

  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: Computational Geophysics and Data Analysis

  3. Auto-correlation Auto-correlation Computational Geophysics and Data Analysis

  4. Cross-correlation Cross-correlation Lag between two functions Computational Geophysics and Data Analysis

  5. Cross-correlation: Random functions Computational Geophysics and Data Analysis

  6. Auto-correlation: Random functions Computational Geophysics and Data Analysis

  7. Auto-correlation: Seismic signal Computational Geophysics and Data Analysis

  8. Theoretical relation rotation rate and transverse accelerationplane-wave propagation Acceleration Plane transversely polarized wave propagating in x-direction with phase velocity c Rotation rate Rotation rate and acceleration should be in phase and the amplitudes scaled by two times the horizontal phase velocity Computational Geophysics and Data Analysis

  9. Mw = 8.3 Tokachi-oki 25.09.2003transverse acceleration – rotation rate From Igel et al., GRL, 2005 Computational Geophysics and Data Analysis

  10. Max. cross-corr. coefficient in sliding time windowtransverseacceleration – rotation rate P-onset Aftershock Love waves S-wave Small tele-seismic event Computational Geophysics and Data Analysis

  11. M8.3 Tokachi-oki, 25 September 2003phase velocities ( + observations, o theory) Horizontal phase velocity in sliding time window From Igel et al. (GRL, 2005) Computational Geophysics and Data Analysis

  12. Sumatra M8.3 12.9.2007 P P Coda Computational Geophysics and Data Analysis

  13. … CC as a function of time …observable for all events! Computational Geophysics and Data Analysis

  14. Rotational signals in the P-coda?azimuth dependence Computational Geophysics and Data Analysis

  15. P-Coda energy direction… comes from all directions … correlations in P-coda window Computational Geophysics and Data Analysis

  16. Noise correlation - principle From Campillo et al. Computational Geophysics and Data Analysis

  17. Uneven noise distribution Computational Geophysics and Data Analysis

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

  19. Surface wave dispersion Computational Geophysics and Data Analysis

  20. US Array stations Computational Geophysics and Data Analysis

  21. Recovery of Green‘s function Computational Geophysics and Data Analysis

  22. Disersion curves All from Shapiro et al., 2004 Computational Geophysics and Data Analysis

  23. Tomography without earthquakes! Computational Geophysics and Data Analysis

  24. Global scale! Nishida et al., Nature, 2009. Computational Geophysics and Data Analysis

  25. Correlations and the coda Computational Geophysics and Data Analysis

  26. Velocity changes by CC Computational Geophysics and Data Analysis

  27. Remote triggering (from CCs) Taka’aki Taira, Paul G. Silver, Fenglin Niu & Robert M. Nadeau: Remote triggering of fault-strength changes on the San Andreas fault at Parkfield Nature 461, 636-639 (1 October 2009) | doi:10.1038/nature08395; Received 25 April 2009; Accepted 6 August 2009 Computational Geophysics and Data Analysis

  28. Seismic network Remote triggering of fault-strength changes on the San Andreas fault at Parkfield Taka’aki Taira, Paul G. Silver, Fenglin Niu & Robert M. Nadeau Key message: • Connection between significant changes in scattering parameters and fault strength and dynamic stress Computational Geophysics and Data Analysis

  29. Principle 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) Computational Geophysics and Data Analysis

  30. True? • 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) Computational Geophysics and Data Analysis

  31. Correlations and random media: Generation of random media: • Define spectrum • Random Phase • Back transform usig inverse FFT Computational Geophysics and Data Analysis

  32. Random media: Computational Geophysics and Data Analysis

  33. P-SH scattering simulations with ADER-DG translations rotations Computational Geophysics and Data Analysis

  34. P-SH scatteringsimulations with ADER-DG Computational Geophysics and Data Analysis

  35. Random mantle models Computational Geophysics and Data Analysis

  36. Random models Computational Geophysics and Data Analysis

  37. Convergence to the right spectrum Computational Geophysics and Data Analysis

  38. Mantle models Computational Geophysics and Data Analysis

  39. Waves through random models Computational Geophysics and Data Analysis

  40. 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) Computational Geophysics and Data Analysis

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