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CorrelationsComputational Geophysics and Data Analysis 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

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CorrelationsComputational 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: 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:

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CorrelationsComputational Geophysics and Data Analysis 3 Auto-correlation

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

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CorrelationsComputational Geophysics and Data Analysis 5 Cross-correlation: Random functions

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CorrelationsComputational Geophysics and Data Analysis 6 Auto-correlation: Random functions

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CorrelationsComputational Geophysics and Data Analysis 7 Auto-correlation: Seismic signal

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

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

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

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

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CorrelationsComputational Geophysics and Data Analysis 12 Sumatra M P P Coda

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

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

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

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

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CorrelationsComputational Geophysics and Data Analysis 17 Uneven noise distribution

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

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CorrelationsComputational Geophysics and Data Analysis 19 Surface wave dispersion

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CorrelationsComputational Geophysics and Data Analysis 20 US Array stations

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CorrelationsComputational Geophysics and Data Analysis 21 Recovery of Greens function

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

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CorrelationsComputational Geophysics and Data Analysis 23 Tomography without earthquakes!

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

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CorrelationsComputational Geophysics and Data Analysis 25 Correlations and the coda

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CorrelationsComputational Geophysics and Data Analysis 26 Velocity changes by CC

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

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

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CorrelationsComputational Geophysics and Data Analysis 29 Principle 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)

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CorrelationsComputational Geophysics and Data Analysis 30 What happens?

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CorrelationsComputational Geophysics and Data Analysis 31 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) True?

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CorrelationsComputational Geophysics and Data Analysis 32 Correlations and random media: Generation of random media: Define spectrum Random Phase Back transform usig inverse FFT

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CorrelationsComputational Geophysics and Data Analysis 33 Random media:

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CorrelationsComputational Geophysics and Data Analysis 34 P-SH scattering simulations with ADER-DG translations rotations

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CorrelationsComputational Geophysics and Data Analysis 35 P-SH scattering simulations with ADER-DG

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CorrelationsComputational Geophysics and Data Analysis 36 Random mantle models

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CorrelationsComputational Geophysics and Data Analysis 37 Random models

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CorrelationsComputational Geophysics and Data Analysis 38 Convergence to the right spectrum

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CorrelationsComputational Geophysics and Data Analysis 39 Mantle models

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CorrelationsComputational Geophysics and Data Analysis 40 Waves through random models

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CorrelationsComputational Geophysics and Data Analysis 41 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 Greens 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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