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1Correlations
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
2Correlations
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:
1,,2,1,0
1 1
0
Nk
fgN
rkN
iikik
17Correlations
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.
18Correlations
Surface waves and noise
Cross-correlate noise observed over long
time scales at different locations
Vary frequency range, dispersion?
29Correlations
Changes due to earthquake
Velocity changes in 1-3s period bandChen, Froment, Liu and Campillo 2010
34Correlations
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
35Correlations
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)
37Correlations
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)
38Correlations
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)
39Correlations
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)