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

3Correlations

Auto-correlation

Auto-correlation

4Correlations

Cross-correlation

Lag between two functions

Cross-correlation

5Correlations

Cross-correlation: Random functions

6Correlations

Auto-correlation: Random functions

7Correlations

Auto-correlation: Seismic signal

8Correlations

Basic theory

9Correlations

Basic Theory

10Correlations

Basic theory

11Correlations

Basic theory

12Correlations

Noise correlation - principle

From Campillo et al.

13Correlations

Uneven noise distribution

14Correlations

Theory

15Correlations

Green‘s function retrieval

16Correlations

Noise on our planet

Stutzmann et al. 2009

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?

19Correlations

Surface wave dispersion

20Correlations

US Array stations

21Correlations

Recovery of Green‘s function

22Correlations

Dispersion curves

All from Shapiro et al., 2004

23Correlations

Tomography without earthquakes!

24Correlations

Global scale!

Nishida et al., Nature, 2009.

25Correlations

Time dependent changes in seismic velocity

26Correlations

Time dependent changes in seismic velocity

27Correlations

Time-dependent changes

28Correlations

Chinese network

29Correlations

Changes due to earthquake

Velocity changes in 1-3s period bandChen, Froment, Liu and Campillo 2010

30Correlations

Virtual sources

31Correlations

Industrial application

32Correlations

Reflectivity from noise

33Correlations

Reflectivity

Wapenaar, Snieder, Physics Today, 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)