correlationscomputational geophysics and data analysis 1 correlations correlation of time series...

Computational Geophysics and Data Analysis1

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

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


Correlations

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


Correlations

Auto-correlation

Auto-correlation


Correlations

Cross-correlation

Lag between two functions

Cross-correlation


Correlations

Cross-correlation: Random functions


Correlations

Auto-correlation: Random functions


Correlations

Auto-correlation: Seismic signal


Correlations

Theoretical relation rotation rate and transverse acceleration

plane-wave propagation

Plane transversely polarized wave propagating in x-direction with phase velocity c Plane transversely polarized wave propagating in x-direction with phase velocity c

kctkxftxu y /)(),( kctkxftxu y /)(),(

)(),(),( 2 tkxftxutxa yy )(),(),( 2 tkxftxutxa yy Acceleration

ctxtxa 2),(/),( ctxtxa 2),(/),(

Rotation rate and acceleration should be in phase and the amplitudes scaled by two times the horizontal phase velocity

Rotation rate and acceleration should be in phase and the amplitudes scaled by two times the horizontal phase velocity

Rotation rate

)(

2

1,0,00,,0

2

1),( tkxfkutx y

)(

2

1,0,00,,0

2

1),( tkxfkutx y


Correlations

Mw = 8.3 Tokachi-oki 25.09.2003transverse acceleration – rotation rate

From Igel et al., GRL, 2005


Correlations

Max. cross-corr. coefficient in sliding time window transverse acceleration – rotation rate

Small tele-seismic event

P-onset

S-waveLove waves Aftershock


Correlations

M8.3 Tokachi-oki, 25 September 2003phase velocities ( + observations, o theory)

From Igel et al. (GRL, 2005)

Horizontal phase velocity in sliding time window


Correlations

Sumatra M8.3 12.9.2007

P

P Coda


Correlations

… CC as a function of time …observable for all events!


Correlations

Rotational signals in the P-coda?azimuth dependence


Correlations

P-Coda energy direction… comes from all directions …

correlations in P-coda window


Correlations

Noise correlation - principle

From Campillo et al.


Correlations

Uneven noise distribution


Correlations

Surface waves and noise

Cross-correlate noise observed over long

time scales at different locations

Vary frequency range, dispersion?


Correlations

Surface wave dispersion


Correlations

US Array stations


Correlations

Recovery of Green‘s function


Correlations

Disersion curves

All from Shapiro et al., 2004


Correlations

Tomography without earthquakes!


Correlations

Global scale!

Nishida et al., Nature, 2009.


Correlations

Correlations and the coda


Correlations

Velocity changes by CC


Correlations

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


Correlations

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

Seismic network


Correlations

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)


Correlations

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?


Correlations

Correlations and random media:

Generation of random media:

Define spectrum Random Phase Back transform usig

inverse FFT


Correlations

Random media:


Correlations

P-SH scattering simulations with ADER-DG

translations

rotations


Correlations

P-SH scatteringsimulations with ADER-DG


Correlations

Random mantle models


Correlations

Random models


Correlations

Convergence to the right spectrum


Correlations

Mantle models


Correlations

Waves through random models


Correlations

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)

correlationscomputational geophysics and data analysis 1 correlations correlation of time series...

Documents

data analysis

autocorrelation slide

cc slide

p p coda slide

pcoda window slide

seismic signal slide

sliding time window

passive imaging slide