Tracking the originof the seismic noise

Tracking the originof the seismic noise

Tracking the origin of the seismic noise

Apparent origin of the noise Average sea wave height

winter

summer

Importance of scattering: a simple laboratory experiment with a few sources

receiverssources

A

Xs

C(A,X)

Correlations in presence of scattering

Correlations in water

G(A,X)travel time

THE 2D SCALAR CASE

Azimuthal average over ψ leads to

)()(])cos[exp(2

1)(),(),( 0

22

0

2* krJFdkrFvv

ixy

),,(Im4)(),(),( 220* yxxy GEkrJEvv SHSH

2222222/

)/(

2

1)exp(),,(

2

1),,(

rt

rtHdtGtG

iyxyx

SPAC method k C

H(2)n(kr)=Jn(kr) − iYn(kr)

y θn

ψ

x3 x

x1

Illumination by plane waves

SH waves in a homogeneous elastic mediumPropagation takes place in the x1-x3 plane. Therefore, the antiplane (out-of-plane) displacement v(x,t) fulfils the wave

equation

2

2

223

2

21

2 1

t

v

x

v

x

v

where β = shear wave velocity and t = time.A typical harmonic, homogeneous plane wave can be written as

)exp(i)iexp(),(),,( tnxFtv jj x

where, F(ω, ψ) = complex waveform, ω=circular frequency, xT = (x1, x3) = Cartesian coordinates

x1 = r cosθ = , x3 = r sinθ = , with r, θ = polar coordinates

nj = direction cosines (n1= cos ψ , n3 = sin ψ )

Consider the auto-correlation of the motion, evaluated at positions x and y, respectively. For simplicity assume y at the origin:

]cos[ rrnxn jjjj

])cos[exp(),(),(),(),( ** krFFvv ixy

Keiiti Aki

A isotropic distribution of plane waves in an homogeneous body : the local approachTHE 2D SCALAR CASE

y θn

ψ

x3 x

x1

Cross-correlations of seismic noise: ANMO - CCMCross-correlations of seismic noise: ANMO - CCM(from Shapiro and Campillo, GRL, 2004)

30 days of vertical motionDispersion analysis

global model by Ritzwoller et al. 2002

PHL - MLAC 290 km correlations computed over four different three-week

periods

band-passed

15 - 30 s

band-passed5 - 10 s

repetitive measurements provide uncertainty estimations

Causality

2

2221

rt

rtHG

r

HG )2(0i4

1

/r t

t/r

/rG/2

(Im, Re)(Re)

(Im)

/r