tracking the origin of the seismic noise. apparent origin of the noiseaverage sea wave height winter...
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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