Seismic interferometry: Who needs a seismic source?

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Seismic interferometryWho needs a seismic
source?
Roel Snieder Center for Wave Phenomena Colorado
School of Mines email rsnieder_at_mines.edu http//w
ww.mines.edu/rsnieder download publications
from http//www.mines.edu/rsnieder/Publications.
html
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Fluctuation-dissipation theorem
(Kubo, Rep. Prog. Phys., 29, 255-284, 1966)
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Very Long Baseline Interferometry
http//www.lupus.gsfc.nasa.gov/brochure/bintro.htm
l
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Distance between USA and Germany
http//www.lupus.gsfc.nasa.gov/brochure/btoday2.ht
ml
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Pseudo-random source
Piezo-electric vibrator from CGG
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Coda wave interferometry
45C 50C
(Snieder et al., Science, 295, 2253-2255, 2002)
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1D example
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Cross-correlation

• sum of causal and acausal response
• uncorrelated left- and rightgoing waves

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Right-going wave only
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Right-going wave only
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DC-component must vanish
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Need to extend this to include

• heterogeneous media
• - more space dimensions

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Derivation based on normal-modes
(Lobkis and Weaver, JASA, 110, 3011-3017, 2001)
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Displacement response
Heaviside function
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Velocity response
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Uncorrelated excitation
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Correlation
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Correlation as sum over modes
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For uncorrelated modes
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For uncorrelated modes
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Correlation
Greens function
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Correlation
Greens function
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Correlation
Greens function
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Correlation and Greens function

• sum of causal and acausal Greens function
• holds for arbitrary heterogeneity

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Dealing with with acausal Greens function

• truncate correlation for tlt0
• average correlation for tlt0 and tgt0

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Displacement instead of velocity
Conclusion time derivative may appear
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(Weaver and Lobkis, Ultrasonics, 40, 435-439,
2002)
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(Weaver and Lobkis, Ultrasonics, 40, 435-439,
2002)
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Representation theorem
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Acoustic waves
Greens function
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Time reversal complex conjugation
Time-reversed solution
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Time-reversal
When is a solution. then
is a solution as well N.B. this does
not hold in the presence of attenuation
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Representation theorem
replace
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Left hand side
reciprocity
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Right hand side
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For spherical surface far away
Radiation condition
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Virtual-sources
(Wapenaar, Fokkema, and Snieder, JASA, 118,
2783-2786 2005 heuristic derivation Derode et
al., JASA, 113, 2973-2976, 2003)
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Computing synthetic seismograms
(Van Manen et al., Phys. Rev. Lett., 94,
164301,2005)
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Field example of virtual sources
complicated overburden
reservoir
(Bakulin and Calvert, SEG expanded abstracts,
2477-2480, 2004)
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Peace River 4D VSP
Component used, along-the-well (450)
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Image from virtual sources
top
bottom
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Virtual source
Surface
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Virtual-sources
(Wapenaar, Fokkema, and Snieder, JASA, 118,
2783-2786 2005 heuristic derivation Derode et
al., JASA, 113, 2973-2976, 2003)
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Excitation by uncorrelated sources on surface

• Uncorrelated sources can be
• sequential shots
• uncorrelated noise

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Response to uncorrelated noise
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Greens function from uncorrelated sources
(For elastic waves Wapenaar, Phys. Rev. Lett,
93, 254301, 2004)
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Raindrop model

• Sources can be
• real sources
• secondary sources (scatterers)

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Response to random sources
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Response to random sources
Correlation
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Double sum over sources
diagonal terms
cross-terms
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Cross-terms

• vanish on average
• in a single realization

(Snieder, Phys. Rev. E, 69, 046610, 2004)
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For dense scatterers
n scatterer density
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Correlation as volume integral
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Stationary phase contribution
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Stationary phase regions
anti-Fresnel zones
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Stationary phase integration
(Snieder, Phys. Rev. E, 69, 046610, 2004, for
reflected waves see Snieder, Wapenaar, and
Larner, Geophysics, in press, 2005)
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Yet another type of illumination
(Weaver and Lobkis, JASA, 116, 2731-2734)
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Four types of averaging
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Ultrasound experiment
(Malcolm et al., Phys. Rev. E, 70, 015601, 2004)
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Surface waves
(Campillo and Paul, Science, 299, 547-549, 2003)
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correlation
Greens tensor
Z/Z
Z/R
Z/T
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correlation
Greens tensor
Z/Z
Z/R
Z/T
R/Z
R/R
R/T
T/Z
T/R
T/T
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Surface wave Greens function
(Snieder, Phys. Rev. E, 69, 046610, 2004)
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Surface wave dispersion from noise
(Shapiro and Campillo, Geophys. Res. Lett., 31,
L07614, 2004)
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Seismic interferometry in Millikan Library
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Deconvolution with top floor
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Deconvolution with bottom floor
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normal modes
traveling waves
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Deconvolution with bottom floor
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Sheiman-interpretation
-
-


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Fundamental mode
-

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Borehole data from Treasure Island
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T Deconvolved (4.5 to 15 sec)
depth (m)
time (sec)
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T Deconvolved (4.5 to 15 sec)
ß
100 m/s
ß
150 m/s
ß
250 m/s
ß
200 m/s
ß
550 m/s
depth (m)
time (sec)
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Z Deconvolved (1 to 15 sec)
depth (m)
time (sec)
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Z Deconvolved (1 to 15 sec)
a
1500 m/s
a
1250 m/s
a
1350 m/s
a
1600 m/s
depth (m)
a
2200 m/s
time (sec)
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R Deconvolved (4.5 to 15 sec)
depth (m)
time (sec)
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R Deconvolved (4.5 to 15 sec)
ß
100 m/s
ß
150 m/s
ß
250 m/s
ß
200 m/s
ß
550 m/s
depth (m)
time (sec)
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Borehole data from Treasure Island
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R Deconvolved (1 to 4.5 sec)
depth (m)
time (sec)
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R Deconvolved (1 to 4.5 sec)
ß
100 m/s
ß
150 m/s
ß
250 m/s
ß
200 m/s
ß
550 m/s
depth (m)
time (sec)
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Receiver Function
depth (m)
time (sec)
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Receiver Function
depth (m)
time (sec)
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Advantage (1), virtual sources atnew locations
salt
reservoir
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Advantage (1), virtual sources atnew locations
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Advantage (2), virtual sources atall times
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Seismic interferometry in Millikan Library
(Snieder and Safak, Bull. Seismol. Soc. Am., in
press, 2005)
111
Deconvolution with top floor
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Advantage (3), get better illumination
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Use surface bounce
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Use surface bounce
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Schuster trick
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Advantage (4), use other type of data
earthquake
correlation (1 year)
correlation (1 month)
(Shapiro et al., Science, 307, 1615-1618, 2005)
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0.01
0.01
1
0.1
10
Frequency (Hz)
119
5-10 sec.
0.01
0.01
1
0.1
10
Frequency (Hz)
120
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