Download - Center for Wave Phenomena Department of Geophysics Colorado School of Mines Golden, Colorado
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Center for Wave Phenomena
Department of GeophysicsColorado School of Mines
Golden, Colorado
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CWP FacultyIlya Tsvankin
“We are committed to quality education.”
Roel SniederDave Hale
Ilya Tsvankin
Paul SavaNorm Bleistein
Ken Larner
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What do we offer?• Full financial support
• Diverse and enthusiastic faculty
• State-of-the-art research
• Industry contacts and internships
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Need more Information?Prof. Ilya [email protected]
Prof. Roel Snieder [email protected]
www.cwp.mines.edu
Center for Wave PhenomenaColorado School of Mines
Golden, CO 80401
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Problem with sub-salt imaging
reservoir
salt
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What if we had virtual sources below the salt?
reservoir
salt
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Response to random sources
Ar Br
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Response to random sources
Ar Br
dttptpC B
T
AAB ),(),()(0
rrCorrelation:
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Very Long Baseline Interferometry
http://www.lupus.gsfc.nasa.gov/brochure/bintro.html
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Distance between USA and Germany
http://www.lupus.gsfc.nasa.gov/brochure/btoday2.html
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1D example
)/()/(),( cxtLcxtRtxu
cxtR / cxtL /
0x Hx
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Cross-correlation
)/()/()()0( cHtCcHtCHxuxu LR
t
cH / cH /
• sum of causal and acausal response• uncorrelated left- and rightgoing waves
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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
m
mmmmm
m tbtautu
cossin)(),( rr
)(sin)'()(),',( tHtuutGm
mm
mm
rrrr
Heaviside function
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Velocity response
m
mmmmm tbtautv sincos)(),( rr
)(cos)'()(),',()( tHtuutGm
mmmv rrrr
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Uncorrelated excitation
m
mmmmm tbtautv sincos)(),( rr
0
2
2
mn
nmmn
nmmn
ba
Fbb
Faa
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Correlation
),(),()()( tvtvC BAvAB rr
m
mmmmBAmBA tbtautv sincos)(),( ,, rr
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Correlation as sum over modes
ttbb
ttab
ttba
ttaa
uuC
mnmn
mnmn
mnmn
mnmn
mnBmAn
vAB
sinsin
cossin
sincos
coscos
)()()(,
)( rr
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For uncorrelated modes
ttbb
ttab
ttba
ttaa
uuC
mnmn
mnmn
mnmn
mnmn
mnBmAn
vAB
sinsin
cossin
sincos
coscos
)()()(,
)( rr
nmF 2
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For uncorrelated modes
ttbb
ttab
ttba
ttaa
uuC
mnmn
mnmn
mnmn
mnmn
mnBmAn
vAB
sinsin
cossin
sincos
coscos
)()()(,
)( rr
nmF 2
mcos
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Correlation
m
mBmAmvAB uuFC cos)()()( 2)( rr
Green’s function
)(cos)()(),,()( HuuGm
mBmAmBAv rrrr
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Correlation and Green’s function
),,(),,()( )()(2)( tGtGFtC BAv
BAvv
AB rrrr
- sum of causal and acausal Green’s function
- holds for arbitrary heterogeneity
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(Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)
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20 30 40 50 60 70 80 90 100 110-4500
-4000-3500-3000-2500
-2000-1500-1000
-500
0500
100015002000
-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.01.1
time (microseconds)
Pulse/echo
noiseautocorrelation
(Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)
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Raindrop model
Sources can be:
- real sources
- secondary sources (scatterers)
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Extract response by correlation
Ar Br
Sr
dttptpC B
T
AAB ),(),()(0
rrCorrelation:
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Non-stationary source point
Ar Br
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Non-stationary source point
Ar Br
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Stationary source point
Ar Br
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Stationary source point
Ar Br
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Stationary phase regions
“anti-Fresnel zones”
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Stationary phase integration
R
ikReR
ikReCAB
44)(
)()()( * RGRGCAB
(Snieder, Phys. Rev. E, 69, 046610, 2004)
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Four types of averaging
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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
(Bakulin and Calvert, SEG expanded abstracts, 2477-2480, 2004)
reservoir
complicated overburden
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Peace River 4D VSP
1 0.5 00.5
1x
10.50
0.51y
1 0.50
0.51
z
1 0.5 00.5
1x
10.50
0.51y
Component used,along-the-well (450)
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Image from virtual sources
topbottom
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Virtual source Surface
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Surface waves
(Campillo and Paul, Science, 299, 547-549, 2003)
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correlation Green’s tensor
Z/Z
Z/R
Z/T
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Surface wave Green’s function
iG
iGC klkl
kl )(
(Snieder, Phys. Rev. E, 69, 046610, 2004)
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Seismic interferometry in Millikan Library
(Snieder and Safak, Bull. Seismol. Soc. Am., 96, 586-598, 2006)
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Deconvolution with top floor
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Deconvolution with bottom floor
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traveling waves normal modes
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Four new wave states
(Snieder, Sheiman, and Calvert, Phys. Rev. E., 73, 066620, 2006)
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building borehole
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Advantage (1), virtual sources atnew locations
reservoir
salt
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Advantage (1), virtual sources atnew locations
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Advantage (2), virtual sources at“all” times
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Advantage (3), use other type of data
(Shapiro et al., Science, 307, 1615-1618, 2005)
earthquake
correlation(1 year)
correlation(1 month)
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5-10sec.
1010.10.010.01Frequency (Hz)
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More information
www.mines.edu/~rsnieder
email [email protected]
www.mines.edu/~rsnieder/SPICE06_Snieder.ppt