virtual source imaging vs interferometric imaging gerard t. schuster, andrey bakulin and rodney...
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Virtual Source Imaging vs Interferometric Imaging
Gerard T. Schuster, Andrey Bakulin and Rodney Calvert
Outline Outline
Data Illustration
Summary
Theory
D(D(s’s’||ss))
s
U(g’|s’)U(g’|s’)
s’ g’
U(g’|s) = G(g’|s’) U(g’|s) = G(g’|s’) D(D(s’s’||ss))ds’ds’
Greens Thm: Every pt along well acts as a secondary sourceGreens Thm: Every pt along well acts as a secondary source
Greens Function for s & g in wellGreens Function for s & g in well
G(g’|s’) ~ U(g’|s)G(g’|s’) ~ U(g’|s)D(D(s’s’||ss)*)*dsds
Redatumed data for s & g in wellRedatumed data for s & g in well
WWD(D(s’|ss’|s))
g g D*D*uu((gg,,MM,s,s)= )= d(d(gg|s)|s) d(M|s)* d(M|s)*
ss,s,s
Outline Outline
Data Illustration
Summary
Theory
Tim
e (s
)
0.3
030 900Depth (ft)
Raw Data(CRG15)
D(D(s’s’||ss))
U(g’|s)U(g’|s)
G(g’|s’) ~ U(g’|s)G(g’|s’) ~ U(g’|s)D(D(s’s’||ss)*)*dsds
G(g’|s’)G(g’|s’)
Outline Outline
Data Illustration
Summary
Theory
Summary Summary
VSP DirectVSP DirectVSP GhostVSP Ghost
u = u = DDgg
U(g’|s) = G(g’|s’) U(g’|s) = G(g’|s’) D(D(s’s’||ss))ds’ds’1.
CDP Refl.CDP Refl.
g =[g =[D*D] D*D*D] D*uu-1-1
2.
G(g’|s’)G(g’|s’)
[[D*D]D*D]-1-1
~ 1/W~ 1/W Interferometry RedatumingInterferometry Redatuming
[[D*D]D*D]-1-1
~ 1/D~ 1/D Virtual Source ReadtumingVirtual Source Readtuming
Tim
e (s
)
0.3
030 900Depth (ft)
Ghosts
Tim
e (s
)
0.3
030 900Depth (ft)
Exxon Raw Data(CRG15)
Tim
e (s
)
0.3
030 900Depth (ft)
Ghosts (Exxon)
D(g’|s)D(g’|s)
Tim
e (s
)
0.3
030 900Depth (ft)
Primary(Exxon)
5 24Trace No.
Tim
e (s
)
1.2
0.2 xcorr data (muted)
Tim
e (s
)
1.4
0.55 24Trace No.
Exxon CSG 25
Raw data (muted)
Master trace Master trace
Dep
th (
ft)
1300
2000 400X (ft)
Xcorr. mig
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Tim
eT
ime
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0
T – T – T T > -> -TT
ghostdiffraction
s
min(T – min(T – T) T) = -= -TT s
DiffDiffractionraction
TTTTTT
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Tim
eT
ime
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0
T – T – T T > -> -TT
ghostdiffraction
s
min(T – min(T – T) T) = -= -TT s
DiffDiffractionraction
TTTTTT
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Tim
eT
ime
Diffraction Diffraction
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0
T – T – T T > -> -TT
ghostdiffraction
min(T – min(T – T) T) = -= -TT s
s
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Tim
eT
ime
Diffraction Diffraction
Specular Specular Reflection Reflection
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0
T – T – T T > -> -TT
ghostdiffraction
min(T – min(T – T) T) = -= -TT s
s
Uninteresting PartUninteresting Part of Mediumof Medium
Tim
eT
ime
Minimum Time Difference = Specular Reflection Time Minimum Time Difference = Specular Reflection Time
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0
T – T – T T > -> -TT
ghostdiffraction
min(T – min(T – T) T) = -= -TT s
Uninteresting PartUninteresting Part of Mediumof Medium
Tim
eT
ime
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0
T – T – T T > -> -TT
ghostdiffraction
min(T – min(T – T) T) = -= -TT s
SummarySummary
1.1. Fermat’s PrincipleFermat’s Principle: min(T – : min(T – T) T) = -= -TT
2.2. No need to know velocity model or source location.No need to know velocity model or source location.
3.3. VSP Data VSP Data CDP Data + Tomography+Mig. CDP Data + Tomography+Mig.
4.4. Redatums buried sources to surfaceRedatums buried sources to surface
Outline Outline
Target Oriented Fermat’s Interferometric Principle
Fermat’s Interferometric Principle
Numerical Example
Interferometry Background
Uninteresting PartUninteresting Part of Mediumof Medium
VSP Tomostatics Problem:VSP Tomostatics Problem: From VSP Data Find From VSP Data FindFull Coverage Velocity Tomogram Full Coverage Velocity Tomogram
Uninteresting PartUninteresting Part of Mediumof Medium
VSP Tomostatics Problem:VSP Tomostatics Problem: From VSP Data Find From VSP Data FindFull Coverage Velocity Tomogram Full Coverage Velocity Tomogram
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For VSP MultipleFermat’s Interferometric Principle For VSP Multiple
TomographyTomography
00 600 m600 m
600 m600 m
0 m0 m3.5 km/s3.5 km/s
1.4 km/s1.4 km/s
Weathering zoneWeathering zone
VSP Data:VSP Data: 120 shots on surface, 120 receivers in well 120 shots on surface, 120 receivers in well
Goal:Goal: Determine weathering zone velocity by interferometric tomography Determine weathering zone velocity by interferometric tomography
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For MultipleFermat’s Interferometric Principle For Multiple
TomographyTomography
00 600 m600 m
600 m600 m
0 m0 m3.5 km/s3.5 km/s
1.4 km/s1.4 km/s
Weathering zoneWeathering zone
min(T – min(T – T) T) = = TT TTTT
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For MultipleFermat’s Interferometric Principle For Multiple
TomographyTomography
00 600 m600 m
0 s0 s
0.135 s0.135 s
Tim
e (s
)T
ime
(s) Ghost ReflectionGhost Reflection
min(T – min(T – T) T) = = TT
Depth (m)Depth (m)
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For MultipleFermat’s Interferometric Principle For Multiple
TomographyTomography
00 600 m600 m
0 s0 s
0.135 s0.135 s
Tim
e (s
)T
ime
(s) Ghost ReflectionGhost Reflection
Primary ReflectionPrimary Reflection
min(T – min(T – T) T) = = TT
==
Depth (m)Depth (m)X (m)X (m)
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For MultipleFermat’s Interferometric Principle For Multiple
TomographyTomography
00 600 m600 m
0 s0 s
0.135 s0.135 s3.5 km/s3.5 km/s
1.4 km/s1.4 km/s
Tim
e (s
)T
ime
(s) Ghost ReflectionGhost Reflection
Primary ReflectionPrimary Reflection
Interfer. ReflectionInterfer. Reflection
min(T – min(T – T) T) = = TT
Depth (m)Depth (m)X (m)X (m)
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For MultipleFermat’s Interferometric Principle For Multiple
TomographyTomography
00 600 m600 m
1.35 km/s1.35 km/s
Vel
ocit
y (k
m/s
)V
eloc
ity
(km
/s)
1.65 km/s1.65 km/s
ActualActual
InterferometricInterferometric
min(T – min(T – T) T) = = TT
VSP SummaryVSP Summary
T T TTdirectdirect primprim
gggg ssgg- - T T >> --
multmult
sgsgmin( )min( )gg
1.1.
2. VSP 2. VSP CDP traveltimes CDP traveltimes
3.3. Removes rec. statics & multiple tomo.Removes rec. statics & multiple tomo.
Tcdp(Tcdp(ss,,gg) =min[min( Tdirect() =min[min( Tdirect(gg,:) - Tmult(,:) - Tmult(s,:s,:) )]) )]
s s gg
TT TTTT
gg
s s gg
gg
Outline Outline
Target Oriented Fermat’s Interferometric Principle
Fermat’s Interferometric Principle
Numerical Example
Interferometry Background
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0 ghostdiffraction
s
DiffDiffractionraction
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0 reflectiondiffractions
DiffDiffractionraction
Target Oriented Interferometric Tomography
AcknowledgmentsAcknowledgments
UTAM sponsorsUTAM sponsors
Exxon for 2-D field dataExxon for 2-D field data
J. Claerbout + J. RickettJ. Claerbout + J. Rickett
II evolved from daylight II evolved from daylight imagingimaging
Earthquake Data typically Use Direct Earthquake Data typically Use Direct Waves => TomographyWaves => Tomography
Uninteresting PartUninteresting Part of Mediumof Medium
Tim
eT
ime
Direct Direct
Direct Direct
Problem: Uninteresting Parts of Medium Distort Problem: Uninteresting Parts of Medium Distort TomogramTomogram
Goal: Transform TravelGoal: Transform Traveltimestimes into Primary Reflection into Primary ReflectionTraveltimesTraveltimes
Specular ReflectionSpecular Reflection
Specular ReflectionSpecular Reflection
Basin
Uninteresting PartUninteresting Part of Mediumof Medium
Direct Direct
Specular ReflectionSpecular Reflection
Tim
eT
ime
Goal: Transform TravelGoal: Transform Traveltimestimes into Primary Reflection into Primary ReflectionTraveltimesTraveltimes
Fermat’s Principle: T - Fermat’s Principle: T - TT > 0 > 0 multmult multmultsgsg sgsg ==When is there equality?When is there equality?Fermat’s Interferometric Principle For MultipleFermat’s Interferometric Principle For Multiple
TomographyTomography
00 600 m600 m
0 s0 s
0.135 s0.135 s3.5 km/s3.5 km/s
1.4 km/s1.4 km/s
Tim
e (s
)T
ime
(s) Ghost ReflectionGhost Reflection
Primary ReflectionPrimary Reflection
Interfer. ReflectionInterfer. Reflection
min(T – min(T – T) T) = = TT
CDP SummaryCDP Summary
T T TTprimprim primprim
ssgg gggg- - T T >> --
multmult
sgsgmin( )min( )ss
1.1.
2. Extend CDP sources laterally2. Extend CDP sources laterally
3.3. Removes 1/3 statics & multiple tomo.Removes 1/3 statics & multiple tomo.
Tdatum(Tdatum(gpgp,,gg) =min[min( Tprim(:,) =min[min( Tprim(:,gpgp) + Tmult(:,) + Tmult(:,gg) )]) )]
s s g g gg
s s g g gg
TTTT TT
Uninteresting PartUninteresting Part of Mediumof Medium
Specular ReflectionSpecular Reflection
Fermat’s Principle: T+Fermat’s Principle: T+TT – – T T >0 >0 reflectiondiffractions
DiffDiffractionraction