Local Migration with Extrapolated VSP Local Migration with Extrapolated VSP Green’s FunctionsGreen’s Functions
Xiang Xiao and Gerard SchusterXiang Xiao and Gerard Schuster
Univ. of UtahUniv. of Utah
OutlineOutline
MotivationMotivation
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
Numerical TestsNumerical Tests
Sigsbee VSP Data SetSigsbee VSP Data Set
GOM VSP Data Set GOM VSP Data Set
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
Numerical TestsNumerical Tests
Sigsbee VSP Data SetSigsbee VSP Data Set
GOM VSP Data Set GOM VSP Data Set
ConclusionsConclusions
MotivationMotivation
ProblemProblem: VSP Migration image distorted by overburden+statics: VSP Migration image distorted by overburden+statics
SolutionSolution: Local VSP Migration: Local VSP Migration
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
Numerical TestsNumerical Tests
Sigsbee VSP Data SetSigsbee VSP Data Set
GOM VSP Data Set GOM VSP Data Set
ConclusionsConclusions
Theory: Theory: StandardStandard VSP Migration VSP Migration
directdirect
reflectionreflection
Reflections: R(g)
reflectionreflection gG(x|g)*R(g)
g
x G(x|s)W()x
Backproject Backproject Forwardproject Forwardproject
Standard VSP migration image: m(x) = G(x|g)*R(g)g
/G(x|s)W()
Backprojected refl. Forwardproject. direct
Src. Wavelet: Src. Wavelet: W(W())
s
~~ G(x|g)*R(g)g
G(x|s)*W()*
Theory: Theory: LocalLocal VSP Migration VSP Migration
directdirect
reflectionreflection
Reflections: R(g)
reflectionreflection gG(x|g)*R(g)
g
x
Backproject Backproject
directdirect
Theory: Theory: LocalLocal VSP Migration VSP Migration
directdirect
reflectionreflection
Backproject Direct waves: Backproject Direct waves: D(D(gg))Reflections: R(g)
reflectionreflection gG(x|g)*R(g)
g
x
Backproject Backproject
directdirect
D(g)G(x|g)*D(g)
g
Backprojected refl. Backproject. direct
Local VSP migration image: m(x) = G(x|g)*D(g)g
G(x|g)*R(g)g
~~ G(x|g)*R(g)g
G(x|g)D(g)*g
Static killerStatic killerFAST 3D RTMFAST 3D RTM
Local vs Local vs StandardStandard VSP Migration VSP MigrationReflection Illumination ZonesReflection Illumination Zones
~~LocalLocal VSP migration image: m(x) VSP migration image: m(x) G(x|g)*R(g)G(x|g)*R(g)[[g
G(G(xx||gg)*D()*D(gg)]*)]*g
StandardStandard VSP migration image: m(x) VSP migration image: m(x) ~~ G(x|g)*R(g)G(x|g)*R(g)g
[G([G(xx||ss)W()W(
Backprojected refl.Forwardprojected direct.
Backproject. direct
Standard VSP ReflectionStandard VSP ReflectionIllum. ZoneIllum. Zone
Local VSP ReflectionLocal VSP ReflectionIllum. ZoneIllum. Zone
Benefits of Local VSP MigrationBenefits of Local VSP Migration• Target oriented!Target oriented!– Only a local velocity model near the well is needed.Only a local velocity model near the well is needed.
– Salt and overburden are avoided.Salt and overburden are avoided.
– Fast 3D RTM Fast 3D RTM
• Source statics are automatically accounted for.Source statics are automatically accounted for.
Liabilities of Local VSP MigrationLiabilities of Local VSP Migration• Limited illumination ZoneLimited illumination Zone
Standard VSP ReflectionStandard VSP ReflectionIllum. ZoneIllum. Zone
Local VSP ReflectionLocal VSP ReflectionIllum. ZoneIllum. Zone
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
Numerical TestsNumerical Tests
Sigsbee & Schlumberger VSP DataSigsbee & Schlumberger VSP Data
GOM VSP Data Set GOM VSP Data Set
ConclusionsConclusions
Sigsbee P-wave Velocity ModelSigsbee P-wave Velocity Model00
Dep
th (
km)
Dep
th (
km)
9.29.2
45004500
15001500
m/sm/s
-12.5-12.5 12.512.5Offset (km)Offset (km)
279 shots279 shots
150 receivers150 receivers
15
Local Reverse Time Migration Results
4.6
9.2
Dep
th (
km)
-3 3Offset (km)
True modelMigration image
f = fault
f
d
d
(1)
(2)
(3)
d = diffractor
Virtual well
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
Numerical TestsNumerical Tests
Sigsbee & Schlumberger VSP DataSigsbee & Schlumberger VSP Data
GOM VSP Data Set GOM VSP Data Set
ConclusionsConclusions
17
Dep
th
(km
)
Offset (km)
10-12 12
0
Schlumberger 2D Isotropic Elastic Model
0
291 shots
287 receivers
Direct P
PPS
PSS
Dep
th
Dep
th
(km
)(k
m)
Time (s)Time (s)
88
00 8
VSP CSG X-componentVSP CSG X-component
VSP CSG Z-componentVSP CSG Z-component44
Dep
th
Dep
th
(km
)(k
m)
88
44
Two-component VSP Synthetic Data SetTwo-component VSP Synthetic Data Set
(Acknowledge VSFusion)
4.5
2.0
km/s(a) P-wave submodel
Dep
th
(km
)
8.7
6.0
Dep
th
(km
)
8.7
6.0
Offset (km)0 1.8
(b) P-wave background1D model
4.5
2.0
km/s
Offset (km)0 1.8
Dep
th
Dep
th
(km
)(k
m)
8.78.7
6.06.0
Offset (km)Offset (km)00 1.21.2
Local RTM Image
OutlineOutline
MotivationMotivation
Local VSP Migration Theory Local VSP Migration Theory
Numerical TestsNumerical Tests
Sigsbee & Schlumberger VSP DataSigsbee & Schlumberger VSP Data
GOM VSP Data Set GOM VSP Data Set
ConclusionsConclusions
Dep
th
Dep
th
(m)
(m)
Offset (m)Offset (m)
48784878
0 18291829
00
GOM VSP Well and Source LocationSource @150 m offsetSource @150 m offset
2800 m2800 m
3200 m3200 m
SaltSalt
82 82 receiversreceivers
@600 m offset@600 m offset @1500 m offset@1500 m offset
Z-Component VSP DataZ-Component VSP DataD
epth
D
epth
(m
)(m
)
Traveltime (s)Traveltime (s)
26522652
38873887
1.21.2 3.03.0
SaltSalt
Direct PDirect P
Reflected PReflected P
ReverberationsReverberations
24
150 m offset
(1)
(2)
(3)
(1) specular zone, (2) diffraction zone, (3) unreliable zone
3.3
Dep
th (
km)
3.9
0 100Offset (m)
39receivers
reflectivity
Local VSP Migration Images Local VSP Migration Images 600m and 1500 m offsets600m and 1500 m offsets
3.33.3
4.44.4
00 600600
Dep
th (
km)
Dep
th (
km)
Offset (m)Offset (m) 00 600600Offset (m)Offset (m)
600 m Image600 m Image 1500 m Image1500 m Image
ConclusionsConclusions
• Synthetic tests show accurate imaging around Synthetic tests show accurate imaging around well by Local VSP. Field data results?well by Local VSP. Field data results?
• Advantages: Advantages:
Only local velocity model neededOnly local velocity model needed
Inexpensive target oriented RTMInexpensive target oriented RTM
Statics removedStatics removed
• Disadvantages: Disadvantages:
Smaller illumination zone: Smaller illumination zone:
Less resolutionLess resolution
vsvs
G(g|x)*G(g|x)*G(x|s)*G(x|s)* vs vs G(g|x)*G(g|x)*G(x|s)G(x|s)
AcknowledgmentAcknowledgment
• We thank the sponsors of the 2007 We thank the sponsors of the 2007 UTAM consortium for their support.UTAM consortium for their support.
• We thank VSFusion for Schlumberger We thank VSFusion for Schlumberger modelmodel
• We thank BP for VSP DataWe thank BP for VSP Data
• Prev. WorkPrev. Work
Yonghe Sun (UTAM report 2004)Yonghe Sun (UTAM report 2004)Jianhua Yu (UTAM report 2005)Jianhua Yu (UTAM report 2005)Xiao Xiang (Geophysics 2006)Xiao Xiang (Geophysics 2006)
28
Subsalt Imaging
s
x
G(x|g) g
G(x|s)
m(x) ~
~ G(x|s)
Forwarddirect
sds
*
D(g|s)
G(x|g)*
Backward reflection
g
D(g|s)dg
Errors in the overburden
and salt body velocity model
Defocusing
Overview SSPVSP Local RTM Local RTM PS Summary
29
Local Reverse Time Migration
s
x
G(x|g) g
G(x|s)
g’
G(x|s)= G(x|g’)* D(g’|s)dg’
Backward Direct wave
g’ Local VSP Green’s function
Overview SSPVSP Local RTM Local RTM PS Summary
30
m(x) ~ s
~ dsg’
G(x|g’)* D(g’|s) dg’
Backward D(g’|s)
G(x|g)* D(g|s)dg
Backward D(g|s)
g
*
x1(1)
(2)
x2
x3
(3)
s
g
g’
Illumination Zones
(1) specular zone, (2)diffraction zone, (3) unreliable zone,
TheoryMotivation Numerical Tests Conclusions
31
Dep
th
(km
)
10
0
Offset (km)-12 120
(a) Ray tracing direct P
(c) PPS events (d) Pp events
(b) PSS events
Dep
th
(km
)
10
0
Offset (km)-12 120
Aperture by Ray Tracing
Introduction Numerical Tests ConclusionsTheory
Theory: Theory: LocalLocal VSP Migration VSP Migration
directdirect
reflectionreflection
Direct waves: Direct waves: D(g)D(g)Reflections: R(g)
reflectionreflection gG(x|g)*R(g)
g
x
Backproject Backproject
Backproject Backproject
Migration image: m(x) = G(x|g)*R(g)g
G(x|g)W()
Backprojected refl. Forwardproject. directG(x|g)W()
directdirect
D(g)
Sigsbee P-wave Velocity ModelSigsbee P-wave Velocity Model00
Dep
th (
km)
Dep
th (
km)
11.011.0
45004500
15001500
m/sm/s
12.512.5Offset (km)Offset (km)
279 shots
150 receivers287 recs
291 recs
35
X-Component VSP DataD
epth
(m
)
Traveltime (s)
2652
3887
1.2 3.0
Salt
Direct P
Reflected P
Reverberations Direct S
Introduction Numerical Tests ConclusionsTheory
36
150 m offset
3.3
3.9
0 100
Dep
th (
km)
Offset (m) 0 100Offset (m)
Without deconvolution
With deconvolution
Introduction Numerical Tests ConclusionsTheory
Dep
th
Dep
th
(km
)(k
m)
1313
00
VSP CSGVSP CSG
00 1313Time Time (s)(s)