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Imaging Every Bounce inImaging Every Bounce in
a Multiplea Multiple
G. G. Schuster, J. Yu, R. HeSchuster, J. Yu, R. He
U of UtahU of Utah
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Migrating every BounceMigrating every Bounce
Numerical Results Numerical Results
Summary. Summary.
Why Migrate Multiples?Why Migrate Multiples?
Wider CoverageWider Coverage
Better FoldBetter Fold
Better Vert. Res.Better Vert. Res.
Motivation 1: Extend Coverage 3DMotivation 1: Extend Coverage 3D
Courtesy of B. Paulsson PGSICourtesy of B. Paulsson PGSI
Shot radius
160 level Receiver array Depth in Well: 4,000-12,000 ft
22,000 ft
20,000 ft
22,000 ft
The 3D Image Volume from a Massive 3D VSPThe 3D Image Volume from a Massive 3D VSP®®
SurveySurvey
Courtesy of B. Paulsson PGSICourtesy of B. Paulsson PGSI
3D View of the image volume around the 3D 3D View of the image volume around the 3D VSP wellVSP well
3D View of the image volume around the 3D 3D View of the image volume around the 3D VSP wellVSP well
3D View of the image volume around the 3D 3D View of the image volume around the 3D VSP wellVSP well
3D View of the image volume around the 3D 3D View of the image volume around the 3D VSP wellVSP well
00
8 km8 km0 (Zhang & McMechan 1997) 24 km0 (Zhang & McMechan 1997) 24 km
Motivation 2: Peek Around Corners with Motivation 2: Peek Around Corners with MultiplesMultiples
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Migrating every BounceMigrating every Bounce
Numerical Results Numerical Results
Summary. Summary.
Migrating Every BounceMigrating Every Bounce
1. Predict Multiple Traveltimes from Data1. Predict Multiple Traveltimes from Data
PrimaryPrimary
Pick t(s,Pick t(s,g’g’))ss g’g’
Migrating Every BounceMigrating Every Bounce
1. Predict Multiple Traveltimes from Data1. Predict Multiple Traveltimes from Data
ss g’g’ggss g’g’ gg
PrimaryPrimary
ss g’g’ gg
t(s,t(s,g’g’) + t() + t(g’g’,g),g)t(s,t(s,g’,g’,g) = min( ) g) = min( )
Asakawa & Matsuoka, 2002Asakawa & Matsuoka, 2002
0 m 180 m0 m 180 m
0.1 s0.1 s
0.0 s0.0 s
Tim
e (s
)T
ime
(s)
X (m)X (m)
3rd-order3rd-order
2nd-order2nd-order
1st-order1st-order
primaryprimary
Free-Surface Multiples & 2-Layer ModelFree-Surface Multiples & 2-Layer Model
Migrating Every BounceMigrating Every Bounce
1. Predict Multiple Traveltimes from Data1. Predict Multiple Traveltimes from Data
ss gg
2. Migrate Multiples2. Migrate MultiplesSum Data along Predicted T(Sum Data along Predicted T(ss,x,,x,gg))
d(d(gg, , t(s,g’)t(s,g’) + + t(t(g’,g’,x,g’’) + x,g’’) + t(g’’,t(g’’,gg) ) ) ) gg
m(x) =m(x) =
Predicted from DataPredicted from Data
xx
g’g’ g’’g’’
Migrating Every BounceMigrating Every Bounce
1. Predict Multiple Traveltimes from Data1. Predict Multiple Traveltimes from Data
ss gg
2. Migrate Multiples2. Migrate MultiplesSum Data along Predicted T(Sum Data along Predicted T(ss,x,,x,gg))
d(d(gg, t(, t(ss,x,g’),x,g’) + t(g’,g’’) + + t(g’,g’’) + t(g’’,t(g’’,gg) ) ) ) gg
m(x) =m(x) =
xx
Modeling PeglegsModeling Peglegs
(Jakubowicz; Reshef, Keydar, Landa; (Jakubowicz; Reshef, Keydar, Landa;
Weglein, Gasparotto, et al).Weglein, Gasparotto, et al).
ss ggX yX y
t(s1y) + t(s1y) + t(t(x2gx2g)) - - t(xot(xoy) = y) = t(s1o2g)t(s1o2g)
11 22
oo
??PrimariesPrimaries PeglegPegleg
AA
BB
Choose x & yChoose x & y
so incidence anglesso incidence angles
agreeagree
SummarySummary
ss gg
Migrate MultiplesMigrate Multiples
d(d(gg, t(, t(ss,x,g’),x,g’) + t(g’,g’’) + + t(g’,g’’) + t(g’’,t(g’’,gg) ) ) ) gg
m(x) =m(x) =
xx
modelmodel modelmodel
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Migrating every BounceMigrating every Bounce
Numerical Results Numerical Results
Summary. Summary.
dd
0 km X 5 km0 km X 5 km 0 km X 5 km0 km X 5 km
0 km0 km
ZZ
2.5 km2.5 km
0 km0 km
ZZ
2.5 km2.5 km
m0 + m1 + m2m0 + m1 + m2 m0m0
m1m1 m2m2
2-Layer Model: Migration 1 CSG2-Layer Model: Migration 1 CSG
0 km X 5 km0 km X 5 km
m0 + m1m0 + m1
m0m0
XXzz
XXzz
m0 vs m1: 2-Layer Migration Imagesm0 vs m1: 2-Layer Migration Images
Even IlluminationEven Illumination
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Migrating every BounceMigrating every Bounce
Numerical Results Numerical Results
Summary. Summary.
One part of SMAART modelOne part of SMAART model
Depth (ft)
0
30KOffset (ft)0 50.55K
reflector 0
reflector 1
reflector 2
reflector 3
Multiple migration resultMultiple migration result
Offset (ft)
Depth (ft)
Depth (ft)
3750 26,250
6,750
6,7509,375
9,375
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Migrating every BounceMigrating every Bounce
Numerical Results Numerical Results
Summary. Summary.
SummarySummary
Use data to design migration kernel Use data to design migration kernel
Benefits: Better resol. & fold kernel Benefits: Better resol. & fold kernel
Use Delft method predict multiplesUse Delft method predict multiples
Test on field data Test on field data
Primary MigrationPrimary Migration
xx
Sum Data along Predicted T(g)Sum Data along Predicted T(g)
Predicted by Ray TracingPredicted by Ray Tracing
Multiple MigrationMultiple Migration
xx
Sum Data along Predicted T(g)Sum Data along Predicted T(g)
Predicted from DataPredicted from Data
Predicted from Ray TracingPredicted from Ray Tracing
Prediction+SubtractionPrediction+Subtraction Predict or pick the traveltime of a multiple.
NMO the multiple within a time window.
If a significant overlaying primary is suppressed at the same time, use the same strategy to predict it and fill the gap.
Predict the multiple by a multichannel two-way prediction filter.
Subtract the predicted multiple.
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Prediction of Multiple T(g) Prediction of Multiple T(g)
Joint Migration Pattern Recog. Joint Migration Pattern Recog.
Joint Migration LSM. Joint Migration LSM.
What Good are Natural T(s,What Good are Natural T(s,g’,g’,g)?g)?
PrimaryPrimary
g’g’ ggs’s’
t(s,t(s,g’g’,g) = ,g) = minmin(t(s,(t(s,g’g’) + t() + t(g’g’,g)),g))gg’’
Answer 1: Natural Decon of MultiplesAnswer 1: Natural Decon of Multiples
PrimaryPrimary
g’g’ ggs’s’
Actual MultipleActual MultiplePredicted MultiplePredicted Multiple
Adaptive SubtractionAdaptive SubtractionDeblurring: d = G dDeblurring: d = G d11 00
Answer 2: Semi-Natural Migration of MultiplesAnswer 2: Semi-Natural Migration of Multiples
g’g’ss
Actual MultipleActual Multiple
Predicted MultiplePredicted Multiple
xx
d(g, d(g, t(t(ss,,g’g’) + ) + tt((g’g’,,xx)) + t(x,g) ) + t(x,g) ) gg
m(x) =m(x) =
gg
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Prediction of Multiple T(g) Prediction of Multiple T(g)
Joint Migration Pattern Recog. Joint Migration Pattern Recog.
Joint Migration LSM. Joint Migration LSM.
Joint Joint MigrationMigration: LS Multiple Migration: LS Multiple Migration
PROBLEMPROBLEM: Multiples get Coherently Migrated: Multiples get Coherently Migrated
PrimaryPrimary
MultipleMultiple
SOLUTION:SOLUTION: Least Squares Joint Migration Least Squares Joint Migration
MultipleMultiplePrimaryPrimary
L0 m0 + L1 m1 = dL0 m0 + L1 m1 = d
(L0 + L1) m = d(L0 + L1) m = d
0 km 5 km0 km 5 km 0 km 5 km0 km 5 km
0 km 5 km0 km 5 km0 km 5 km0 km 5 km
0 km 0 km
7 km7 km0 km 0 km
7 km7 km
LL 00
LL 00 LL 11 LL 22++ ++
Standard MigrationStandard MigrationLL 11
LL 22 Correlation WtCorrelation Wt
Correlation WtCorrelation Wt
LL 00
LL 00 LL 11 LL
LL 11
LL 22
ss
0 km 5 km0 km 5 km 0 km 5 km0 km 5 km
0 km 5 km0 km 5 km0 km 5 km0 km 5 km
0 km 0 km
7 km7 km0 km 0 km
7 km7 km
Migration with Correlation WeightsMigration with Correlation Weights
Correlation WeightsCorrelation Weights
0 km 5 km0 km 5 km 0 km 5 km0 km 5 km
0 km 5 km0 km 5 km0 km 5 km0 km 5 km
0 km 0 km
7 km7 km0 km 0 km
7 km7 km
Ground Truth MigrationGround Truth Migration
OUTLINE OUTLINE
Why Migrate Multiples? Why Migrate Multiples?
Prediction of Multiple T(g) Prediction of Multiple T(g)
Joint Migration Pattern Recog. Joint Migration Pattern Recog.
Joint Migration LSM. Joint Migration LSM.
Multiple MigrationMultiple Migration
xx
Sum Data along Predicted T(g)Sum Data along Predicted T(g)
Predicted from DataPredicted from Data
Predicted from Ray TracingPredicted from Ray Tracing
Middle Bounce MigrationMiddle Bounce Migration
xx Predicted from Ray TracingPredicted from Ray Tracing
d(g, d(g, t(s,g’)t(s,g’) + + t(g’,x,g’’) + t(g’,x,g’’) + t(g’’,gt(g’’,g) ) ) ) gg
m(x) =m(x) =
Predicted from DataPredicted from Data
Rigorous Theory? Rigorous Theory?
D(g) = R f + R f + ….. D(g) = R f + R f + ….. 121121 121121
22
datadata primaryprimary 1st-order1st-order
11
22
Frechet Derivative Frechet Derivative
D(g) = R f + R f + ….. D(g) = R f + R f + ….. 121121 121121
22
11
22
rr rr rr
rrRR 121121 ffRR 121121
rrRR 121121 ffRR 121121++
product ruleproduct rule
dd
0 km X 5 km0 km X 5 km 0 km X 5 km0 km X 5 km
0 km0 km
ZZ
2.5 km2.5 km
0 km0 km
ZZ
2.5 km2.5 km
m0 + m1 + m2m0 + m1 + m2 m0m0
m1m1 m2m2
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