imaging every bounce in a multiple g. schuster, j. yu, r. he u of utah

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

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




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’



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



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’’



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

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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

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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

TimeTime (s)(s)

00

99

Geophone(#)Geophone(#)11 540540

Free-Surface MultipleFree-Surface Multiple

TimeTime (s)(s)

00

99

Geophone(#)Geophone(#)11 540540

Another MultipleAnother Multiple

KM before de-multipleKM before de-multiple

Depth (ft)

0

30K

Offset (ft)1 50.55K

KM after de-multipleKM after de-multiple

Depth (ft)

0

30K

Offset (ft)1 50.55K

Multiple migrationMultiple migration

Depth (ft)

0

30KOffset (ft)0 50.55K

Using multiple 02020

Multiple migration resultMultiple migration result

Depth (ft)

0

30K

Offset (ft)1 50.55K

Multiple migration resultMultiple migration result

Offset (ft)

Depth (ft)

Depth (ft)

3750 26,250

6,750

6,7509,375

9,375

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Summary. Summary.

Raw Data of CRG#15 Ghosts of CRG# 150

0.37

Tim

e (s

)

1000 ft 1000 ft 0 0

Raw Data of CRG#15 Primary of CRG# 150

0.37

Tim

e (s

)

1000 ft 1000 ft 0 0

Primary Image 1st Ghost Image0

1

Dep

th (

kft

)

445 ft 445 ft0 0

Primary Image 1st Order Ghost Image0

1

Dep

th (

kft

)

445 ft 445 ft0 0

Well & Primary Image Well & 1st Ghost Image

0

1

Dep

th (

kft

)

Offset=105ft

Well & Primary Image Well & 1st Ghost Image

0

1

Dep

th (

kft

)

Offset=200 ft

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



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


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





0 km 5 km0 km 5 km

0 km 0 km

7 km7 km

Salt ModelSalt Model

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 0 km

7 km7 km0 km 0 km

7 km7 km

Migration with Correlation WeightsMigration with Correlation Weights

Correlation WeightsCorrelation Weights



0 km 0 km

7 km7 km0 km 0 km

7 km7 km

Ground Truth MigrationGround Truth Migration

OUTLINE OUTLINE





Multiple MigrationMultiple Migration

xx



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) =


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

Multiple 01020Multiple 01020

Time (s)

0

9

Geophone(#)1 540

Multiple 0202010Multiple 0202010

Time (s)

0

9

Geophone(#)1 540

0 km 2 km0 km 2 km

0 km0 km

2 km2 km0 km0 km

2 km2 km0 km0 km

2 km2 km

Graben ModelGraben Model

Standard MigrationStandard Migration

Least Squares MigrationLeast Squares Migration

GhostsGhosts

imaging every bounce in a multiple g. schuster, j. yu, r. he u of utah

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ft slide

x slide

g sg slide

illumination slide

csg slide

g g mx

data xgg slide

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