Reduced-Time Reduced-Time Migration of Migration of

Converted WavesConverted Waves

David SheleyDavid SheleyUniversity of UtahUniversity of Utah

OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data Results Synthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work

PP vs PS Transmission MigrationPP vs PS Transmission MigrationD

epth

Dep

th

OffsetOffset

00

ZZ

Rec

eive

r W

ell

Sou

rce

Wel

l

XX00

PP Reflection MigrationPP Reflection Migration

XX

Sou

rce

Wel

l

Rec

eive

r W

ell

PP

P = ?P = ?

PP

=?=?

00

Dep

thD

epth

ZZ00 OffsetOffset

Rec

eive

r W

ell

Converted Wave MigrationConverted Wave MigrationS

ourc

e W

ell

XX

PP

PP PSPS

PSPS

VVpp,V,Vss = ? = ?

=?=?

00

Dep

thD

epth

ZZ00 OffsetOffset

OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data Results Synthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work

Conventional MigrationConventional Migration

m(r) = S(zm(r) = S(zgg, , sr sr ++ rgrg))

srsr rgrgss

rr

gg

PS Transmission MigrationPS Transmission Migration

m(r) = S(zm(r) = S(zgg, d, dsrsr/V/Vp p ++ ddrgrg/V/Vss))

ddsrsr/V/Vpp ddrgrg/V/Vssss gg

rr

km/seckm/sec

6.06.0

5.05.0

7.07.0

ProblemProblem

WellWell

00

2020

4040

6060

505000

ReceiverReceiverWellWell

SourceSource

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

Reduced-Time MigrationReduced-Time Migration• Data time shiftData time shift

S’(g, t) = S(zS’(g, t) = S(zgg, t + , t + sg sg sgsgObserved direct-P timeObserved direct-P time

obsobs

obsobs

Dep

th (

m)

Dep

th (

m)

00

1141142020 3535Time (ms)Time (ms)

Original DataOriginal Data

Dep

th (

m)

Dep

th (

m)

00

1141148822 Time (s)Time (s)

Shifted Muted DataShifted Muted Data

SPSPPSPS

PP

PSPS SS

SPSP

Data ShiftData Shift

Reduced-Time MigrationReduced-Time Migration• Data time shiftData time shift

S’(zS’(zgg, t) = S(z, t) = S(zgg, t + , t + sg sg

sgsgObserved direct-P timeObserved direct-P time

obsobs

obsobs

• Modify the migration equationModify the migration equation

m(r) = S(zm(r) = S(zgg, , sr sr ++ rg rg - - sg sg ++ sg sg ))obsobscalccalc

calccalcm(r) = S’(zm(r) = S’(zgg, , sr sr ++ rg rg –– sg sg ))

OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data Results Synthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work

Error Analysis -- CWMError Analysis -- CWM

• Single traceSingle trace• Homogeneous mediaHomogeneous media• True velocity = True velocity = cc

• Migration velocityMigration velocity

c’ = c + c’ = c + cc• VVpp/V/Vss = = psrpsr

Assumptions:Assumptions:

m(r) = S(zm(r) = S(zgg, , sr sr ++ rg rg psrpsr))

m(r) = S(zm(r) = S(zgg, (d, (dsr sr ++ ddrg rg psrpsr)/)/c’c’ ))

Error Analysis Error Analysis Conventional MigrationConventional Migration

(d(dsr sr ++ ddrg rg psrpsr)/)/c’c’ (d(dsr sr ++ ddrg rg psrpsr)/()/(c + c + c)c)==

~~ (d(dsr sr ++ ddrg rg psrpsr)()(s – s s – s c)c)22~~

(d(dsr sr ++ ddrg rg psrpsr) ) s s cc

22

cmcm

m(r) = S(g,m(r) = S(g,

Error Analysis Error Analysis Reduced-Time MigrationReduced-Time Migration

))obsobscalccalcsr sr ++ rg rg - - sg sg ++ sgsg

Error Analysis Error Analysis Reduced-Time MigrationReduced-Time Migration

obsobscalccalcsr sr ++ rg rg - - sg sg ++ sgsg

==(d(dsr sr ++ ddrg rg psr psr -- ddsgsg)()(s s –– s s c) + c) + ddsg sg ss

22

(d(dsr sr ++ ddrg rg psr psr -- ddsgsg) ) s s cc

rtmrtm22

Error FunctionsError FunctionsCWM vs. RTM CWM vs. RTM

rtmrtm(d(dsr sr ++ ddrg rg psr psr -- ddsgsg) ) s s cc

22

cmcm(d(dsr sr ++ ddrg rg psrpsr) ) s s cc

22

rtmrtm

cmcm

00

0000

00250250

250250

500500

500500

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

00

1212

88

44

1616

Imaging-Time ErrorImaging-Time Error

ImagingImaging ErrorError (ms)(ms)

OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data ResultsSynthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work

Crosswell ModelCrosswell Model

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m) 11411400114114

00

VV22

VV11

V = 5500 m/sV = 5500 m/s22

V = 5000 m/sV = 5000 m/s11

VVpp /V /Vss = 1.5 = 1.5

Well Separation Well Separation = 100 m= 100 m

Source = 1500 HzSource = 1500 Hzds = 2 mds = 2 mdg = 2 mdg = 2 m

Synthetic DataSynthetic DataD

epth

(m

)D

epth

(m

)

00

1141142020 3535Time (ms)Time (ms)

Original DataOriginal Data

Dep

th (

m)

Dep

th (

m)

00

1141148822 Time (s)Time (s)

Shifted Muted DataShifted Muted Data

SPSPPSPS

PP

PSPS SS

SPSP

PS Transmission Migration PS Transmission Migration True VelocityTrue Velocity

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)00114114

00

114114

Conventional PS MigrationConventional PS Migration+ 10 % Velocity+ 10 % Velocity

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)00114114

00

114114

Reduced-Time PS MigrationReduced-Time PS Migration+ 10% Velocity+ 10% Velocity

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)00114114

00

114114

OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data ResultsSynthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work

• Time Delay = 3 ms ?Time Delay = 3 ms ?

• Well locationWell location

• Velocity ModelVelocity Model

Data ProblemsData Problems

km/seckm/sec

6.06.0

5.05.0

7.07.0

Kidd CreekKidd Creek

WellWell

00

2020

4040

6060

505000

ReceiverReceiverWellWell

SourceSource

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

66Time (ms)Time (ms)

00

2020

4040

6060

Dep

th (

m)

Dep

th (

m)

00

Time Shifted CRGTime Shifted CRG

Conventional PS MigrationConventional PS Migration00

2020

4040

6060

505000

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

Reduced-Time PS MigrationReduced-Time PS Migration00

2020

4040

6060

505000

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

RTM-PS CRG #8RTM-PS CRG #800

2020

4040

6060

505000

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

Kidd CreekKidd Creek00

2020

4040

6060

505000 Offset (m)Offset (m) 505000 Offset (m)Offset (m)

OutlineOutline• MotivationMotivation• Migration TheoryMigration Theory• Error AnalysisError Analysis• Synthetic Data ResultsSynthetic Data Results • Field Data ResultField Data Result• Conclusions & Future WorkConclusions & Future Work

Discussion & ConclusionsDiscussion & Conclusions

• PS migration can image structure PS migration can image structure invisible to reflection migration.invisible to reflection migration.

• Reduced-time migraton decreases the Reduced-time migraton decreases the error of an incorrect velocity model. error of an incorrect velocity model.

• Converted wave reduced-time Converted wave reduced-time migration can successfully image a migration can successfully image a transmitting boundary.transmitting boundary.

Future WorkFuture Work• Model and migrate salt proximity Model and migrate salt proximity

VSP data with converted wave VSP data with converted wave RTM. RTM.

• Model and test PP RTM.Model and test PP RTM.• Search for other applications of Search for other applications of

RTM.RTM.• Graduate.Graduate.