Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah.

Reduced-Time Reduced-Time Migration of Migration of

Converted WavesConverted Waves

David Sheley and Gerard T. David Sheley and Gerard T. SchusterSchuster

University of UtahUniversity of Utah

OutlineOutline• MotivationMotivation• Reduced-Time Migration TheoryReduced-Time Migration Theory• Error AnalysisError Analysis• ResultsResults

– Synthetic DataSynthetic Data– Field DataField Data

• ConclusionsConclusions




Problem: Dark FlanksProblem: Dark FlanksD

epth

Dep

th

OffsetOffset

00

ZZ

Rec

eive

r W

ell

Sou

rce

Wel

l

XX00

?? ??

PPPP

?? ???? ??

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

PP

Solution: PS Transmission MigrationSolution: PS Transmission MigrationD

epth

Dep

th

OffsetOffset

00

ZZ

Rec

eive

r W

ell

Sou

rce

Wel

l

XX00

PSPSPP

PSPS

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

MotivationMotivation

• Solutions:Solutions:1.1. PS Transmission MigrationPS Transmission Migration

• Problems:Problems:1.1. Dark FlanksDark Flanks


• Solutions:Solutions:1. PS Transmission Migration

• Problems:Problems:1. Dark Flanks

2.2. Velocity Errors (Vp, Vs)Velocity Errors (Vp, Vs)


• Solutions:Solutions:1. PS Transmission Migration2.2. Reduced-Time MigrationReduced-Time Migration

• Problems:Problems:1. Dark Flanks

2.2. Velocity Errors (Vp, Vs)Velocity Errors (Vp, Vs)




Reduced-Time MigrationReduced-Time Migration1. Data time shift1. Data time shift

Dep

th (

m)

Dep

th (

m)

Time (ms)Time (ms)PP

PSPS

SS

d(zd(zgg, t , t

d(zd(zgg, t , t


Time (ms)Time (ms)

PPPSPS

SS

Dep

th (

m)

Dep

th (

m)

obsobsd’(g, t) = d(zd’(g, t) = d(zgg, t + , t + sg sg


d’(zd’(zgg, t) = d(z, t) = d(zgg, t , t

sgsgObserved direct-P traveltimeObserved direct-P traveltimeobsobs

2. Modify the migration equation2. Modify the migration equation

m(r) = d’(zm(r) = d’(zgg, , sr sr ++ rg rg ))

obsobssgsg

calccalc–– sgsg




Focusing-Time ErrorFocusing-Time ErrorConventional vs. Reduced-TimeConventional vs. Reduced-Time

Reduced-TimeReduced-Time (d(dsr sr ++ ddrg rg psr psr --

ddsg)sg)c/cc/c

ConventionalConventional (d(dsr sr ++ ddrg rg psrpsr))c/cc/c22

22

00

0000

00250250

250250

500500

500500

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)

Dep

th (

m)

Dep

th (

m)


00

1212

88

44

1616

Focusing-Time ErrorFocusing-Time Error

ImagingImaging ErrorError (ms)(ms)

ConventionalConventionalTrans. PSTrans. PSMigrationMigration

Reduced-Reduced-TimeTimeMigrationMigration




Crosswell ModelCrosswell Model

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m) 11411400114114

00

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

5000 m/s5000 m/s

5500 m/s5500 m/s

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 (ms)Time (ms)

Shifted Muted DataShifted Muted Data

SPSPPSPS

PP

PSPS SS

SPSP

Conventional PS Conventional PS Transmission Migration Transmission Migration

Dep

th (

m)

Dep

th (

m)

Offset (m)Offset (m)00114114

00

100100

True VelocityTrue Velocity

Conventional PS Conventional PS Transmission Migration Transmission Migration

Dep

th (

m)

Dep

th (

m)


00

100100

True VelocityTrue Velocity + 10 % Velocity+ 10 % Velocity

Offset (m)Offset (m)00 100100

Dep

th (

m)

Dep

th (

m)


00

100100


Reduced-Time PS MigrationReduced-Time PS Migration

Dep

th (

m)

Dep

th (

m)


00

100100


Reduced-Time PS MigrationReduced-Time PS Migration

+ 10 % Velocity+ 10 % Velocity


Dep

th (

m)

Dep

th (

m)


00

100100

Conventional PSConventional PS

Comparison +10% VelocityComparison +10% Velocity

Recuced-TimeRecuced-Time





km/s

eckm

/sec6.06.0

5.05.0

7.07.0

Kidd Creek CrosswellKidd Creek Crosswell

WellWell

00

2020

4040

6060

505000

ReceiverReceiverWellWell

SourceSource

Dep

th (

m)

Dep

th (

m)


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

• Well LocationWell Location

• Velocity ModelVelocity Model

Data ProblemsData Problems

66Time (ms)Time (ms)

00

2020

4040

6060

Dep

th (

m)

Dep

th (

m)

00

Time Shifted CRGTime Shifted CRG

ConventionalConventional00

2020

6060

505000 Offset (m)Offset (m)

Dep

th (

m)

Dep

th (

m)

ConventionalConventional00

2020

6060

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

Reduced-TimeReduced-TimeD

epth

(m

)D

epth

(m

)




ConclusionsConclusions• Transmission PS migration can image Transmission PS migration can image

structure invisible to reflection migration.structure invisible to reflection migration.

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

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

AcknowledgementsAcknowledgements

I sincerely thank the 1999 sponsors I sincerely thank the 1999 sponsors of the UTAM consortium for their of the UTAM consortium for their financial support.financial support.

Reduced-Time Migration of Converted Waves David Sheley and Gerard T. Schuster University of Utah.

Documents

time ps migration slide

time migration problems

ms slide

data time shift depth

time error conventional

time ms original data

velocity recucedtime

data time shift dz g