LEAST SQUARES WAVEPATH LEAST SQUARES WAVEPATH MIGRATIONMIGRATION

Y. Liu and H. SunY. Liu and H. Sun

Geology and Geophysics Department Geology and Geophysics Department University of UtahUniversity of Utah

OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions

ObjectiveObjective Least-Squares MigrationLeast-Squares Migration a. Advantages:a. Advantages:• Apply to Incomplete dataApply to Incomplete data• Reduce acquisition footprintReduce acquisition footprint• Improve Image resolutionImprove Image resolution b. Disadvantage:b. Disadvantage:• Need more calculation timeNeed more calculation time

• Forward Modeling: fastForward Modeling: fast

• Migration: slowMigration: slow

ObjectiveObjective

Least Squares Migration:Least Squares Migration:

• Save calculation timeSave calculation time• Suppress artifactsSuppress artifacts

Wavepath MigrationWavepath Migration::

ObjectiveObjective

Advantages:Advantages:

Least-Squares Wavepath Migration:Least-Squares Wavepath Migration:

ObjectiveObjective

Advantages:Advantages:• Apply to Incomplete dataApply to Incomplete data• Reduce acquisition footprintReduce acquisition footprint• Improve resolutionImprove resolution• Save calculation timeSave calculation time

OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions

Wavepath MigrationWavepath Migration

KM : Fat Ellipsoid, 3-D CPUKM : Fat Ellipsoid, 3-D CPUWM: Hatched Area, 1.5-D CPUWM: Hatched Area, 1.5-D CPU

( ( Xg, 0 )Xg, 0 )

Fat Fat EllipsoidEllipsoid

Fat RayFat Ray

Traveltime + Ray DirectionTraveltime + Ray Direction

TrueReflection point

SmallMigration Aperture

FewerFewerArtifactsArtifacts

LessLessExpensiveExpensive

SEG Overthrust Model ResultsSEG Overthrust Model Results

Offset (km)Offset (km)00 1818

00

44

De

pth

(k

m)

De

pth

(k

m)

KM Image (CPU: KM Image (CPU: 1.01.0)) WM Image (CPU: WM Image (CPU: 0.780.78))

Offset (km)Offset (km)00 1818

00

De

pth

(k

m)

De

pth

(k

m)

44

BBAA

BBAA

SEG/EAGE Salt DataSEG/EAGE Salt Data

KM: KM: 11 WM: WM: 1/331/33

CPU Comparison in 3-DCPU Comparison in 3-D

West Texas Field DataWest Texas Field Data

KM: KM: 11 WM: WM: 1/141/14

OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions

ForwardForward : : d=Lm d=Lm (1)(1) Migration:Migration: m mstst=L d =L d (2)(2) Objective Function:Objective Function:

P(m)=|| Lm-d ||P(m)=|| Lm-d || (3)(3)

LSWM:LSWM: mmstst==[[LLLL]] Ld Ld (4)(4)

Least Square Wavepath MigrationLeast Square Wavepath Migration

TT

TT

TT-1-1

22

00

Least Square Wavepath MigrationLeast Square Wavepath Migration

Field DataField Data

Wavepath MigrationWavepath Migration

ForwardForward

Wavepath MigrationWavepath Migration

Y/NY/N

Iteration process:Iteration process:

Synthetic DataSynthetic Data Stop Stop CriteriaCriteria

OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions

Point Scatterer modelPoint Scatterer model

X(km)X(km)00

Tim

e (s

)T

ime

(s)

2.52.544

00 44X (km)X (km)

Dep

th(k

m)

Dep

th(k

m)

0044

..

00

Scatterer ImageScatterer Image

KM image KM image WM image WM image LSWM imageLSWM image

..

00 44X (km)X (km) 00 44X (km)X (km) 00 44X (km)X (km)00

44

Dep

th(k

m)

Dep

th(k

m)

OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions

CSG for Mobil DataCSG for Mobil Data

GEOMETRYGEOMETRY

Shots: 668Shots: 668Trace: 120Trace: 120Total: 80160Total: 80160Ns=1500Ns=1500Dt=4msDt=4msDs=25mDs=25mDg=25mDg=25mMin/Offset=262mMin/Offset=262m

TraceTrace11 120120

Tim

e(s)

Tim

e(s)

00

55

Velocity ModelVelocity Model

Dx=12.5Dx=12.5Dz=12.5Dz=12.5Nx=1594Nx=1594Nz=281Nz=281CDP=12.5CDP=12.5 D

epth

(km

)D

epth

(km

)00

3.53.5

00 19.919.9CDP NumberCDP Number

1.51.5

3.53.5

(Km

/s)

(Km

/s)

WM vs. LSWMWM vs. LSWMX(Km)X(Km)

Dep

th(K

m)

Dep

th(K

m)

X(Km)X(Km)4.84.8

3.43.4

19.019.0 19.019.0

After 15 iternationsAfter 15 iternations

X(m)X(m)

Dep

th(m

)D

epth

(m)

WM Image for Mobil DataWM Image for Mobil Data

LSWM image (15)LSWM image (15)

WM image (0)WM image (0)

12.012.0 18.018.0

12.012.0 18.018.0

2.82.8

2.82.8

Dep

th(m

)D

epth

(m)

OutlineOutline. . Objective Objective . Wavepath Migration. Wavepath Migration. Least Squares Wavepath Migration. Least Squares Wavepath Migration. Numerical Results. Numerical Results. Field Data Results . Field Data Results . Conclusions. Conclusions

ConclusionsConclusions • Suppress artifactsSuppress artifacts• Improve ResolutionImprove Resolution

• Computation time (Mobil Data) Computation time (Mobil Data) WM CPU 1.0WM CPU 1.0 LSWM CPU (15): LSWM CPU (15): 8.58.5

• Slightly sensitive to velocitySlightly sensitive to velocity

AcknowledgementsAcknowledgements

We thank 2001 UTAM We thank 2001 UTAM sponsors for their financial sponsors for their financial

supportssupports