Kirchhoff vs Crosscorrelation Kirchhoff vs Crosscorrelation MigrationMigration

0.5 km

2.5 km0.5 km 2.5 km

0.5 km

2.5 km0.5 km 2.5 km

Kirchhoff Mig.Kirchhoff Mig. Crosscorr. Mig.Crosscorr. Mig.

Kirchhoff vs Crosscorrelation Kirchhoff vs Crosscorrelation MigrationMigration

0.5 km

2.5 km0.5 km 2.5 km

0.5 km

2.5 km0.5 km 2.5 km

Kirchhoff Mig.Kirchhoff Mig. Crosscorr. Mig.Crosscorr. Mig.

VSP Images withVSP Images withStatic ErrorsStatic Errors

0.5 km

2.5 km0.5 km 2.5 km

0.5 km

2.5 km0.5 km 2.5 km

Kirchhoff Mig.Kirchhoff Mig. Crosscorr. Mig.Crosscorr. Mig.

VSP Images withVSP Images withStatic ErrorsStatic Errors

0.5 km

2.5 km0.5 km 2.5 km

0.5 km

2.5 km0.5 km 2.5 km

Kirchhoff Mig.Kirchhoff Mig. Crosscorr. Mig.Crosscorr. Mig.

Field RVSP Images withField RVSP Images withStatic ErrorsStatic Errors

0.0 km

.9 km0.0 km .12 km 0.0 km .12 km

Kirchhoff Mig.Kirchhoff Mig. Crosscorr. Mig.Crosscorr. Mig.

Enhancing Illumination Coverage of VSP by Crosscorrelation Migration

Jianhua Yu

Gerard T. Schuster

University of Utah

Interferometric Imaging

Outline Outline

Motivation

Crosscorrelation Migration

SEG/EAGE Model

2-D RVSP Field Data

Conclusions

Outline Outline

Motivation

Crosscorrelation Migration

SEG/EAGE Model

2-D RVSP Field Data

Conclusions

Problems with VSP Imaging Problems with VSP Imaging Quality? Quality?

Limited recording apertureLimited recording aperture

Narrow illumination coverageNarrow illumination coverage

Static errors at VSP well Static errors at VSP well caused by location errorscaused by location errors

Solution: Xcorr Migration of Ghost ReflectionsSolution: Xcorr Migration of Ghost Reflections

Widens illumination coverage VSP CDP

Solution: Xcorr Migration of Ghost ReflectionsSolution: Xcorr Migration of Ghost Reflections

Widens illumination coverage VSP CDP

Eliminates Rec. Statics: No Need to Know Rec. Location

Eliminates ~ ½ of the Raypath

Outline Outline

Motivation

Crosscorrelation Migration

SEG/EAGE Model

2-D RVSP Field Data

Conclusions

Crosscorrelation MigrationCrosscorrelation Migration

m(x) = (g, m(x) = (g, ss, t + t ), t + t )

gg ssxxgxgx

Kirchhoff Migration of CrosscorelogramsKirchhoff Migration of Crosscorelograms

ss

gg

ss ggss

Uninteresting Part of MediumUninteresting Part of Medium

How do you remove kinematic effects of propagatingHow do you remove kinematic effects of propagatingthrough unintersting parts of medium?through unintersting parts of medium?

Uninteresting Part of MediumUninteresting Part of Medium

{{MMTT

Pick Direct Arrival Time T and shift allPick Direct Arrival Time T and shift allTraces by T Traces by T

MM

MM

MM

Uninteresting Part of MediumUninteresting Part of Medium

Pick Direct Arrival Time T and shift allPick Direct Arrival Time T and shift allTraces by T Traces by T

MM

MM

MM

Uninteresting Part of MediumUninteresting Part of Medium

Shifting Traces Removes Kinematic EffectsShifting Traces Removes Kinematic EffectsOf Propagating through Uninteresting Parts of MediumOf Propagating through Uninteresting Parts of Medium

MM

Uninteresting Part of MediumUninteresting Part of Medium

Shifting Traces Removes Kinematic EffectsShifting Traces Removes Kinematic EffectsOf Propagating through Uninteresting Parts of MediumOf Propagating through Uninteresting Parts of Medium

MM

Shifting Traces Removes Kinematic EffectsShifting Traces Removes Kinematic EffectsOf Propagating through Uninteresting Parts of Medium.Of Propagating through Uninteresting Parts of Medium.

..

MM

MM MM

m(x) = (g, t + t )m(x) = (g, t + t )

gxgx gg MMxxgxgx

Kirchhoff Migrate psuedo-shot gathersKirchhoff Migrate psuedo-shot gathers

gg

Source Moved to SurfaceSource Moved to Surface

Can replace time-shifted traces by crosscorrelogramsCan replace time-shifted traces by crosscorrelograms

Interferometric SummaryInterferometric Summary

??

Above SourceAbove SourceImagingImaging {{

Wider CoverageWider Coverage

VSPVSP

Wider, taller coverage. Eliminates Wider, taller coverage. Eliminates well statics and uninteresting parts of well statics and uninteresting parts of the medium.the medium.

Above SourceAbove SourceImagingImaging {{

Wider CoverageWider Coverage

VSPVSP

Interferometric SummaryInterferometric SummaryWider, taller coverage. Eliminates Wider, taller coverage. Eliminates well statics and uninteresting parts of well statics and uninteresting parts of the medium.the medium.

MM MM

m(x) = (g, t + t )m(x) = (g, t + t )

gxgx gg MMxxgxgx

Kirchhoff Migrate psuedo-shot gathersKirchhoff Migrate psuedo-shot gathers

Outline Outline

Motivation

Crosscorrelation Migration

SEG/EAGE Model

2-D RVSP Field Data

Conclusions

Well

2

0D

epth

(k

m)

0 3X (km)

SEG/EAGE Model

256 Sources

V = 1.5 - 3.0 km/s

Well

2

0D

epth

(k

m)

0 3X (km)

Receiver interval: 10 m

Receiver depth range: 0.1 -1 km

Receiver number: 91

Sample interval: 1 ms

Recording length: 3 s

Well location: (1.5 km, 0 km)

Source interval: 10 m

Source number: 256

Acquisition Parameters:

1 km

Tim

e (s

)

3

00.2 0.9Depth (km)

CSG 160

Tim

e (s

)

3

00.2 0.9Depth (km)

Ghosts (CSG 160)

Tim

e (s

)

3

00 2.4X (km) 1.4 2.4X (km)

Xcross 60CRG 60

2.0

0.5

Dep

th (

km

)

0.5 2.5X (km)

Kirchh Mig (45) Xcorr Mig (45) Xcorr. Mig(15’)

2.52.5 0.5 0.5

Sta

tic

erro

rs (

ms)

-50

500 900Well Depth (m)

Raw Data

Static Errors at Well

2.0

0.5

Dep

th (

km

)

0.5

Kirchhoff MigrationStatic Error: 0

X (km)

Static Error: 25 ms

2.5

Static Error: 50ms

2.52.5 0.5 0.5

2.0

0.5

Dep

th (

km

)

0.5

Crosscorrelation MigrationStatic Error: 0

X (km)

Static Error: 25ms

2.5

Static Error: 50 ms

2.52.5 0.5 0.5

Velocity ModelVelocity Model Primary vs Multiple ImagePrimary vs Multiple Image

00

111100 1616 00 1616X (km)X (km) X (km)X (km)

Dep

th (k

m)

Dep

th (k

m)

Contents Contents

Motivation

Crosscorrelation Imaging Condition

SEG/EAGE Model

2-D RVSP Field Data

Conclusions

Tim

e (s

)

0.3

030 900Depth (ft)

Raw Data(CRG15)

Tim

e (s

)

0.3

030 900Depth (ft)

Ghosts

5 24Trace No.

Tim

e (s

)

1.2

0.2 xcorr data (muted)

Tim

e (s

)

1.4

0.55 24Trace No.

Field Data (CSG 25)

Raw data (muted)

Master trace Master trace

Dep

th (

ft)

1300

2000 400X (ft) 0 400X (ft)

Standard mig Xcorr. mig

Dep

th (

ft)

1100

0

Standard Well data Xcorr.

Exxon Data

Outline Outline

Motivation

Crosscorrelation Migration

SEG/EAGE Model

2-D RVSP Field Data

Conclusions

Crosscorrelogram Migration Conclusions Crosscorrelogram Migration Conclusions

Eliminate the static errors in the well

No need to know source (RVSP) or receiver location (VSP)

Half sensitivity to velocity migration errors than mult. migration by “mirrors”.

Increased illumination coverage in the VSP image. VSP ->CDP

Conclusions Conclusions Loss of some lateral resolution?

Be careful about virtual multiple

Xcorr

Narrow Angle

Kirchhoff

Wide Angle

vs

Ghost is weaker than primaryExtra summation compared to KM

AcknowledgmentsAcknowledgments

UTAM sponsorsUTAM sponsors

Exxon for 2-D field dataExxon for 2-D field data

J. Claerbout + J. RickettJ. Claerbout + J. Rickett

II evolved from daylight II evolved from daylight imagingimaging

Dep

th (

ft)

1300

2000 400X (ft) 0 400X (ft)

Standard mig Xcorr. mig

Geological ModelGeological Model0 4

0

3

Dep

th(k

m)

X(km)

(2001)(2001)

Migration Result Using Crosscorrelation ImagingMigration Result Using Crosscorrelation Imaging

1.6

0

2.2

Tim

e (s

)

2.1X (km)

Too simple?

Widen illumination?

If there are static errors in well?

Why Use Crosscorrelation Why Use Crosscorrelation Migration?Migration?

Widen the illumination coverage in the VSP image

VSP geometryEquivalent surface geometry

Xcorr

Seismic Ghost ReflectionSeismic Ghost Reflection

DirectDirect

GhostGhost

??Find R(x,z) but not know source locationFind R(x,z) but not know source location

DirectDirect

GhostGhost

1 2DirectDirect xx

DirectDirectxx

MasterMasterSeismic Ghost ReflectionSeismic Ghost ReflectionSeismic Interferogram: Correlate TracesSeismic Interferogram: Correlate Traces

t}

MM

m(x) = (g, t + t )m(x) = (g, t + t )

gxgx gg MMxxgxgxMM

Kirchhoff Migrate psuedo-shot gathersKirchhoff Migrate psuedo-shot gathers

GhostGhost Direct Direct has kinematics of primary reflectionhas kinematics of primary reflectionxx

MM

WellWell

SourceSource

ReceiverReceiver

Primary

Direct Wave

Ghost

RVSP

x

g

s xg

xg ' sg

'sg

Ghost Reflection Imaging ConditionGhost Reflection Imaging Condition:

'g

xgxgsg

''

sg

'sg

x

g

s xg

xg ' sg

'sg

After Crosscorrelation of Two Traces at After Crosscorrelation of Two Traces at Locations g & g’Locations g & g’

'g

xgxgsg

''

sg

'sg

'sg

x

g

s xg

xg '

After Crosscorrelation of Two Traces at After Crosscorrelation of Two Traces at Locations g & g’Locations g & g’

'g

xgxg

'

sg

'sg

x

g

s

After Crosscorrelation of Two Traces at After Crosscorrelation of Two Traces at Locations g & g’Locations g & g’

'g

xg

xg '

xgxg

'

sg

'sg

Recall Green’s TheoremRecall Green’s TheoremEvery Surface Point = Source PointEvery Surface Point = Source Point

xgxgsgg

''''

Why is there insensitivity to static errors in the well?

ssgsg

'''

xgxgxcorrg

''

s

g’ g

xStatic errors

''sg

xgxgsgg

''''

Crosscorrelogram MigrationCrosscorrelogram Migration

''')( )()( dgdgxgxgggDCorr xm

Migrated ImageMigrated Image

Crosscorrelograms

Crosscorrelation Crosscorrelation Imaging ConditionImaging Condition

Dep

th (

ft)

1100

0

Well data Xcorr. Migration

Field Data

Dep

th (

ft)

1100

0

Well data Standard Migration

Exxon Data