v.2 wavepath migration

V.2 V.2 Wavepath MigrationWavepath Migration OverviewOverview

Kirchhoff migration smears a reflection along a fat Kirchhoff migration smears a reflection along a fat ellipsoid, so that most of the reflection energy is placed in ellipsoid, so that most of the reflection energy is placed in regions far from the actual specular reflection point. This is regions far from the actual specular reflection point. This is both inefficient and artifact-prone. To place the reflection both inefficient and artifact-prone. To place the reflection energy at or near its specular reflection point we first perform energy at or near its specular reflection point we first perform a local slant stack on the trace, and propagate it along its a local slant stack on the trace, and propagate it along its associated wavepath cosnistent with the incident angle of the associated wavepath cosnistent with the incident angle of the arrival. The reflection is now smeared along the portion of the arrival. The reflection is now smeared along the portion of the wavepath centered about the specular reflection point. Thus wavepath centered about the specular reflection point. Thus wavepath migration smears the reflection energy along a small wavepath migration smears the reflection energy along a small portion of a wavepath, which reduces both cost and aliasing portion of a wavepath, which reduces both cost and aliasing artifacts. The drawback is the sensitivity of the incidence angle artifacts. The drawback is the sensitivity of the incidence angle calculation due to noise or inaccurate migration velocities.calculation due to noise or inaccurate migration velocities.

• Problem & MotivationProblem & Motivation• TheoryTheory• Synthetic Numerical ExamplesSynthetic Numerical Examples• Field Data Numerical ExamplesField Data Numerical Examples• ConclusionsConclusions

OutlineOutline

ExpenseExpense

Acc

urac

yA

ccur

acy

Full-WaveFull-Wave

Ray-BeamRay-BeamKirchhoffKirchhoff

Migration Accuracy vs $$$Migration Accuracy vs $$$

Target RTMTarget RTM

No Approx.No Approx.

Multiple ArrivMultiple Arriv

Anti-aliasingAnti-aliasingPhase-ShiftPhase-Shift

3-D KM of a Single Trace3-D KM of a Single Trace

RR SSAA

AA

BB

BB

CC

CC

ProblemProblem

Problem & SolutionProblem & Solution ProblemProblem:: Kirchhoff Migration Expensive; Kirchhoff Migration Expensive; O(N ) per TraceO(N ) per Trace Reflection Energy Smeared Reflection Energy Smeared AllAll Along EllipseAlong Ellipse

SolutionSolution: Wavepath Migration. Smear: Wavepath Migration. Smear Energy along Wavepaths notEnergy along Wavepaths not Ellipses; O(N )per TraceEllipses; O(N )per Trace

33

1.51.5

SS RR

ImageImagePointPoint

Fresnel ZoneFresnel Zone

Smear Reflection along WavepathSmear Reflection along WavepathInc. AngleInc. Angle

by Slant Stackby Slant Stack

MVA ObjectivesMVA Objectives

• Can WMVA effectively improve theCan WMVA effectively improve the migration velocity?migration velocity?

• Whether the WMVA updated velocity Whether the WMVA updated velocity differs much from the KMVA updateddiffers much from the KMVA updated velocity?velocity?

• Can WMVA be much faster than Can WMVA be much faster than KMVA?KMVA?

RR SSAA

BBCC

AABB

CC

3-D WM of a Single 3-D WM of a Single TraceTrace

SolutionSolution

Problem & SolutionProblem & Solution ProblemProblem:: Kirchhoff Migration Expensive; Kirchhoff Migration Expensive; O(N ) per TraceO(N ) per Trace Reflection Energy Smeared Reflection Energy Smeared AllAll Along EllipseAlong Ellipse

SolutionSolution: Wavepath Migration. Smear: Wavepath Migration. Smear Energy along Wavepaths notEnergy along Wavepaths not Ellipses; O(N )per TraceEllipses; O(N )per Trace

33

1.51.5

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model

3-D Prestack KM Point Scatterer Response3-D Prestack KM Point Scatterer Response R

efle

ctiv

ityR

efle

ctiv

ity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.5-0.5

00

11

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.01-0.01

00

0.020.02

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.05-0.05

00

0.10.1

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.2-0.2

00

0.40.4

11

1111

11

Z0Z0

Z0-1Z0-1Z0-9Z0-9

Z0+8Z0+8

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.5-0.5

00

11

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.01-0.01

00

0.020.02

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.05-0.05

00

0.10.1

Ref

lect

ivity

Ref

lect

ivity

Y Offset (km)Y Offset (km) X Offset (km)X Offset (km)11

-0.2-0.2

00

0.40.4

11

1111

11

3-D Prestack WM Point Scatterer Response3-D Prestack WM Point Scatterer Response

Z0Z0

Z0-1Z0-1Z0-9Z0-9

Z0+8Z0+8

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model• 2-D SEG/EAGE overthrust 2-D SEG/EAGE overthrust

modelmodel

Velocity ModelVelocity Model 0km0km 15km15km10km10km5km5km

00

15015000

45004500

30003000Dep

th (m

)D

epth

(m)

60006000

25025000

Velocity (m

/sec)V

elocity (m/sec)

Wavepath vs Kirchhoff Migration

Offset (km)4 10

Dep

th (k

m)

0.5

2.5

4 Offset (km) 10 4 Offset (km) 10

WM Image (CPU: 0.088) KM Image (CPU: 1.0)Structure(Slant Stack)

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model• 2-D Canadian Land Data2-D Canadian Land Data

A Raw CSG of Husky Field DataA Raw CSG of Husky Field Data

Trace NumberTrace Number11 300300

Tim

e (s

ec)

Tim

e (s

ec)

00

3.03.0

Husky Field Data ResultsHusky Field Data Results

Offset (km)Offset (km)00 141400

77

Dep

th (k

m)

Dep

th (k

m)

KM KM (CPU:(CPU:1.01.0))

AA

BB

WM WM (CPU: (CPU: 2.232.23))

Offset (km)Offset (km)00 1414

AA

BB

Husky Field Data ResultsHusky Field Data Results

Offset (km)Offset (km)2.52.5 5.55.52.52.5

5.05.0

Dep

th (k

m)

Dep

th (k

m)

KM Image (Box A)KM Image (Box A) WM Image (Box A)WM Image (Box A)

Offset (km)Offset (km)2.52.5 5.55.52.52.5

Dep

th (k

m)

Dep

th (k

m)

5.05.0

Husky Field Data ResultsHusky Field Data Results

Offset (km)Offset (km)00 141400

77

Dep

th (k

m)

Dep

th (k

m)

KM KM (CPU:(CPU:1.01.0))

AA

BB

WM WM (Slant Stack, CPU: (Slant Stack, CPU: 0.240.24))

Offset (km)Offset (km)00 1414

AA

BB

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model• 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model• 2-D Canadian Land Data2-D Canadian Land Data

Receiver DistributionReceiver DistributionC

ross

line

(m)

Cro

sslin

e (m

)

4480448023202320

19201920

19201920 Inline (m)Inline (m)

Inline Velocity ModelInline Velocity ModelOffset (km)Offset (km)00 9.29.2

Dep

th (k

m)

Dep

th (k

m)

00

3.83.8

SALTSALT

Inline KMInline KM (CPU=1)(CPU=1) Inline WMInline WM (CPU=1/33)(CPU=1/33)Offset (km)Offset (km)00 9.29.2

00

3.3.88

Dep

th (k

m)

Dep

th (k

m)

Offset (km)Offset (km)00 9.29.2

Zoom Views of Inline Sections Zoom Views of Inline Sections

Offset: 3~6.5 km, Depth: 0.3~1.8 kmOffset: 3~6.5 km, Depth: 0.3~1.8 km

WMWM

ModelModel

KirchhoffKirchhoff

SubSubWMWM

ModelModel

Migration of SEG Salt Data (Crossline Sections) Migration of SEG Salt Data (Crossline Sections)

Offset: 1.8~4 km, Depth: 0.6~2.1 kmOffset: 1.8~4 km, Depth: 0.6~2.1 km

WMWMKM KM

SubSubWMWM

Inline: 1.8~7.2 km, Crossline: 0~4 kmInline: 1.8~7.2 km, Crossline: 0~4 km

WMWM

ModelModel

KM KM

SubSubWMWM

Migration of SEG Salt Data (Horizontal Slices) Migration of SEG Salt Data (Horizontal Slices)

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model• 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model

• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model• 2-D Canadian Land Data2-D Canadian Land Data

• 3-D W. Texas Data3-D W. Texas Data

A Common Shot GatherA Common Shot GatherTrace NumberTrace Number5454 193193

Tim

e (s

ec)

Tim

e (s

ec)

00

3.43.4

Receiver DistributionReceiver DistributionC

ross

line

(km

)C

ross

line

(km

)

4.54.51.21.2

3.53.5

1.51.5 Inline (km)Inline (km)

Receiver DistributionReceiver DistributionC

ross

line

(km

)C

ross

line

(km

)

4.54.51.21.2

3.53.5

1.51.5 Inline (km)Inline (km)

Inline KM Inline KM (CPU=1)(CPU=1) Inline WMInline WM (CPU=1/14)(CPU=1/14)

Offset (km)Offset (km)0.40.4 4.54.5

0.80.8

3.83.8

Dep

th (k

m)

Dep

th (k

m)

Offset (km)Offset (km)0.40.4 4.54.5

Inline KMInline KM (CPU=1)(CPU=1) Inline WMInline WM (CPU=1/50)(CPU=1/50)

Offset (km)Offset (km)0.40.4 4.54.5

0.80.8

3.83.8

Dep

th (k

m)

Dep

th (k

m)

Offset (km)Offset (km)0.40.4 4.54.5

(subsample)(subsample)

Crossline KM Crossline KM (CPU=1)(CPU=1) Crossline WMCrossline WM (CPU=1/14)(CPU=1/14)Offset (km)Offset (km)0.30.3 3.53.5

0.80.8

3.33.3

Dep

th (k

m)

Dep

th (k

m)

Offset (km)Offset (km)0.30.3 3.53.5

Crossline KMCrossline KM (CPU=1)(CPU=1) Crossline WMCrossline WM (CPU=1/50)(CPU=1/50)(subsample)(subsample)

Offset (km)Offset (km)0.30.3 3.53.5

0.80.8

3.33.3

Dep

th (k

m)

Dep

th (k

m)

Offset (km)Offset (km)0.30.3 3.53.5

Inline: 0~4.6 km, Crossline: 0~3.8Inline: 0~4.6 km, Crossline: 0~3.8

KM (CPU=1)KM (CPU=1)

Horizontal Slices (Depth=2.5 km) Horizontal Slices (Depth=2.5 km)

WM (CPU=1/14)WM (CPU=1/14) WM (Sub, CPU=1/50)WM (Sub, CPU=1/50)

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model• 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model

• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model• 2-D Canadian Land Data2-D Canadian Land Data

• 3-D W. Texas Data3-D W. Texas Data• MVAMVA

Initial Migration VelocityInitial Migration Velocity

0000

1818

1.51.5

Horizontal Distance (km)Horizontal Distance (km)

Dep

th (k

m)

Dep

th (k

m) 2.12.1

1.51.5

(km

/s)

(km

/s)

KM Image with Initial VelocityKM Image with Initial Velocity0000

18 km18 km

1.51.5

Dep

th (k

m)

Dep

th (k

m)

00

1.51.5

Dep

th (k

m)

Dep

th (k

m)

KMVA Velocity Changes in the 1st IterationKMVA Velocity Changes in the 1st Iteration

5050

00

(m /s

)(m

/s)

KM Image with Initial VelocityKM Image with Initial Velocity

KM Image with Updated VelocityKM Image with Updated Velocity

9 km9 km

12601260

Dep

th (m

)D

epth

(m)

2 km2 km10701070

12601260

Dep

th (m

)D

epth

(m)

10701070

KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity00

1.51.5

Dep

th (k

m)

Dep

th (k

m)

KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity

0000

18 km18 km

1.51.5

Dep

th (k

m)

Dep

th (k

m)

00

1.51.5

Dep

th (k

m)

Dep

th (k

m)

KMVA Velocity Changes in the 1st Iteration (KMVA Velocity Changes in the 1st Iteration (CPU=6CPU=6))

5050

00

(m /s

)(m

/s)

WMVA Velocity Changes in the 1st Iteration (WMVA Velocity Changes in the 1st Iteration (CPU=1CPU=1))

5050

00

(m /s

)(m

/s)

WM Image with Initial VelocityWM Image with Initial Velocity

WM Image with Updated VelocityWM Image with Updated Velocity

9 km9 km

12601260

Dep

th (m

)D

epth

(m)

2 km2 km10701070

12601260

Dep

th (m

)D

epth

(m)

10701070

WMVA CIGs with Initial VelocityWMVA CIGs with Initial Velocity00

1.51.5

Dep

th (k

m)

Dep

th (k

m)

WMVA CIGs with Updated VelocityWMVA CIGs with Updated Velocity

KM Image with Initial VelocityKM Image with Initial Velocity 9 km9 km

12601260

Dep

th (m

)D

epth

(m)

2 km2 km10701070

KM Image with KMVA Updated VelocityKM Image with KMVA Updated Velocity

12601260

Dep

th (m

)D

epth

(m)

10701070

KM Image with WMVA Updated VelocityKM Image with WMVA Updated Velocity

12601260

Dep

th (m

)D

epth

(m)

10701070

Numerical TestsNumerical Tests

• 3-D Pt. Scatterer Model3-D Pt. Scatterer Model• 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model

• 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model• 2-D Canadian Land Data2-D Canadian Land Data

• Crosswell DataCrosswell Data

ModelModel

Crosswell Imaging of Synthetic Fault Data Crosswell Imaging of Synthetic Fault Data WMWMKM KM

00

210210

Dep

th (m

)D

epth

(m)

0 900 90

ConclusionsConclusions

• Typically WM has fewer artifacts than Typically WM has fewer artifacts than KMKM• Typically WM 2-50 times faster than than Typically WM 2-50 times faster than than KMKM• Tradeoff between quality and speedTradeoff between quality and speed• Conflicting dip arrivals still an issueConflicting dip arrivals still an issue

• Slant stack traces essential for efficiency Slant stack traces essential for efficiency • Fast velocity analysis toolFast velocity analysis tool

ConclusionsConclusions

Subdivision method is able to account Subdivision method is able to account for lateral-velocity variations and for lateral-velocity variations and attenuate some far-field artifactsattenuate some far-field artifacts

A post-migration processing: Cost 2XA post-migration processing: Cost 2X

Works on synthetic and field Works on synthetic and field poststack time migration data, poststack time migration data, improve resolution, mitigate some improve resolution, mitigate some migration artifactsmigration artifacts

ExpenseExpense

Acc

urac

yA

ccur

acy

Full-WaveFull-Wave

Ray-BeamRay-BeamKirchhoffKirchhoff

Migration Accuracy vs $$$Migration Accuracy vs $$$

Target RTMTarget RTM

No Approx.No Approx.

Multiple ArrivMultiple Arriv

Anti-aliasingAnti-aliasingPhase-ShiftPhase-Shift