Adaptive Grid Reverse-Time Migration Yue Wang. Outline Motivation and ObjectiveMotivation and Objective Reverse Time MethodologyReverse Time Methodology

Adaptive Grid Adaptive Grid Reverse-Time MigrationReverse-Time Migration

Yue WangYue Wang

OutlineOutline

• Motivation and ObjectiveMotivation and Objective

• Reverse Time MethodologyReverse Time Methodology

• Salt Dome Model TestSalt Dome Model Test

• Field Data TestField Data Test

• ConclusionsConclusions

ProblemProblem

• Kirchhoff migration is not Kirchhoff migration is not optimal for complex velocity optimal for complex velocity model.model.

Marmousi ModelMarmousi Model

Distance (km)Distance (km)

Dep

th (

km

)D

epth

(k

m)

33

00

00 99

Low-velocity wedgeLow-velocity wedge

ProblemProblem

Using first arrival time Using first arrival time

Difficulty in imagingDifficulty in imaging

Kirchhoff migrationKirchhoff migration

ProblemProblem

Reverse-Time Migration RTM) Reverse-Time Migration RTM)

Image complex structure Image complex structure ExpensiveExpensive

Using multi-arrival time Using multi-arrival time

SolutionSolution

Fast RTM Fast RTM

Variable grid size Variable grid size Variable time step Variable time step

ObjectiveObjective

• Develop fast reverse time migration for Develop fast reverse time migration for land and marine multi-component dataland and marine multi-component data

OutlineOutline






Reverse Time OperatorReverse Time Operator

Elastic wave equationElastic wave equation

A 2-4 staggered-grid FD solverA 2-4 staggered-grid FD solver

Variable Grid SizeVariable Grid Size

DistanceDistance

Dep

thD

epth

Low velocity Low velocity

High velocity High velocity


Fine grid (dx dz)Fine grid (dx dz)

Coarse grid (3dx 3dz)Coarse grid (3dx 3dz)

zz


Use wave equation to Use wave equation to propagate wavespropagate waves

Fine gridFine grid

Coarse gridCoarse grid

Variable Time StepVariable Time Step

coarse grid, fine time stepcoarse grid, fine time step

coarse grid, coarse time stepcoarse grid, coarse time step

DistanceDistance

Dep

thD

epth


zz

dtdt

tt

dtdt

3 dt3 dt

dtdt


zz

Fine time stepFine time step

Coarse time stepCoarse time step

tt

Use wave equation to Use wave equation to propagate wavespropagate waves


Falk et al. (1998, Geophys. Pros. ):Falk et al. (1998, Geophys. Pros. ):

1. Non-staggered-grid FD1. Non-staggered-grid FD

2. 2x time step change2. 2x time step change


The new method :The new method :

1. Staggered-grid FD1. Staggered-grid FD

2. 3x time step change2. 3x time step change

Numerical ResultsNumerical Results

Fine time stepFine time step

Time t1Time t1

Am

pli

tud

eA

mp

litu

de

Coarse time step Coarse time step DepthDepth

DepthDepth

Time t2Time t2

Am

pli

tud

eA

mp

litu

de

No artificial reflectionsNo artificial reflections

OutlineOutline






Salt ModelSalt Model


Dep

th (

km

)D

epth

(k

m)

2.72.7

00

00 4.54.5

Velocity ProfileVelocity Profile

Velocity (km/s)Velocity (km/s)

Dep

th (

km

)D

epth

(k

m)

Velocity (km/s)Velocity (km/s)1.51.5 44 00 222.72.7

00

Dep

th (

km

)D

epth

(k

m)

2.72.7

00

PP SS

Velocity ProfileVelocity Profile

Velocity (km/s)Velocity (km/s)

Dep

th (

km

)D

epth

(k

m)

Velocity (km/s)Velocity (km/s)1.51.5 44 00 222.72.7

00

PP SSFine grid sizeFine grid sizeFine time stepFine time step

Coarse grid sizeCoarse grid sizeCoarse time stepCoarse time step

Shot GatherShot GatherNormal StressNormal StressVerticalVerticalHorizontalHorizontal

Tim

e (s

) T

ime

(s)

Distance (km)Distance (km)22

00

0.90.9 3.63.6 Distance (km)Distance (km)0.90.9 3.63.6 Distance (km)Distance (km)0.90.9 3.63.6

Kirchhoff MigrationKirchhoff Migration


Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

Kirchhoff MigrationKirchhoff Migration


Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

Reverse Time MigrationReverse Time Migration


Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05


Dep

th (

km

)D

epth

(k

m)

2.52.5

00

0.450.45 4.054.05

Reverse Time MigrationReverse Time Migration

OutlineOutline






Processed CSGProcessed CSG

2.72.7

00Radial Component Radial Component Vertical Component Vertical Component

Tim

e (s

) T

ime

(s)

Trace NumberTrace Number Trace NumberTrace Number00 8080 00 8080

Common Offset GatherCommon Offset Gather((Vertical Component)Vertical Component)


Dep

th (

km

)D

epth

(k

m)

44

00

00 2727

Signal/Noise Ratio HighSignal/Noise Ratio High

Common Offset GatherCommon Offset Gather((Radial Component)Radial Component)


Dep

th (

km

)D

epth

(k

m)

44

00

00 2727

Signal/Noise Ratio LowSignal/Noise Ratio Low

Kirchhoff MigrationKirchhoff Migration((Vertical Component)Vertical Component)


Dep

th (

km

)D

epth

(k

m)

44

00

00 2727

Kirchhoff MigrationKirchhoff Migration((Radial Component)Radial Component)


Dep

th (

km

)D

epth

(k

m)

44

00

00 2727

RTMRTM


Dep

th (

km

)D

epth

(k

m)

44

00

00 2727

Comparison Comparison


Dep

th (

km

)D

epth

(k

m)

44

00

00 2727Distance (km)Distance (km)00 2727

RTMRTM KMKM

OutlineOutline





• Conclusions and Future WorkConclusions and Future Work

ConclusionsConclusions

• Variable RTM Variable RTM 10 times faster10 times faster than standard RTM than standard RTM• Migrates Land and marine multi-component dataMigrates Land and marine multi-component data• Use primary and multiple reflections for imagingUse primary and multiple reflections for imaging

AcknowledgementAcknowledgement

We are grateful to the 1999 sponsors We are grateful to the 1999 sponsors of the UTAM consortium for the of the UTAM consortium for the financial supportfinancial support

Raw CSGRaw CSGT

ime

(s)

Tim

e (s

)

2.72.7

00Radial Component Radial Component Vertical Component Vertical Component

00 8080 00 8080Trace NumberTrace Number Trace NumberTrace Number

Main Processing FlowMain Processing FlowGeometry assignment, datuming and so on

Trace editing

Surface wave attenuation, amplitude balancing

P-velocity analysis

S-velocity analysis

Relative gain compensation, surface velocity estimation

KM RTM

Shallow VelocityShallow Velocity


Dep

th (

km

)D

epth

(k

m)

0.40.4

00

00 2727

Future WorkFuture Work

• Apply the RTM scheme for data set with Apply the RTM scheme for data set with more complex structures.more complex structures.

Documents

Adaptive Grid Reverse-Time Migration Yue Wang. Outline Motivation and ObjectiveMotivation and Objective Reverse Time MethodologyReverse Time Methodology