LEAST-SQUARES MIGRATION LEAST-SQUARES MIGRATION OF BOTH PRIMARIES AND OF BOTH PRIMARIES AND

MULTIPLESMULTIPLES

Ruiqing He, Gerard Schuster

University of Utah

Oct. 2003

OutlineOutline

• Introduction

• Joint least-squares migration

• Experiment

• Conclusion

Former worksFormer works

• Brown (2002)• Duquet and Marfurt (1999)• Liu (1998)• Nemeth (1999) • Wang (1998)

IntroductionIntroduction

• Kirchhoff migration

-

-

-

d Lm' Tm L d

1 'TL L m m

Least-squares migrationLeast-squares migration

• Least-squares migration

-

- Iterative solution

Conjugate Gradient (CG) method

1( )T Tm L L L d

Joint least-squares migrationJoint least-squares migrationof primaries and multiplesof primaries and multiples

( )p md L L m

1[( )( )] ( )T T T Tp m p m p mm L L L L L L d

Modeling OperatorsModeling Operators

• Travel-times

• Geometric spreading

• Reflectance (angle-dependent)

• Non-linear

Multiple conditionMultiple condition

0

1

2

S Gg’

Tmultiple(S,G) = ming’[Tprimary(S,g’)+Tprimary(g’,G)]

Part of SMARRT modelPart of SMARRT model(m/s)

4500

1500

3000Depth (m)

Offset (m) 7,000

15,000

0

0

Synthetic zero-offset dataSynthetic zero-offset data

Offset (m) 7,0000

Time(sec.)

8.8

0

Kirchhoff migrationKirchhoff migration

Depth (m)

Offset (m) 7,000

15,000

0

0

Joint least-squares migrationJoint least-squares migration

Depth (m)

Offset (m) 7,000

15,000

0

0

Stack-of-scattering dataStack-of-scattering data

Time(sec.)

8.8

0

0 Offset (m) 7,000

Kirchhoff migrationKirchhoff migration

Depth (m)

Offset (m) 7,000

15,000

0

0

Joint least-squares migrationJoint least-squares migration

Depth (m)

Offset (m) 7,000

15,000

0

0

ConclusionConclusion

• Primary migration is improved.

• It is possible to attenuate multiple migration.

• Accurate forward modeling is vital.

• Optimum iteration number is a balance.

• It is costly.

ThanksThanks

Thank you.2002 members of UTAM for financial

support.