LEAST-SQUARES MIGRATION LEAST-SQUARES MIGRATION OF BOTH PRIMARIES AND OF BOTH PRIMARIES AND
MULTIPLESMULTIPLES
Ruiqing He, Gerard Schuster
University of Utah
Oct. 2003
Former worksFormer works
• Brown (2002)• Duquet and Marfurt (1999)• Liu (1998)• Nemeth (1999) • Wang (1998)
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)]
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.