LSMF for Suppressing MultiplesLSMF for Suppressing Multiples

Jianhua YuJianhua Yu

University of UtahUniversity of Utah

Contents Contents

Motivation

LSMF Inversion

Numerical Examples

Conclusions

Contents Contents

Motivation

LSMF Inversion

Numerical Examples:

Conclusions

Demultiple Methods Demultiple Methods

Radon transformRadon transform

Inverse scattering theoryInverse scattering theory

Prediction+subtractionPrediction+subtraction

Benefits: Benefits:

Demultiple for coarse acquisition Demultiple for coarse acquisition geometrygeometry

Use both primary and multiple Use both primary and multiple informationinformation

Contents Contents

Motivation

LSMF Inversion

Numerical Examples:

Conclusions

Assuming that seismic data can be written mathematically as

D : seismic data

L : Primary forward operatorp

L : Multiple forward operatorm

R : Primary model p

R : Multiple model m

mmpp LLD RR

D : seismic dataobs

R : Primary model p

R : Multiple model m

LSMF equation (Nemeth, 1996) :

Minimize the misfit function||LLD||E mmppobs RR

d

T

T

TT

TT

m

p

mmpm

mppp

m

p

L

L

LLLL

LLLL

R

R1

LSMF Inversion:LSMF Inversion:

Algorithm: Conjugate Gradient (CG)

twtxRtxx pprs

p (),(),,( 0 d

Primary Modeling OperatorPrimary Modeling Operator

000 )),|,(),|,( dxdttxzxzxtx rrss

Wp

a weight

Rp

A primary model

dp

primary reflections

twtxRtxx mmmrs

m (),(),,( 0 d

Multiple Modeling OperatorMultiple Modeling Operator

000 )),|,(),|,( mmrr

mss

mm dxdttxzxzxtx

Wm

a weight

Rm

A multiple model

dm

multiples reflections

Operators for primary and Operators for primary and multiple migration are the multiple migration are the transpose of modeling operators transpose of modeling operators

Multiple initial modelMultiple initial model

Wang (Geophys, 2003)Wang (Geophys, 2003)

Demultiple Using LSMF Demultiple Using LSMF

Input CMP gathers

d

T

T

TT

TT

m

p

mmpm

mppp

m

p

L

L

LLLL

LLLL

R

R1

Solving the following equation by CG algorithm

Demultiple using LSMF Demultiple using LSMF

Predicted multiple M

Subtract multiple M from raw data D and get primary P

P=D-M

Contents Contents

Motivation

LSMF Inversion

Numerical Examples

Conclusions

Model

P+M P M

P+M P M

LSMFTim

e (s

)

P+M M P

CMP 300 (NS) T

ime

(s)

P+M M P

CMP 1700 (NS) T

ime

(s)

P+M M P

CMP 1300 (NS)T

ime

(s)

Before LSMF After LSMF

VelocityT

ime

(s)

CMP 1300 (NS)

Velocity

3.5

1.4 40

0

Before LSMF After LSMF

VelocityT

ime

(s)

CMP 1300 (NS)

Velocity

3.5

1.4 4

P+M M P

CMP 800 (Unocal)T

ime

(s)

P+M M P

CMP 900 (Unocal)T

ime

(s)

P+M M P

CMP 1100 (Unocal)T

ime

(s)

Tim

e (s

)

4

01.4 3.2 1.4 3.2

Velocity Velocity

Before LSMF After LSMF

Contents Contents

Motivation

LSMF Inversion

Numerical Examples:

Conclusions

Conclusions Conclusions

Works for synthetic data and real dataNo limit to coarse geometry

Straightforward to extend to 3D

Regularization strategy required for shallow reflections1-D model

ACKNOWLEDGMENTSACKNOWLEDGMENTS

2003 UTAM Sponsors

Unocal and Mobil for 2-D field data

CHPC