LSMF for Suppressing Multiples Jianhua Yu University of Utah

Contents Motivation LSMF Inversion Numerical Examples Conclusions

Contents Motivation LSMF Inversion Numerical Examples: Conclusions

Demultiple Methods Radon transform Inverse scattering theory Prediction+subtraction

Benefits: Demultiple for coarse acquisition geometry Use both primary and multiple information

Contents Motivation LSMF Inversion Numerical Examples: Conclusions

Assuming that seismic data can be written mathematically as D : seismic data L : Primary forward operator p L : Multiple forward operator m R : Primary model R : Multiple model

LSMF equation (Nemeth, 1996) : Minimize the misfit function D : seismic data obs R : Primary model p R : Multiple model m

LSMF Inversion: Algorithm: Conjugate Gradient (CG)

Primary Modeling Operator W p a weight R A primary model d primary reflections

Multiple Modeling Operator W m a weight R m A multiple model d m multiples reflections

Operators for primary and multiple migration are the transpose of modeling operators Multiple initial model Wang (Geophys, 2003)

Demultiple Using LSMF Input CMP gathers Solving the following equation by CG algorithm

Demultiple using LSMF P=D-M Predicted multiple M Subtract multiple M from raw data D and get primary P P=D-M

Contents Motivation LSMF Inversion Numerical Examples Conclusions

Model Time (s) P+M P M LSMF P+M P M

CMP 300 (NS) Time (s) P+M M P

CMP 1700 (NS) Time (s) P+M M P

CMP 1300 (NS) Time (s) P+M M P

Before LSMF After LSMF Velocity Time (s) CMP 1300 (NS) 3.5 1.4 4

Before LSMF After LSMF Velocity Time (s) CMP 1300 (NS) 3.5 1.4 4

CMP 800 (Unocal) Time (s) P+M M P

CMP 900 (Unocal) Time (s) P+M M P

CMP 1100 (Unocal) Time (s) P+M M P

Velocity Velocity 1.4 3.2 1.4 3.2 Time (s) 4 Before LSMF After LSMF

Contents Motivation LSMF Inversion Numerical Examples: Conclusions

Conclusions Works for synthetic data and real data No limit to coarse geometry Straightforward to extend to 3D Regularization strategy required for shallow reflections 1-D model

ACKNOWLEDGMENTS 2003 UTAM Sponsors Unocal and Mobil for 2-D field data CHPC