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M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007

Delve into the counter-intuitive nature of LOIS and HOIS in inverse scattering, exploring performance differences and the impact of shifting arguments. Find out how deeper mediums influence interface location and the counter-intuitive results of LOIS.

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M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007

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  1. Towards understanding the intermediate activity within the inverse scattering series Jingfeng Zhang, Fang Liu, Kris Innanen and Arthur B. Weglein M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007 M-OSRP report pages: 149-159

  2. Keypoints • LOIS is counter-intuitive, • Some terms have been inadvertently included • It’s just an intermediate step • There are examples in inverse scattering subseries where intermediate steps seem to working at cross purposes to the overall goal. • That apparent cross purposes is in fact entirely purposeful (e.g., FSMR). • Careful consideration of the diagrams is necessary in order to seek further progress on imaging • LOIS; HOIS two possibilities

  3. Inverse Scattering Series Forward scattering (Born) Series: Definition of “data” Assume:

  4. Inverse Scattering Series Linear Non-linear Imaging subseries

  5. LOIS and HOIS Leading-Order Imaging Series: High-Order Imaging Series: 1. What are their the performance? 2. What difference it will make if the complicated argument moved to the other side of the equation? Count-intuitive

  6. LOIS and HOIS Leading-Order Imaging Series: High-Order Imaging Series: 1. What are their the performance? 2. What difference it will make if the complicated argument moved to the other side of the equation? Count-intuitive

  7. Performance of LOIS and HOIS • LOIS: provides encouraging results for small contrast models • HOIS: • For 1D medium, HOIS can accurately locate the second interface • Very good results even for big contrast models (e.g. salt model)

  8. LOIS and HOIS Leading-Order Imaging Series: High-Order Imaging Series: 1. What are their the performance? 2. What difference it will make if the complicated argument moved to the other side of the equation? Count-intuitive

  9. distance to be shifted Z Z Leading Order Imaging Series Count-intuitive Deeper medium contributes to the location of shallower interface Deeper events/primary has information that has nothing to do with the location of shallower interface

  10. distance to be shifted Z Z Leading Order Imaging Series Deeper medium does not contributes to the location of shallower interface

  11. High Order Imaging series High-Order Imaging Series: Original “deduced” High-Order Imaging Series: This is Fang Liu’s intuitive leap: guarantee only shallower medium information will help the location of an interface Deeper events/primary has information that has nothing to do with the location of shallower interface

  12. Why counter-intuitive LOIS results? • Two possibilities: • In the derivation of the original LOIS, we inadvertently collected terms that included contributions from deeper within the medium. • There is no inadvertent collecting, this is just an intermediate step, after more imaging terms been added, comprehensible results will be obtained (i.e., deeper medium will not contribute). • Example: ISS free surface multiple removal algorithm (Carvalho, 1992 and Weglein et.al., 1997)

  13. FSMR results (point receiver data) At (3750,2.5) 1st order FSM Using the 1st term in the ISS FSMR series

  14. Free surface multiple removal

  15. Concluding Remarks • LOIS is counter-intuitive, • Some terms have been inadvertently included • It’s just an intermediate steps • There are examples in inverse scattering subseries where intermediate steps seem to working at cross purposes to the overall goal. • That apparent cross purposes is in fact entirely purposeful (e.g., FSMR). • Careful consideration of the diagram is necessary in order to seek further progress on imaging • LOIS; HOIS two possibilities

  16. Acknowledgements • M-OSRP sponsors and colleagues • Simon Shaw (ConocoPhillips) are thanked for valuable discussions

  17. Thank you Prof. Weglein ConocoPhillips, Geotrace, BP

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