Jingfeng Zhang, Fang Liu, Kris Innanen and Arthur B. Weglein

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Presentation transcript:

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

Key points 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

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

Inverse Scattering Series Linear Non-linear Imaging subseries

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

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

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)

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

Leading Order Imaging Series distance to be shifted Z Z 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

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

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

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)

FSMR results (point receiver data) 1st order FSM Using the 1st term in the ISS FSMR series

Free surface multiple removal

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

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

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