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:

2. 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

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. 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

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

11. 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)
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

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