1. Inverse scattering internal multiple elimination
Adriana C. Ramírez (M-OSRP), Arthur B. Weglein (M-OSRP) and Simon A. Shaw (ConocoPhillips).
A part of this project project was done at ConocoPhillips (Summer, 2006).
M-OSRP 2006 Annual Meeting, June 5 ~ June 7, 2007
M-OSRP report pages: 1-11

2. Key questions What are internal multiples?
Why should they be removed from the data?
What are the existing methods?
What does the Inverse Scattering internal multiple processing provides?

3. Outline Motivation History and background
ISS Internal multiple algorithms
Assumptions
Characteristics
Examples
Remarks
Acknowledgements

4. What are internal multiples?
Events
didn’t reflect in the earth FS
Reflected in the earth
no ghost
ghost
free surface multiples
primaries
internal multiples

5. “Primaries only” assumption
Why should they be removed from the data?
“Primaries only” assumption
AVO (amplitudes)
Velocity analysis
Misinterpretation of events
Coherent noise

6. What are the existing methods?
What do the Inverse Scattering
internal multiple processing algorithms
provide?
There are many methods that have been developed to deal with internal multiples that are effective within their assumptions.
e.g. radon transform, deconvolution, inverse scattering series, layer stripping, etc.

7. Inverse Scattering internal multiple algorithms
Require no subsurface information
Predict the arrival time of all internal multiples exactly
Predict amplitude information of internal multiples

8. Internal Multiple Prediction
Predicted multiple
Input
Result of adaptive subtraction

9. Internal Multiple Prediction
The more accurate the predicted multiple, the better the result of multiple attenuation
Predicted multiple
Input
Result of adaptive subtraction

10. Outline Motivation History and background
ISS Internal multiple algorithms
Assumptions
Characteristics
Examples
Remarks
Acknowledgements

11. Background Scattering Theory Inverse Scattering series Approach:
Identify task specific subseries
Free Surface Multiple Elimination
Internal Multiple Elimination
Depth imaging
Non-linear AVO
Data driven algorithms
No subsurface information required

12. History highlights time Weglein, Boyse and Anderson, 1981
Stolt and Jacobs, 1981
Inverse Scattering Series is
introduced to exploration seismology
Araújo, 1994
Weglein, Gasparotto, Carvalho and Stolt, 1997
Internal multiple attenuator IMA
(model-type independent formulation)
Coates and Weglein, 1996
Implementation of the IMA (elastic synthetics)
Matson, 1997
Matson, Corrigan, Young, 1998
IMA elastic background formulation &
1st implementation on field data
Weglein, Araújo, Carvalho, Stolt, Matson,
Coates, Corrigan, Foster, Shaw and Zhang, 2003.
Subevent interpretation of the internal
multiple algorithm.
Topical Review: Inverse Scattering Series
IMA displacements formulation
& implementation
Otnes, Hokstad and Sollie, 2004
Nita and Weglein, 2005
Study of headwaves as subevents
in the IMA, 1.5D analytical example.
Ramírez and Weglein, 2005
Leading order eliminator IME, amplitude
analysis & higher order terms.
Kaplan, Innanen, Otnes and Weglein, 2005
Implementation of the IMA
machine/architecture adaptive & efficiency improvement

13. Outline Motivation History and background
ISS Internal multiple algorithms
Assumptions
Characteristics
Examples
Remarks
Acknowledgements

14. Marine experiment and data preprocessingFS
Pre-processing
wavelet deconvolution
direct wave removal
deghosting
FS multiple elimination
primaries and internal multiples

15. Internal multiple attenuator
Araujo, 1994 and Weglein et al. 1997
where
i.e. it is a scaled data.
The internal multiple attenuator is a data-driven and model type independent algorithm.
It predicts the perfect time and always significantly reduces but doesn’t eliminate the 1st order internal multiples.

16. Data IN
Multiples OUT
Time of =
time of + -

17. Data IN
Multiples OUT
Amplitude of =
amplitude of *

18. Attenuation factor j=1 * = T01T10 T01R2T10 x R1 x T01R2T10 =
T01T T01R2R1R2T10 *
True amplitude

19. Attenuation factor j=1 j=2 T12T21 (T01T10)2 = T12T21*(T01T10)2*
True amplitude

20. T01T10
T12T21
(T01T10)2

21. Motivation for multiple elimination
“Primaries only” assumption
Adaptive subtraction is not always effective enough.
Destructive interference between primaries and multiples
The predicted amplitudes of converted waves multiples is 22% or less.

22. One multiple prediction?
Correct time
Correct amplitude
Wrong
amplitude

23.  Inverse Scattering Series
We solve the inverse scattering series by identifying task-specific subseries.
The internal multiple attenuator was identified as the first term in an infinite subseries.
 Strategy
Improve the attenuator’s amplitude prediction by: Identifying and selecting higher order terms for the internal multiple elimination series.

24. Solution Challenge
T01T10
T12T21
(T01T10)2

25. Solution Challenge
T01T10
DATA
attenuator
DATA
DATA
T12T21
(T01T10)2

26. Leading order closed form
Ramírez and Weglein, 2005. + + +
+ …
Attenuator
Leading order series (main contribution)

27. Higher order closed form
Ramírez and Weglein, 2005.

28. Outline Motivation History and background
ISS Internal multiple algorithms
Assumptions
Characteristics
Examples
Remarks
Acknowledgements

29. Model 1

30. Model 1

31. Attenuator True Amplitude of Primary(3.5s) = 0.0686118 p p p p Data
Data with attenuated multiples p p p p
p + im =

32. Closed form True Amplitude of Primary(3.5s) = 0.0686118 p p p p Data
Attenuator
Data with attenuated multiples p p p p
p + im =

33. Implementation Input Data(x,t) Forward Fourier Transforms Data(kgx,ω)
Multiply by (-2iqs) factor
b1(kgx, ω)= -2ikz Data(kgx, ω)
Stolt migration b1(kgx,z)
Non-linear “w” computation
Divide by (-2iqs) factor
Data_IM(kgx, ω )=b3(kgx, ω)/(-2iqs)
Inverse Fourier Transform

34. Divide by (-2iqs) factor Data_IM(kgx, ω )=b3(kgx, ω)/(-2iqs)

35. What happens when we have acoustic background and an elastic perturbation?
From Ken Matson’s thesis (1997), the first term in the inverse series with an elastic background is
We can write the effective data as
The internal multiple attenuator is given by

36. What happens when we have acoustic background and an elastic perturbation?
The internal multiple attenuator is given by
K. H. Matson 1997

37. What happens when we have acoustic background and an elastic perturbation?
The leading order closed form does not eliminate converted-wave multiples

38. Internal Multiple Prediction
Output
Input
Prediction
Input

39. The inverse scattering internal multiple elimination series is a model type independent theory.
The attenuator is a model-type independent algorithm as well as the leading order eliminator.

40. Density only model
Data
Prediction
AGC 1sec

41. Outline Motivation History and background
ISS Internal multiple algorithms
Assumptions
Characteristics
Examples
Remarks
Acknowledgements

42. Remarks
The first term in the removal series is an attenuator. It predicts the perfect time and always significantly attenuates the 1st order internal multiples.
Higher order terms towards elimination are determined by non-linear mathematical expressions that only involve the measured data and the reference medium.
The removal series for 1st order internal multiples, based on inverse scattering theory, is model-type independent.
A closed form for the leading order subseries allows for the elimination of a type of internal multiples.
Explain more , predict more
More effective
More realism
Pushing the boundaries
Whenever you can use physics to predict…
Don´t give adaptive more responsability

43. Acknowledgements
I would like to acknowledge the internship opportunity I had at ConocoPhillips (summer 2006), and thank the Subsurface Technology group for the excellent environment and encouragement of this research. Fernanda Araújo, Doug Foster, Bob Keys, Richard Day and Dan Whitmore are thanked for useful discussions.
Ken Matson (BP) and Sam Kaplan (Univ. of Alberta) are acknowledged for useful discussions.