Internal multiples in complex media: pseudo-depth/vertical-time monotonicity and

1. Internal multiples in complex media: pseudo-depth/vertical-time monotonicity and higher dimension analytic analysis Bogdan G. Nita --University of Houston-- M-OSRP Annual Meeting 20-21 April, 2005 University of Houston

2. What’s new in this talk • Analysis of the capability/limitation of the algorithm and ways of generalizing it without requiring a velocity model • First analysis of the pseudo-depth monotonicity assumption in the algorithm • First prestack analysis of the amplitude and phase properties of the inverse scattering internal multiple algorithm using analytic data.

3. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

4. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

5. Motivation and strategy • The industry’s trend is to explore in more complex and often ill defined subsurface conditions. • Data collected over these structures contain a wider range of events. • This research analyzes internal multiples in complex multi-D media and the capability of the inverse scattering algorithm to address them

6. Capability & limitations • The inverse scattering algorithm • Is part of a full series for inversion: its identification/separation from it assumes pseudo-depth monotonicity • It is the first term in a sub-series for removal – attenuation algorithm

7. Capability & limitations • Several M-OSRP efforts to study the potential of the inverse scattering attenuator and generalize its current capability • Nita and Weglein: analyze the monotonicity condition for complex arrivals • Ramirez and Weglein: from attenuation to elimination • Kaplan et al.: code development – tool for testing beyond analytic analysis

8. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

9. Primary and multiple • The concepts and definitions of what these terms mean evolve as we move to a heterogeneous multi-D earth • Sometimes we develop algorithms that address a given definition / concept and sometimes the algorithm itself suggests a broader definition

10. Evolution of “Primary” and “Multiple” • 1D normal incidence • upward + downward reflections + transmission • define • primary: one upward reflection • multiple: two or more • 2D-3D and specular reflection model • upward reflection • downward reflection • neither “Up” and “down” are defined with respect to the measurement surface.

11. Primary = one upward reflection = primary • First order internal multiple = 2 upward and 1 downward reflection = multiple

12. what about … ?

13. Definitions suggested by the inverse scattering internal multiple algorithm Prime and composite events • A prime event is not decomposable into other recorded events such that those subevent ingredients combine by adding and/or subtracting time of arrival to produce the prime. • A composite event is composed of subevents that combine in the above described manner to produce the event. Weglein and Dragoset (2005) editors: Internal multiples, SEG Reprint Volume

14. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

15. Internal multiple attenuation algorithm See e.g. Weglein et al. (2003) Inverse Problems Topical Review

16. Multiples are predicted by combining amplitude and phase information from three subevents - + Time of = time of

17. Internal multiple attenuation algorithm - Data - Predicted internal multiples Data with internal multiples attenuated

18. Experiment and data Pre-processing FS • wavelet deconvolution • direct wave removal • deghosting • FS multiples elimination primaries and internal multiples

19. Pre-requisites • Wavelet deconvolved from the data (Z. Guo) • Source and receiver ghosts eliminated (J. Zhang) • Free surface multiples eliminated • Appropriate sampling – data reconstruction (F. Miranda PhD) • Source and receiver arrays – (J. Zhang and Z. Guo)

20. Prediction of multiples • no wavelet • no direct wave • deghosted • no FS multiples FT over time coordinate FT over source & receiver horizontal coordinates

21. Prediction of multiples

22. Prediction of multiples IFT over vertical wavenumber Interpretation: FK migration – downward continuation –imaging

23. Internal multiple attenuation algorithm

24. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

25. Pseudo-depth monotonicity • The algorithm is searching for three arrivals in the data satisfying Pseudo-depth relation • Similar relation is satisfied by the actual depths

26. A monotonic function

27. Vertical-time monotonicity • The algorithm is searching for three arrivals in the data satisfying Actual vertical-times relation

28. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

29. Analytic example: model and data R and T are angle dependent

30. Analytic example: imaging the primaries • downward continuation (with ) OR • Imaging (Bruin imaging condition, Bruin et al. Geophysics 1990)

31. Internal multiple attenuation algorithm

32. Analytic example: the IM prediction OR

33. Conclusions of the analytic example • The algorithm exactly predicts the total time of the internal multiple • The amplitude is well approximated: for each p there is an extra T01T10 factor which is close to 1 but less than one. The overall predicted amplitude will also be smaller than but close to the actual. • Multiples with headwaves sub-events are also predicted

34. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared totraveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

35. Vertical time vs. traveltime monotonicity Example provided by Adriana Ramirez Actual depths of the subevents satisfy Vertical-times of the subevents satisfy Total travel-times of the subevents satisfy

36. Therefore… • This type of internal multiple is attenuated by the inverse scattering algorithm

37. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

38. Breaking the monotonicity High velocity zone Similar example provided by ten Kroode 2002 Wave Motion • Due to the high velocity zone, the vertical time of the blue event could be shorter than that of the red event • The blue event will be migrated at a higher pseudo-depth than the red event • The algorithm will not select these sub-events to predict the multiple

39. Expand the algorithm • Study the creation of such events in the forward scattering series • Matson ’96, ’97 and Weglein ’03 – the lower-higher-lower relationship was pointed to by the forward series • Selecting more terms in the inverse could lead to expansion of the algorithm to address these types of multiples • This expansion would not require a velocity model

40. Outline • Motivation and strategy. • The definition of primaries and multiples. • Inverse scattering internal multiple attenuation algorithm. • Pseudo-depth/vertical-time monotonicity • Analytic example for a vertically varying acoustic 2D medium. • Vertical time compared to traveltime monotonicity • Breaking the monotonicity • Summary and Conclusions

41. Summary • First analysis of the pseudo-depth monotonicity assumption of the internal multiple algorithm • First prestack analysis of the amplitude and phase properties of the inverse scattering internal multiple algorithm using analytic data.

42. Conclusions • Internal multiples in complex media are analyzed along with the assumptions of the attenuation algorithm to determine its capability to attenuate them • The algorithm assumes pseudo-depth/vertical-time monotonicity. • There are cases in which the monotonicity does not hold • The forward scattering series could show a way to generalize the present algorithm to address these types of internal multiples.

43. Acknowledgements • Co-author: Arthur B. Weglein. • Support: M-OSRP sponsors. • Helpful insights/discussions: Jon Sheiman, Fons ten Kroode, Einar Otnes. • Adriana Ramirez is thanked for providing one of the examples.