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Why exactly do multiples need to be removed in direct seismic processing methods? And what about indirect methods?

ARTHUR B. WEGLEIN
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M-OSRP, Physics Department, University of Houston, 3507 Cullen Boulevard, Houston, TX. 77204, U.S.A.,
JSE 2022, 31(1), 1–18;
Submitted: 3 July 2021 | Accepted: 6 December 2021 | Published: 1 February 2022
© 2022 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

Weglein, A.B., 2022. Why exactly do multiples need to be removed in direct seismic processing methods? And what about indirect methods? Journal of Seismic Exploration, 31: 1-18. This paper provides a new and detailed analysis on why multiples need to be removed in all current seismic processing methods - without any exception. We cast a wide and inclusive net - covering all direct methods and indirect methods. That includes methods that use multiples to estimate an image of an unrecorded primary, as well as within model-matching methods, for example, FWI. We include methods that require or do not require subsurface information. We conclude that all methods require multiples to be removed, either initially, or eventually within the method, and its application. A new migration method, Stolt-Claerbout III Migration for Heterogeneous and Discontinuous Media, plays an essential and fundamental role in that new insight, understanding and perspective. This is the first paper of a two-paper set, this one explaining “why” multiples are a pressing, and increasingly prioritized necessity and challenge, now and for the foreseeable future. The second paper describes “how” multiples are removed, with a tool- box perspective, and how to make cost-effective choices among options - and a recognition of both recent progress and challenges and open-issues.

Keywords
multiples
primaries
imaging
migration
direct and indirect
continuous and discontinuous velocity migration
FWI and smooth migration velocity
multiple removal
illumination
References
  1. Ben-Hadj-Ali et al. (2008, 2009), Biondi and Sava (1999), Biondi and Symes(2004), Brandsberg-Dahl et al. (1999), Chavent and Jacewitz (2011), Fitchner(2011), Guasch et al. (2012), Kapoor et al. (2012), Rickett and Sava (2002),
  2. Sava et al. (2005), Sava and Fomel (2003), Sirgue et al. (2009, 2010, 2012),
  3. Symes and Carazzone (1991), Tarantola (1987), Zhang and Biondi (2013).
  4. Many wrong velocity models can and will also satisfy a flat common-image-gather criterion, especially under complex imaging circumstances.
  5. Another type of indirect method, FWI, is a model matching methodologythat can input any data set, consisting of primaries, free surface multiplesand internal multiples. Among FWI references are Brossier et al. (2009),
  6. Crase et al. (1990), Gauthier et al. (1986), Nolan and Symes (1997), Pratt(1999), Pratt and Shipp (1999), Sirgue et al. (2010), Symes (2008), Tarantola(1984, 1986), Valenciano et al. (2006), Vigh and Starr (2008), Zhou et al.(2012). In practice, primaries are considered not enough, not full enough,and primaries and all multiples are apparently too much to match, a bit toofull. And matching primaries and free surface multiples, are the perfectdegree of fullness. Therefore, within current FWI practice, internalmultiples are first removed and then primaries and free surface multiples arematched. Hence, an internal multiple removal is called for in FWI.
  7. The output from FWI is (at best) a smooth velocitymodel, and all multiples need to be removed when migratingwith a smooth velocity model
  8. As was documented in a recent SEG/DGS Workshop on Velocity Model
  9. Building Saad et al. (2021) and the final/wrap-up presentation by Weglein(2021), FWI has been useful in providing an improved smooth velocity formigration. As we pointed out earlier in this paper, with a smooth migrationvelocity model, all multiples must be removed. Hence, within FWI todayinternal multiples need to be removed, and the use of the smooth velocityoutput from FYI, require all multiples to be removed in the use of thatvelocity in migration methods.
  10. Regarding AVO: AVO is a first term in a modeling equation for PP datarun backwards - and, hence, is not a direct method, and assumes that multipleshave been removed before the Zoeppritz equations are applied to estimate therelative changes in earth mechanical properties.
  11. Therefore, either initially or ultimately all multiples must be removed inall indirect seismic methods.We suggest the videos in the link belowhttp://youtube.com/playlist?list=PL41Tzy Y 3tP VenlpnBQRJKurk Sbvmw6X Wsto complement the above analysis and conclusions.CONCLUSIONS
  12. All current migration velocity analysis methods can (at best) produce asmooth continuous migration velocity model. For direct seismic methods,that require subsurface information, for example, migration with a smoothvelocity model, all multiples will cause false images that can masquerade asor interfere with structure - and need to be removed. To clearly analyze therole of primaries and multiples in imaging requires a new form of migration(that we label Stolt Claerbout III for heterogeneous media) that can image ina discontinuous medium without artifacts. With an accurate discontinuousvelocity model, the new Stolt-Claerbout HI Migration for heterogeneousmedia, we showed that multiples cause no harm and provide no benefit. If(in the future) we could find an accurate discontinuous velocity model andused the Stolt-Claerbout III Migration for discontinuous media, we wouldhave no reason to remove multiples. However, currently and for theforeseeable future, we are confined to (at best) improving a smoothapproximate velocity, (e.g., output from FWI) and hence the absolute needto remove all multiples, before migration for structure and amplitudeanalysis, remains in place and of very high priority.
  13. To use a recorded multiple to estimate the RTM image of an unrecordedprimary, we assume the recorded multiple consists of two subevents, onerecorded and the other not recorded. Let’s further assume that the un-recorded subevent is an unrecorded primary. Then the recorded multiple, andthe recorded subevent of the multiple, are used to estimate the image of anunrecorded primary subevent of the multiple. To satisfy the latterassumption, unrecorded subevents of the recorded multiple, that are (notunrecorded primaries but rather) unrecorded multiples, must be removed - sincethe unrecorded event is migrated with a form of RTM using a smooth velocitymodel. Furthermore, the original recorded multiple must be removed to imagerecorded primaries, again with a smooth velocity model. Hence, recordedand unrecorded multiples must be removed to image recorded andunrecorded primaries, respectively.
  14. The inverse scattering series is the only direct inversion method for amulti-dimensional earth, and in addition it doesn’t require any subsurfaceinformation (including velocity) to be known, estimated or determined. Itcontains distinct isolated task subseries that remove free surface and internalmultiples. Only primaries are called for in task specific subseries for structuredetermination, parameter estimation and Q compensation, the latter withoutknowing, estimating or determining Q. If multiples were needed in the onlydirect multidimensional inverse method, the inverse scattering series, toachieve imaging and parameter estimation and Q compensation, it would notcontain isolated task subseries whose sole purpose and existence is designedto remove them. Direct methods are purposeful, and do not remove eventsthat are needed to carry out its purposes.
  15. For indirect methods, based on satisfying a criterium that only relate toprimaries, e.g., CIG flatness, multiples must first be removed.
  16. FWI is model matching of primaries and multiples and currently is able(at best) to output a smooth velocity model for migration. Multiples must beremoved when using a smooth velocity for migration. For the smoothmigration velocity output of FWI to be useful, for imaging and inversion,multiples must first be removed.
  17. Hence, all direct and indirect seismic processing methods require allmultiples to be removed, either initially or eventually.ACKNOWLEDGEMENTS
  18. We appreciate the encouragement and support of M-OSRP sponsors.
  19. Dr. J.D. Mayhan is thanked for his assist in preparing this paper. Dr. Jose
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing
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