ARTICLE

Correction of primary amplitudes for plane-wave transmission loss through an acoustic or absorptive overburden with the inverse scattering series internal multiple attenuation algorithm: an initial study and 1D numerical examples

JOSÉ M. LIRA* KRISTOPHER A. INNANEN ARTHUR B. WEGLEIN ADRIANA C. RAMIREZ**
Show Less
Dept. of Physics, M-OSRP, University of Houston, Houston, TX, U.S.A.,
* Petrobras, CENPES-PDEXP-GEOF, Rio de Janeiro, Brazil.,
** Western-Geco, Houston, TX, U.S.A.,
JSE 2010, 19(2), 103–120;
Submitted: 9 June 2025 | Revised: 9 June 2025 | Accepted: 9 June 2025 | Published: 9 June 2025
© 2025 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/ )
Abstract

The objective of extracting the spatial location of a reflector, and its local angle-dependent reflection coefficient, from seismic data, depends on the ability to identify and to remove the effect on primary amplitudes of propagation down to and back from the reflector. All conventional methods that seek to correct for such transmission loss require estimates of the properties of the overburden. In this paper we propose a fundamentally new approach that will in principle permit correction of primaries for such transmission loss without requiring overburden properties as input. The approach is based on the amplitude of the first term of the inverse scattering series internal multiple attenuation algorithm, which predicts the correct phase and approximate amplitude of first order internal multiples. The amplitude is estimated to within a factor determined by plane wave transmission loss down to and across the reflector producing the event’s shallowest downward reflection. Hence, the amplitude difference between a given predicted and actual multiple, both of which are directly available from the data and the algorithm output, in principle contain all necessary information to correct specific primary reflections for their overburden transmission losses. We identify absorptive overburdens/media as requiring particular focus, so as a first step, previous amplitude analysis of the internal multiple attenuation algorithm is here extended to include stratified absorptive media. Using this newly derived relationship between predicted and actual internal multiples, and existing results for acoustic/elastic media, correction operators, to be applied to specific, isolated primaries in both types of media, are then computed using combinations of multiples and their respective predictions. We illustrate the approach on synthetic data for the absorptive case with three earth models with different Q profiles. Further research into the ampli- tudes of the plane wave internal multiple predictions in 2D and 3D media is a likely pre-requisite to field data application of this concept-level algorithm.

Keywords
absorption
internal multiples
inverse scattering series
transmission losses
References
  1. Aki, K. and Richards, P.G., 2002. Quantitative Seismology, 2nd ed. University Science Books, San
  2. Francisco.
  3. Aratjo, F.V., 1994. Linear and non-linear methods derived from scattering theory: backscattered
  4. tomography and internal multiple attenuation. Ph.D. thesis, Universidade Federal da Bahia,
  5. Brazil.
  6. Araujo, F.V., Weglein, A.B., Carvalho, P.M. and Stolt, R.H., 1994. Internal multiple attenuation.
  7. Extended Abstr., 56th AEGE Conf., Vienna: H036.
  8. Carvalho, P.M., Weglein, A.B. and Stolt, R.H., 1991. Examples of a nonlinear inversion method
  9. based on the T-matrix of scattering theory: Application to multiple suppression. Expanded
  10. Abstr., 61st Ann. Internat. SEG Mtg., Houston: 1319-1322.
  11. Kaplan, S.T., Robinson, W. and Innanen, K.A., 2005. Optimizing internal multiple attenuation
  12. algorithms for large distributed computing systems. Mission-Oriented Seismic Research
  13. Program (M-OSRP) Ann. Report.
  14. Matson, K.H., 1997. An Inverse-scattering Series Method for Attenuating Elastic Multiples from
  15. Multi-component Land and Ocean Bottom Seismic Data. Ph.D. thesis, Univ. of British
  16. Columbia, Vancouver.
  17. Nita, B.G. and Weglein, A.B., 2005. Inverse scattering internal multiple attenuation algorithm in
  18. complex multi-d media. Technical report, Mission-Oriented Seismic Research Project, Univ.
  19. of Houston.
  20. Ramirez, A.C., 2007. I -Inverse scattering subseries for 1:Removal of internal multiples and
  21. 2:Depth imaging primaries; II -Green’s theorem as the foundation of interferomerty and
  22. guiding new practical methods and applications. Ph.D. thesis, Univ. of Houston.
  23. Ramirez, A.C. and Weglein, A.B., 2005a. An inverse scattering internal multiple elimination
  24. method: Beyond attenuation, a new algorithm and initial tests. Expanded Abstr., 75th Ann.
  25. Internat. SEG Mtg;, Houston: 2115-2118.
  26. Ramirez, A.C. and Weglein, A.B., 2005b. Progressing the analysis of the phase and amplitude
  27. prediction properties of the inverse scattering internal multiple attenuation algorithm. J.
  28. Seismic Explor., 13: 283-301.
  29. Weglein, A.B. and Matson, K.H., 1998. Inverse Scattering Internal Multiple Attenuation: An
  30. Analytic Example and Subevent interpretation. Abstr., SPIE Conf. Mathemat. Meth.
  31. Geophys. Imaging: 108-117.
  32. Weglein, A.B. and Stolt, R.H., 1999. Migration-Inversion Revisited. The Leading Edge, 18: 950.
  33. Weglein, A.B. and Dragoset, W.H., 2005. Multiple Attenuation. Geophysics reprint series. SEG,
  34. Tulsa, OK.
  35. Weglein, A.B., Aragjo, F.V., Carvalho, P.M., Stolt, R.H., Matson, K.H., Coats, R.T., Corrigan,
  36. D., Foster, D.J., Shaw, S.A. and Zhang, H., 2003. Inverse scattering series and seismic
  37. exploration. Inverse Problems, 19: R27-R83.
  38. Weglein, A.B., Aratjo Gasparotto, F., Carvalho, P.M. and Stolt, R.H., 1997. An inverse-scattering
  39. series method for attenuating multiples in seismic reflection data. Geophysics, 62: 1975-
Share
Back to top
Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing