1887
Volume 69, Issue 8-9
  • E-ISSN: 1365-2478
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Abstract

ABSTRACT

Seismic migration commonly yields an incomplete reconstruction of the Earth model due to restricted survey aperture, band‐limited frequency content and propagation effects. This affects both illumination and resolution of the structures of interest. Through the application of spatial convolution operators commonly referred to as point‐spread functions, simulated prestack depth‐migrated images incorporating these effects may be obtained. Such simulated images are tailored for analysing distortion effects and enhance our understanding of seismic imaging and subsequent interpretation. Target‐oriented point‐spread functions may be obtained through a variety of waveform and ray‐based approaches. Waveform approaches are generally more robust, but the computational cost involved may be prohibitive. Ray‐based approaches, on the other hand, allow for efficient and flexible sensitivity studies at a low computational cost, but inherent limitations may lead to less accuracy. To yield more insight into the similarities and differences between point‐spread functions obtained via these two approaches, we first derive analytical expressions of both wave‐ and ray‐based point‐spread functions in homogeneous media. By considering single‐point scatterers embedded in a uniform velocity field, we demonstrate the conditions under which the derived equations diverge. The accuracy of wave‐based and ray‐based point‐spread functions is further assessed and validated at selected targets in a subsection of the complex BP Statics Benchmark model. We also compare our simulated prestack depth migrated images with the output obtained from an actual prestack depth migration (reverse time migration). Our results reveal that both the wave‐ and ray‐based approaches accurately model illumination, resolution and amplitude effects observed in the reverse time‐migrated image. Furthermore, although some minor deviations between the wave‐based and ray‐based approaches are observed, the overall results indicate that both approaches can be used also for complex models.

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2021-10-08
2021-10-27
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References

  1. Amini, H., MacBeth, C. and Shams, A. (2020) Seismic modelling for reservoir studies: a comparison between convolutional and full‐waveform methods for a deep‐water turbidite sandstone reservoir. Geophysical Prospecting, 68(5), 1540–1553. https://doi.org/10.1111/1365‐2478.12936
    [Google Scholar]
  2. Aoki, N. and Schuster, G.T. (2009) Fast least‐squares migration with a deblurring filter. Geophysics, 74(6), WCA83–WCA93. https://doi.org/10.1190/1.3155162
    [Google Scholar]
  3. Ayeni, G. and Biondi, B. (2010) Target‐oriented joint least‐squares migration/inversion of time‐lapse seismic data sets. Geophysics, 75(3), R61–R73. https://doi.org/10.1190/1.3427635
    [Google Scholar]
  4. Beylkin, G., Oristaglio, M. and Miller, D. (1985) Spatial resolution of migration algorithms. In: A.J.Berkhout, J.Ridder and L.F.van derWaals, (Eds) Proceedings of the 14th International Symposium on Acoustic Imaging. Plenum Press, pp. 155–167.
    [Google Scholar]
  5. Bleistein, N., Cohen, J.K. and StockwellJr., J.W. (2001) Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion. Springer, New York. https://doi.org/10.1115/1.1399683
    [Google Scholar]
  6. Botter, C., Cardozo, N., Hardy, S., Lecomte, I. and Escalona, A. (2014) From mechanical modeling to seismic imaging of faults: a synthetic workflow to study the impacts of faults on seismic. Marine and Petroleum Geology, 57, 187–207. https://doi.org/10.1016/j.marpetgeo.2014.05.013
    [Google Scholar]
  7. Botter, C., Cardozo, N., Qu, D., Tveranger, J. and Kolyukhin, D. (2017) Seismic characterization of fault facies models. Interpretation, 5(4), SP9–SP26. https://doi.org/10.1190/INT‐2016‐0226.1
    [Google Scholar]
  8. Cao, J. (2013) Resolution/illumination analysis and imaging compensation in 3D dip‐azimuth domain. In: 83rd SEG Annual International Meeting, Houston, TX, USA, Expanded Abstracts, pp. 3931–3936. https://doi.org/10.1190/segam2013‐0380.1
    [Google Scholar]
  9. Carcione, J.M., Herman, G.C. and ten Kroode, A.P.E. (2002) Seismic modeling. Geophysics, 67(4), 1304–1325. https://doi.org/10.1190/1.1500393
    [Google Scholar]
  10. Carrara, W.G., Goodman, R.S. and Majewski, R.M. (1995) Spotlight Synthetic Aperture Radar: Signal Processing Algorithms. Artech House.
    [Google Scholar]
  11. Červený, V., Molotkov, I.A. and Pšenčík, I. (1977) Ray method in seismology. Charles University, Prague.
    [Google Scholar]
  12. Chen, J. and Schuster, G.T. (1999) Resolution limits of migrated images. Geophysics, 64(4), 1046–1053. https://doi.org/10.1190/1.1444612
    [Google Scholar]
  13. Claerbout, J.F. (1971) Toward a unified theory of reflector mapping. Geophysics, 36(3), 467–481. https://doi.org/10.1190/1.1440185
    [Google Scholar]
  14. Doerry, A. (2012) Basics of Polar‐Format Algorithm for Processing Synthetic Aperture Radar Images. Sandia Report, pp. 1–66.
  15. Eide, C.H., Schofield, N., Lecomte, I., Buckley, S.J. and Howell, J.A. (2018) Seismic interpretation of sill complexes in sedimentary basins: Implications for the sub‐sill imaging problem. Journal of the Geological Society, 175, 193–209. https://doi.org/10.1144/jgs2017‐096
    [Google Scholar]
  16. Ellison, D.K. and Innanen, K. (2016) Improved resolution in depth imaging through reflection static corrections derived from model‐based moveout. Crewes Report, 28, 1–12.
    [Google Scholar]
  17. Fehler, M., Huang, L., Wu, R.‐S. and Xie, X.‐B. (2005) Seismic image resolution: Numerical investigation of role of migration operator. In: 75th SEG Annual International Meeting, Houston, TX, USA, Expanded Abstracts, P1870–P1873. https://doi.org/10.1190/1.2148068
    [Google Scholar]
  18. Gelius, L.‐J. (1995) Generalized acoustic diffraction tomography. Geophysical Prospecting, 43(1), 3–29. https://doi.org/10.1111/j.1365‐2478.1995.tb00122.x
    [Google Scholar]
  19. Gelius, L.‐J., Johansen, I., Sponheim, N. and Stamnes, J.J. (1991) A generalized diffraction tomography algorithm. The Journal of the Acoustical Society of America, 89(2), 523–528. https://doi.org/10.1121/1.400376
    [Google Scholar]
  20. Gelius, L.‐J., Lecomte, I. and Tabti, H. (2002a) Analysis of the resolution function in seismic prestack depth imaging. Geophysical Prospecting, 50(5), 505–515. https://doi.org/10.1046/j.1365‐2478.2002.00331.x
    [Google Scholar]
  21. Gelius, L.‐J., Lecomte, I. and Hamran, S.‐E. (2002b) The concept of local parabolic‐wave imaging (LpI) in PSDM. In: 72nd SEG Annual International Meeting, Salt Lake City, UT, USA, Expanded Abstracts, P1184–P1187. https://doi.org/10.1190/1.1816862
    [Google Scholar]
  22. Gjøystdal, H., Iversen, E., Lecomte, I., Kaschwich, T. and Drottning, Å.A.M., J. (2007) Improved applicability of ray tracing in seismic acquisition, imaging, and interpretation. Geophysics, 72(5), SM261–SM271. https://doi.org/10.1190/1.2736515
    [Google Scholar]
  23. Grippa, A., Hurst, A., Palladino, G., Iacopini, D., Lecomte, I. and Huuse, M. (2019) Seismic imaging of complex geometry: forward modeling of sandstone intrusions. Earth and Planetary Science Letters, 513, 51–63. https://doi.org/10.1016/j.epsl.2019.02.011
    [Google Scholar]
  24. Guitton, A. (2004) Amplitude and kinematic corrections of migrated images for nonunitary imaging operators. Geophysics, 69(4), 1017–1024. https://doi.org/10.1190/1.1778244
    [Google Scholar]
  25. Hamran, S.‐E. and Lecomte, I. (1993) Local plane‐wavenumber diffraction tomography in heterogeneous backgrounds. Part 1: Theory. Journal of Seismic Exploration, 2, 133–146.
    [Google Scholar]
  26. Jakowatz, C.V.Jr., Wahl, D.E., Eichel, P.H., Ghiglia, D.C. and Thompson, P.A. (1996) Spotlight‐Mode Synthetic Aperture Radar: A Signal Processing Approach. Kluwer Academic Publishers.
    [Google Scholar]
  27. Jensen, K., Johansen, M.K., Lecomte, I., Janson, X., Tveranger, J. and Kaschwich, T. (2021) Paleokarst reservoirs: efficient and flexible characterization using point‐spread‐function‐based convolution modeling. Interpretation, 9(2), T331–T347. https://doi.org/10.1190/INT‐2020‐0130.1
    [Google Scholar]
  28. Jensen, K., Lecomte, I. and Kaschwich, T. (2018) Analyzing PSDM images in complex geology via ray‐based PSF convolution modeling. In: 88th SEG Annual International Meeting, Anaheim, CA, USA, Expanded Abstracts, pp. P3843–P3847. https://doi.org/10.1190/segam2018‐2995975.1
    [Google Scholar]
  29. Jiang, B. and Zhang, J. (2019) Least‐squares migration with a blockwise Hessian matrix: a prestack time‐migration approach. Geophysics, 84(4), R625–R640. https://doi.org/10.1190/geo2018‐0533.1
    [Google Scholar]
  30. Kjoberg, S., Schmiedel, T., Planke, S., Svensen, H.H., Millett, J.M., Jerram, D.A., et al. (2017) 3D structure and formation of hydrothermal vent complexes at the Paleocene‐Eocene transition, the Møre Basin, mid‐Norwegian margin. Interpretation, 5(3), SK65–SK81. https://doi.org/10.1190/INT‐2016‐0159.1
    [Google Scholar]
  31. Lecerf, D. and Besselievre, M. (2018) A new approach to compensate for illumination differences in 4D surveys with different individual acquisition geometries. First Break, 36, 71–76. https://doi.org/10.3997/1365‐2397.n0073
    [Google Scholar]
  32. Lecomte, I. (2008) Resolution and illumination analyses in PSDM: a ray‐based approach. The Leading Edge, 27, 650–663. https://doi.org/10.1190/1.2919584
    [Google Scholar]
  33. Lecomte, I. and Gelius, L.‐J. (1998) Have a look at the resolution of prestack depth migration for any model, survey and wavefields. In: 68th SEG Annual International Meeting, New Orleans, LA, USA, Expanded Abstracts, pp. P1112–P1115. https://doi.org/10.1190/1.1820082
    [Google Scholar]
  34. Lecomte, I., Gjøystdal, H. and Drottning, Å. (2003) Simulated prestack local imaging: a robust and efficient interpretation tool to control illumination, resolution, and time‐lapse properties of reservoirs. In: 73rd SEG Annual International Meeting, Dallas, TX, USA, Expanded Abstracts, pp. P1525–P1528. https://doi.org/10.1190/1.1817585
    [Google Scholar]
  35. Lecomte, I., Hamran, S.‐E. and Gelius, L.‐J. (2005) Improving Kirchhoff migration with repeated local plane‐wave imaging? A SAR‐inspired signal‐processing approach in prestack depth imaging. Geophysical Prospecting, 53(6), 767–785. https://doi.org/10.1111/j.1365‐2478.2005.00501.x
    [Google Scholar]
  36. Lecomte, I. and Kaschwich, T. (2008) Closer to real earth in reservoir characterization: a 3D isotropic/anisotropic PSDM simulator. In: 78th SEG Annual International Meeting, Las Vegas, NV, USA, Expanded Abstracts, pp. P1570–P1574. https://doi.org/10.1190/1.3059213
    [Google Scholar]
  37. Lecomte, I., Lavadera, P.L., Anell, I., Buckley, S.J., Schmid, D.W. and Heeremans, M. (2015) Ray‐based seismic modeling of geological models: Understanding and analyzing seismic images efficiently. Interpretation, 3(4), SAC71–SAC89. https://doi.org/10.1190/INT‐2015‐0061.1
    [Google Scholar]
  38. Lecomte, I., Lubrano‐Lavadera, P., Botter, C., Anell, I., Buckley, S.J., Eide, C.H., et al. (2016) 2(3)D convolution modelling of complex geological targets – beyond 1D convolution. First Break, 34, 99–107. https://doi.org/10.3997/1365‐2397.34.5.84451
    [Google Scholar]
  39. Lubrano‐Lavadera, P., Senger, K., Lecomte, I., Mulrooney, M.J. and Kühn, D. (2019) Seismic modelling of metre‐scale normal faults at a reservoir‐cap interface in Central Spitsbergen, Svalbard: implications for CO2 storage. Norwegian Journal of Geology, 99(2), 329–347. https://doi.org/10.17850/njg003
    [Google Scholar]
  40. Rabbel, O., Galland, O., Mair, K., Lecomte, I., Senger, K., Spacapan, J.B. and Manceda, R. (2018) From field analogues to realistic seismic modelling: a case study of an oil‐producing andesitic sill complex in the Neuquén Basin, Argentina. Journal of the Geological Society, 175(4), 580–593. https://doi.org/10.1144/jgs2017‐116
    [Google Scholar]
  41. Ristow, D. and Rühl, T. (1994) Fourier finite‐difference migration. Geophysics, 59(12), 1882–1893. https://doi.org/10.1190/1.1443575
    [Google Scholar]
  42. Schuster, G.T. (2017) Seismic Inversion. Society of Exploration Geophysicists. https://doi.org/10.1190/1.9781560803423
    [Google Scholar]
  43. Schuster, G.T. and Hu, J. (2000) Green's function for migration: continuous recording geometry. Geophysics, 65(1), 167–175. https://doi.org/10.1190/1.1444707
    [Google Scholar]
  44. Sjoeberg, T.A., Gelius, L.‐J. and Lecomte, I. (2003) 2‐D deconvolution of seismic image blur. In: 73rd SEG Annual International Meeting, Dallas, TX, USA, Expanded Abstracts, P1055–P1059. https://doi.org/10.1190/1.1817453
    [Google Scholar]
  45. Tang, Y. (2009) Target‐oriented wave‐equation least‐squares migration/inversion with phase‐encoded Hessian. Geophysics, 74(6), WCA95–WCA107. https://doi.org/10.1190/1.3204768
    [Google Scholar]
  46. Thomson, C.J., Kitchenside, P.W. and Fletcher, R.P. (2016) Theory of reflectivity blurring in seismic depth imaging. Geophysical Journal International, 205(2), 837–855. https://doi.org/10.1093/gji/ggw025
    [Google Scholar]
  47. Thorbecke, J., Wapenaar, K. and Swinnen, G. (2004) Design of one‐way wavefield extrapolation operators, using smooth functions in WLSQ optimization. Geophysics, 69(4), 1037–1045. https://doi.org/10.1190/1.1778246
    [Google Scholar]
  48. Toxopeus, G., Petersen, S. and Wapenaar, K. (2003) Improving geological modeling and interpretation by simulated migrated seismics. In: 65th EAGE Annual Conference and Exhibition, Stavanger, Norway, Expanded Abstracts, F34. https://doi.org/10.3997/2214‐4609‐pdb.6.F34
    [Google Scholar]
  49. Toxopeus, G., Thorbecke, J., Wapenaar, K., Petersen, S., Slob, E. and Fokkema, J. (2008) Simulating migrated and inverted seismic data by filtering a geologic model. Geophysics, 73(2), T1–T10. https://doi.org/10.1190/1.2827875
    [Google Scholar]
  50. Valenciano, A.A., Biondi, B. and Guitton, A. (2006) Target‐oriented wave‐equation inversion. Geophysics, 71(4), A35–A38. https://doi.org/10.1190/1.2213359
    [Google Scholar]
  51. Vinje, V., Iversen, E. and Gjøystdal, H. (1993) Traveltime and amplitude estimation using wavefront construction. Geophysics, 58(8), 1157–1166. https://doi.org/10.1190/1.1443499
    [Google Scholar]
  52. Xie, X.‐B., Wu, R.‐S., Fehler, M. and Huang, L. (2005) Seismic resolution and illumination: a wave‐equation based analysis. In: 75th SEG Annual International Meeting, Houston, TX, USA, Expanded Abstracts, P1862–P1865. https://doi.org/10.1190/1.2148066
    [Google Scholar]
  53. Youzwishen, C.F. and Margrave, G.F. (1999) Finite difference modelling of acoustic waves in Matlab. Crewes Report, 11, 1–19.
    [Google Scholar]
  54. Yu, J., Hu, J., Schuster, G.T. and Estill, R. (2006) Prestack migration deconvolution. Geophysics, 71(2), S53–S62. https://doi.org/10.1190/1.2187783
    [Google Scholar]
  55. Zhao, Z. and Sen, M. (2018) Fast image‐domain target‐oriented least‐squares reverse time migration. Geophysics, 83(6), A81–A86. https://doi.org/10.1190/1.2187783
    [Google Scholar]
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  • Article Type: Research Article
Keyword(s): Imaging , Modelling , Rays , Seismics and Wave
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