ARTICLE

Density-sensitivity study about nonlinear multiparameter prestack inversion based on the exact Zoeppritz equation

QIANG GUO1 HONGBING ZHANG1 LIFENG LIANG2 ZUOPING SHANG3 GUOJIAO HUANG1
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1 College of Earth Science and Engineering, Hohai University, Nanjing 210098, P.R. China,
2 Department of Geography, Lingnan Normal University, Zhanjiang 524048, P.R. China,
3 College of Mechanics and Materials, Hohai University, Nanjing 210098, P.R. China,
JSE 2018, 27(3), 277–300;
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

Guo, Q., Zhang, H.B., Liang, L., Shang, Z.P. and Huang, G.J., 2018. Density-sensitivity study about nonlinear multiparameter prestack inversion based on the exact Zoeppritz equation. Journal of Seismic Exploration, 27: 277-300. Density information is of critical in identifying the presence and estimating the saturation of hydrocarbon in the reservoir. However, density is difficult to estimate based on conventional prestack inversion approach. In addition, prestack inversion is a nonlinear and ill-posed problem. In order to alleviate the ill-posedness and obtain reliable density information, we propose a nonlinear multiparameter prestack inversion method by constructing the edge-preserving regularized objective function based on anisotropic Markov random fields; we make an attempt to directly use the exact Zeoppritz equation and employ fast simulated annealing algorithm to solve the nonlinear optimization problem. Numerical analysis indicates that density parameter contributes relatively greater on altering the reflectivity magnitude at small incidence angle. In 2D synthetic test, we employ different gathers with specified angle range to test the inverted results and analyze the sensitivity of density. The synthetic results demonstrate that we can obtain reliable density result with small incidence angle by the proposed inversion method. In addition, density results can be improved by scaling the regularization term of density. The inverted density from the field data reveals detailed structural information and shows good agreement with the logging curves; the satisfactory density inverted results from small angle gather validates the conclusion from the numerical results.

Keywords
density-sensitivity
prestack seismic inversion
exact Zoeppritz equation
edge-preserving regularization
Markov random field
References
  1. Aki, K. and Richards, P.G., 1980. Quantitative Seismology: Theory and Methods. W.H.
  2. Freeman and Co., San Francisco.
  3. Aleardi, M. and Mazzotti, A., 2017. 1D elastic full-waveform inversion and uncertainty
  4. estimation by means of a hybrid genetic algorithm—Gibbs sampler approach.
  5. Geophys. Prosp., 65: 64-85.
  6. Bortfeld, R., 1961. Approximation to the reflection and transmission coefficients of plane
  7. longitudinal and transverse wave. Geophys. Prosp., 9: 485-502.
  8. Chapman, M., Liu, E. and Liu, X.Y., 2006. The influence of fluid sensitive dispersion
  9. and attenuation on AVO analysis. Geophys. J. Internat., 167: 89-105.
  10. Charbonnier, P., Blanc-Féraud, L. and Aubert, G., 1997. Deterministic edge-preserving
  11. regularization in computed imaging. IEEE Transactions on Image Processing, 6:
  12. 298-311.
  13. Chen, J., Zhang, Z. and Liu, E., 2006. Anisotropic inversion of traveltimes and
  14. polarization of wide-angle seismic data using simulated annealing. J. Seismic
  15. Explor., 15: 101-118.
  16. Downton, J. E., 2005. Seismic parameter estimation from AVO inversion. Ph.D. Thesis,
  17. University of Calgary.
  18. Downton, J.E. and Ursenbach, C., 2006. Linearized amplitude variation with offset (AVO)
  19. inversion with supercritical angles. Geophysics, 71: E49-ES5.
  20. Fatti, J.L., Smith, G.C. and Vail, P.J., 1994. Detection of gas in sandstone reservoirs using
  21. AVO analysis: A 3-D seismic case history using the Geostack technique.
  22. Geophysics, 59: 1362-1376.
  23. Geman, D. and Reynolds, G., 1992. Constrained restoration and the recovery of
  24. discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence,
  25. 14: 367-383.
  26. Geman, D. and Yang, C., 1995. Nonlinear image recovery with half-quadratic
  27. regularization. IEEE Transactions on Image Processing, 4: 932-946.
  28. Grossman, J.P., 2003. AVO and AVA inversion challenges: a conceptual overview.
  29. CREWES Research Report, 15.
  30. Guo, Q., Zhang, H., Saeed, W. and Shang, Z., 2016. Features of Markov random field
  31. about simultaneous inversion of pre-stack seismic data in transversely isotropic
  32. media. Extended Abstr., 78th EAGE Conf., Vienna: Th P6 04.
  33. Hilterman, F.J., 2001. Seismic Amplitude Interpretation. Distinguished Instructor Short
  34. Course. SEG/EAGE.
  35. Huang, H., Zhang, R., Shen, G., Guo, F. and Wang, J., 2011. Study of prestack elastic
  36. parameter consistency inversion methods. Appl. Geophys., 8: 311-318.
  37. Ingber, L., 1989. Very fast simulated re-annealing. Mathemat. Comput. Model., 12: 967-
  38. Ji, Y., Singh, S.C. and Hornby, B.E., 2000. Sensitivity study using a genetic algorithm:
  39. inversion of amplitude variations with slowness. Geophys. Prosp., 48: 1053-1073.
  40. Kabir, N., Crider, R., Ramkhelawan, R. and Baynes, C., 2006. Can hydrocarbon saturation
  41. be estimated using density contrast parameter. CSEG Recorder, 31: 31-37.
  42. Liang, L., Zhang, H., Dan, Z., Xu, Zi, Liu, X. and Cao, C., 2017. Prestack density
  43. inversion using the Fatti equation constrained by the P- and S-wave impedance and
  44. density. Appl. Geophys., 14: 133-141.
  45. Lines, L.R., 1998. Density contrast is difficult to determine from AVO. CREWES
  46. Research Report, 10.
  47. Ma, X.Q., 2002. Simultaneous inversion of prestack seismic data for rock properties using
  48. simulated annealing. Geophysics, 67: 1877-1885.
  49. Misra, S. and Sacchi, M.D., 2008. Global optimization with modelspace preconditioning:
  50. Application to AVO inversion. Geophysics, 73: R71-R82.
  51. Ostrander, W.J., 1984. Plane-wave reflection coefficients for gas sands at nonnormal
  52. angles of incidence. Geophysics, 49: 1637-1648.
  53. Paasche, H. and Tronicke, J., 2014. Nonlinear joint inversion of tomographic data using
  54. swarm intelligence. Geophysics, 79: R133-R149.
  55. Sacchi, M.D., Wang, J. and Kuehl, H., 2006. Regularized migration/inversion: new
  56. generation of imaging algorithms. CSEG Recorder, 31: 54-59.
  57. Sen, M.K. and Stoffa, P.L., 1996. Bayesian inference, Gibbs' sampler and uncertainty
  58. estimation in geophysical inversion. Geophys. Prosp., 44: 313-350.
  59. Sen, M.K. and Stoffa, P.L., 2013. Global Optimization Methods in Geophysical Inversion,
  60. Second Ed. Cambridge University Press, Cambridge, UK.
  61. Shuey, R.T., 1985. A simplification of the Zoeppritz equations. Geophysics, 50: 609-614.
  62. Tarantola, A. and Valette, B., 1982. Generalized nonlinear inverse problems solved using
  63. the least squares criterion. Rev.Geophys. Space Phys., 20: 219-232.
  64. Tarantola, A., 2005. Inverse Problem Theory and Model Parameter Estimation. SIAM.
  65. Theune, U., Jensas, I. and Eidsvik, J., 2010. Analysis of prior models for a blocky
  66. inversion of seismic AVA data. Geophysics, 75: C25—C35.
  67. Ursenbach, C., 2002. Optimal Zoeppritz approximations. Expanded Abstr., 72nd Ann.
  68. Internat. SEG Mtg., Salt Lake City:1897-1900.
  69. Varela, O.J., Torres-Verdin, C. and Sen, M.K., 2006. Enforcing smoothness and assessing
  70. uncertainty in non-linear one-dimensional prestack seismic inversion. Geophys.
  71. Prosp., 54: 239-259.
  72. Yan, Z. and Gu, H., 2013. Non-linear prestack seismic inversion with global optimization
  73. using an edge-preserving smoothing filter. Geophys. Prosp., 61: 747-760.
  74. Birr and Sacchi, M.D., 2006. Edge preserving imaging, J. Seismic Explor..
  75. 15: 45-58.
  76. Zhang, H., Shang, Z. and Yang, C., 2007. A non-linear regularized constrained impedance
  77. inversion. Geophys. Prosp., 55: 819-833.
  78. Zhang, H., Shang, Z. and Yang, C., 2009. Adaptive reconstruction method of impedance
  79. model with absolute and relative constraints. J. Appl. Geophys., 67: 114-124.
  80. Zhi, L., Chen, S. and Li, X.Y., 2016. Amplitude variation with angle inversion using the
  81. exact Zoeppritz equations - Theory and methodology. Geophysics, 81: NI-N15.
  82. Zong, Z., Yin, X. and Wu, G., 2012. AVO inversion and poroelasticity with P- and S-
  83. wave moduli. Geophysics, 77: N17—N24.
  84. Zong, Z., Yin, X. and Wu, G., 2013. Elastic impedance parameterization and inversion
  85. with Young’s modulus and Poisson’s ratio. Geophysics, 78: N35—N42.
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing