Applied Geophysics

, Volume 15, Issue 3–4, pp 448–465 | Cite as

Prestack AVA joint inversion of PP and PS waves using the vectorized reflectivity method

  • Wei Liu
  • Yan-Chun WangEmail author
  • Jing-Ye Li
  • Xue-Qing Liu
  • Wei Xie


Most current prestack AVA joint inversion methods are based on the exact Zoeppritz equation and its various approximations. However, these equations only reflect the relation between reflection coefficients, incidence angles, and elastic parameters on either side of the interface, which means that wave-propagation effects, such as spherical spreading, attenuation, transmission loss, multiples, and event mismatching of P- and S-waves, are not considered and cannot accurately describe the true propagation characteristics of seismic waves. Conventional AVA inversion methods require that these wave-propagation effects have been fully corrected or attenuated before inversion but these requirements can hardly be satisfied in practice. Using a one-dimensional (1D) earth model, the reflectivity method can simulate the full wavefield response of seismic waves. Therefore, we propose a nonlinear multicomponent prestack AVA joint inversion method based on the vectorized reflectivity method, which uses a fast nondominated sorting genetic algorithm (NSGA II) to optimize the nonlinear multiobjective function to estimate multiple parameters, such as P- wave velocity, S-wave velocity, and density. This approach is robust because it can simultaneously cope with more than one objective function without introducing weight coefficients. Model tests prove the effectiveness of the proposed inversion method. Based on the inversion results, we find that the nonlinear prestack AVA joint inversion using the reflectivity method yields more accurate inversion results than the inversion by using the exact Zoeppritz equation when the wave-propagation effects of transmission loss and internal multiples are not completely corrected.


Reflectivity method fast nondominated sorting genetic algorithm multiple parameters prestack AVA joint inversion 


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We would like to thank Liu Hai-Hao, Hu Rui-Qing, and Yue Zhan-Wei for assistance and advice. We also grateful to the reviewers for their helpful comments and suggestions.


  1. Aki, K., and Richards, P. G., 1980, Quantitative seismology: Theory and Methods: W. H. Freeman and Co., San Francisco America.Google Scholar
  2. Alkhalifah, T., 1997, Velocity analysis using nonhyperbolic moveout in transversely isotropic media: Geophysics, 62(6), 1839–1854.Google Scholar
  3. Castagna, J. P., 1991, Petrophysical imaging using AVO: The Leading Edge, 12(3), 172–178.Google Scholar
  4. Deb, K., 2000, An efficient constraint handling method for genetic algorithm: Computer Methods in Applied Mechanics and Engineering, 186, 311–338.Google Scholar
  5. Deb, K., and Agrawal, R. B., 1995, Simulated binary crossover for continuous search space: Complex Systems, 9, 115–148.Google Scholar
  6. Deb, K., and Agrawal, S., 1999, A niched–penalty approach for constraint handling in genetic algorithms: International Conference on Artificial Neural Networks and Genetic Algorithms, 235–243.Google Scholar
  7. Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T., 2002, A fast and elitist multi–objective genetic algorithm: NSGA–II: IEEE Transactions on Evolutionary Computation, 6(2), 182–197.Google Scholar
  8. Debski, W., and Tarantola, A., 1995, Information on elastic parameters obtained from the amplitudes of reflected waves: Geophysics, 60(5), 1426–1436.Google Scholar
  9. Fatti, J. L., Smith, G. C., Vail, P. J., Strauss, P. J., and Levitt, P. R., 1994, Detection of gas in sandstone reservoirs using AVO analysis: A 3–D seismic case history using the geostack technique: Geophysics, 59(9), 1362–1376.Google Scholar
  10. Fryer, G. J., 1980, A slowness approach to the reflectivity method of seismogram synthesis: Geophysical Journal International, 63(3), 747–758.Google Scholar
  11. Fryer, G. J., and Frazer, L. N., 1984, Seismic waves in stratified anisotropic media: Geophysical Journal of the Royal Astronomical Society, 78(3), 691–710.Google Scholar
  12. Fuchs, K., and Müller, G., 1971, Computation of synthetic seismograms with the reflectivity method and comparison with observations: Geophysical Journal International, 23(4), 417–433.Google Scholar
  13. Gardner, G. H. F., Gardner, L.W., and Gregory, A. R., 1974, Formation velocity and density–the diagnostic basis for stratigraphic traps: Geophysics, 39(6), 770–780.Google Scholar
  14. Goldberg, D. E., 1989, Genetic algorithms in search, optimization and machine learning: Addison–Wesley.Google Scholar
  15. Gouveia, W. P., and Scales, J. A., 1998, Bayesian seismic waveform inversion: Parameter estimation and uncertainty analysis: Journal of Geophysical Research, 103, 2759–2779.Google Scholar
  16. Gray, F. D., and Andersen, E., 2000, The application of AVO and inversion to the estimation of rock properties: 70th Annual International Meeting, SEG, Expanded Abstracts, 549–552.Google Scholar
  17. Heyburn, R., and Fox, B., 2010, Multi–objective analysis of body and surface waves from the Market Rasen (UK) earthquake: Geophysical Journal International, 181, 532–544.Google Scholar
  18. Jin, S., 1999, Characterizing reservoir by using jointly Pand S–wave AVO analysis: 69th Annual International Meeting, SEG, Expanded Abstracts, 687–690.Google Scholar
  19. Kennett, B. L. N., 1983, Seismic wave propagation in stratified media: Cambridge University Press, UK.Google Scholar
  20. Kozlovskaya, E., Vecsey, L., Plomerova, J., and Raita, T., 2007, Joint inversion of multiple data types with the use of multiobjective optimization: problem formulation and application to the seismic anisotropy investigations: Geophysical Journal International, 171(2), 761–779.Google Scholar
  21. Larsen, J. A., 1999, AVO inversion by simultaneous P–P and P–S inversion: M.S. thesis, University of Calgary.Google Scholar
  22. Li, T., and Mallick, S., 2015, Multicomponent, multiazimuth prestack seismic waveform inversion for azimuthally anisotropic media using a parallel and computationally efficient non–dominated sorting genetic algorithm: Geophysical Journal International, 200(2), 1134–1152.Google Scholar
  23. Liu, H. X., Li, J. Y., Chen, X. H., Hou, B., and Chen, L., 2016, Amplitude variation with offset inversion using the reflectivity method: Geophysics, 81(4), R185–R195.Google Scholar
  24. Lu, J., Yang, Z., Wang, Y., and Shi, Y., 2015, Joint PP and PS AVA seismic inversion using exact Zoeppritz equations: Geophysics, 80(5), R239–R250.Google Scholar
  25. Mahmoudian, F., and Margrave, G. F., 2004, Three parameter AVO inversion with PP and PS data using offset binning: SEG Technical Program Expanded Abstracts, 240–243.Google Scholar
  26. Mallick, S., 1999, Some practical aspects of prestack waveform inversion using a genetic algorithm: An example from the east Texas Woodbine gas sand: Geophysics, 64(2), 326–336.Google Scholar
  27. Mallick, S., and Frazer, L. N., 1987, Practical aspects of reflectivity modeling: Geophysics, 52(10), 1355–1364.Google Scholar
  28. Mukherji, A., Sen, M. K., and Stoffa, P. L., 2005, Travel time computation and prestack time migration in transversely isotropic media: Journal of Seismic Exploration, 13(3), 201–226.Google Scholar
  29. Müller, G., 1985, The reflectivity method: A tutorial: Journal of Geophysics, 58, 153–174.Google Scholar
  30. Ostrander, W. J., 1984, Plane–wave reflection coefficients for gas sands at non–normal angles of incidence: Geophysics, 49(10), 1637–1648.Google Scholar
  31. Padhi, A., and Mallick, S., 2013, Accurate estimation of density from the inversion of multicomponent prestack seismic waveform data using a nondominated sorting genetic algorithm: The Leading Edge, 32(1), 94–98.Google Scholar
  32. Padhi, A., and Mallick, S., 2014, Multicomponent prestack seismic waveform inversion in transversely isotropic media using a non–dominated sorting genetic algorithm: Geophysical Journal International, 196(3), 1600–1618.Google Scholar
  33. Phinney, R. A., Odom, R. I., and Fryer, G. J., 1987, Rapid generation of synthetic seismograms in layered media by vectorization of the algorithm: Bulletin of the Seismological Society of America, 77, 2218–2226.Google Scholar
  34. Sen, M. K., and Mukherji, A., 2003, t–p analysis in transversely isotropic media: Geophysical Journal International, 154(3), 647–658.Google Scholar
  35. Sen, M. K., and Roy, I. G., 2003, Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion: Geophysics, 68(6), 2026–2039.Google Scholar
  36. Shuey, R. T., 1985, A simplification of the Zoeppritz equations: Geophysics, 50(4), 609–614.Google Scholar
  37. Singh, V. P., Duquet, B., Léger, M., and Schoenauer, M., 2008, Automatic wave–equation migration velocity inversion using multi–objective evolutionary algorithms: Geophysics, 73(5), VE61–VE73.Google Scholar
  38. Stewart, R. R., 1990, Joint P and P–SV inversion: CREWES, Research Report 2.Google Scholar
  39. Tigrek, S., Slob, E. C., Dillen, M. W. P., Cloetingh, S. A. P. L., and Fokkema, J. T., 2005, Linking dynamic elastic parameters to static state of stress: Toward an integrated approach to subsurface stress analysis: Tectonophysics, 397, 167–179.Google Scholar
  40. Virieux, J., and Operto, S., 2009, An overview of full waveform inversion in exploration geophysics: Geophysics, 74(6), WCC1–WCC26.Google Scholar
  41. Wang, Y. M., Wang, X. P., Meng, X. J., and Niu, X. M., 2011, Prestack inversion of wide incident angle seismic data: 81th Annual International Meeting, SEG, Expanded Abstracts, 2507–2511.Google Scholar
  42. Zhao, H. S., Ursin, B., and Amundsen, L., 1994, Frequencywavenumber elastic inversion of marine seismic data: Geophysics, 59(12), 1868–1881.Google Scholar
  43. Zheng, X. D., 1991, Approximation of Zoeppritz equation and its application: Oil Geophysical Prospecting (in Chinese), 26(2), 129–144.Google Scholar
  44. Zhi, L. X., Chen, S. Q., and Li, X. Y., 2013, Joint AVO inversion of PP and PS waves using exact Zoeppritz equation: 83th Annual International Meeting, SEG, Expanded Abstracts, 457–461.Google Scholar
  45. Zhi, L. X., Chen, S. Q., Li, X. Y., and Zhang, W. L., 2015, An improved strategy for exact Zoeppritz equations AVA inversion: 85th Annual International Meeting, SEG, Expanded Abstracts, 654–658.Google Scholar

Copyright information

© Editorial Office of Applied Geophysics and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Wei Liu
    • 1
  • Yan-Chun Wang
    • 1
    Email author
  • Jing-Ye Li
    • 2
  • Xue-Qing Liu
    • 3
  • Wei Xie
    • 1
  1. 1.School of Geophysics and Information TechnologyChina University of GeosciencesBeijingChina
  2. 2.College of Geophysics and Information EngineeringChina University of PetroleumBeijingChina
  3. 3.Beijing Energy Oil & Gas Resources Development Co. Ltd.BeijingChina

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