Prestack Multi-Gather Simultaneous Inversion of Elastic Parameters Using Multiple Regularization Constraints

Abstract

Inversion of Young’s modulus, Poisson’s ratio and density from pre-stack seismic data has been proved to be feasible and effective. However, the existing methods do not take full advantage of the prior information, without considering the lateral continuity of the inversion results, and need to invert the reflectivity first. In this paper, we propose multi-gather simultaneous inversion for pre-stack seismic data. Meanwhile, the total variation (TV) regularization, L1 norm regularization and initial model constraint are used. In order to solve the objective function contains L1 norm, TV norm and L2 norm, we develop an algorithm based on split Bregman iteration. The main advantages of our method are as follows: (1) The elastic parameters are calculated directly from objective function rather than from their reflectivity, therefore the stability and accuracy of the inversion process can be ensured. (2) The inversion results are more accordance with the geological prior information. (3) The lateral continuity of the inversion results are improved. The proposed method is illustrated by theoretical model data and experimented with a 2-D field data.

This is a preview of subscription content, log in to check access.

References Cited

  1. Baraniuk, R., 2007. Compressive Sensing. IEEE Signal Processing Magazine, 24(4): 118–121. https://doi.org/10.1109/msp.2007.4286571

    Article  Google Scholar 

  2. Chen, S. S., Donoho, D. L., Saunders, M. A., 2001. Atomic Decomposition by Basis Pursuit. SIAM Review, 43(1): 129–159. https://doi.org/10.1137/s003614450037906x

    Article  Google Scholar 

  3. Donoho, D. L., 2006. Compressed Sensing. IEEE Transactions on Information Theory, 52(4): 1289–1306. https://doi.org/10.1109/TIT.2006.871582

    Article  Google Scholar 

  4. Gholami, A., 2015. Nonlinear Multichannel Impedance Inversion by Total-Variation Regularization. Geophysics, 80(5): R217–R224. https://doi.org/10.1190/geo2015-0004.1

    Google Scholar 

  5. Goldstein, T., Osher, S., 2009. The Split Bregman Method for L1-Regularized Problems. SIAM Journal on Imaging Sciences, 2(2): 323–343. https://doi.org/10.1137/080725891

    Article  Google Scholar 

  6. Hamid, H., Pidlisecky, A., 2015. Multitrace Impedance Inversion with Lateral Constraints. Geophysics, 80(6): M101–M111. https://doi.org/10.1190/geo2014-0546.1

    Article  Google Scholar 

  7. Harris, N. B., Miskimins, J. L., Mnich, C. A., 2011. Mechanical Anisotropy in the Woodford Shale, Permian Basin: Origin, Magnitude, and Scale. The Leading Edge, 30(3): 284–291. https://doi.org/10.1190/1.3567259

    Article  Google Scholar 

  8. Huang, W., Zhou, H. W., 2015. Least-Squares Seismic Inversion with Stochastic Conjugate Gradient Method. Journal of Earth Science, 26(4): 463–470. https://doi.org/10.1007/s12583-015-0553-8

    Article  Google Scholar 

  9. Mavko, G., Mukerji, T., Dvorkin, J., 2009. The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media. Cambridge University Press, New York. 23. https://doi.org/10.1017/CBO9780511626753

    Google Scholar 

  10. Pérez, D. O., Velis, D. R., Sacchi, M. D., 2014. Blocky Inversion of Prestack Seismic Data Using Mixed-Norms. 2014 SEG Annual Meeting, Denver. 3106–3111. https://doi.org/10.1190/segam2014-0801.1

    Google Scholar 

  11. Rickman, R., Mullen, M. J., Petre, J. E., et al., 2008. A Practical Use of Shale Petrophysics for Stimulation Design Optimization: All Shale Plays are not Clones of the Barnett Shale. SPE Annual Technical Conference and Exhibition, Halliburton. 21–24. https://doi.org/10.2118/115258-MS

    Google Scholar 

  12. Rudin, L. I., Osher, S., Fatemi, E., 1992. Nonlinear Total Variation Based Noise Removal Algorithms. Physica D: Nonlinear Phenomena, 60(1/2/3/4): 259–268. https://doi.org/10.1016/0167-2789(92)90242-f

    Article  Google Scholar 

  13. Russell, B. H., Dommico, S., 1988. Introduction to Seismic Inversion Methods. Society of Exploration Geophysicists, Tulsa. https://doi.org/10.1190/1.9781560802303

    Google Scholar 

  14. Russell, B. H., 2014. Prestack Seismic Amplitude Analysis: An Integrated Overview. Interpretation, 2(2): SC19–SC36. https://doi.org/10.1190/int-2013-0122.1

    Article  Google Scholar 

  15. Sena, A., Castillo, G., Chesser, K., et al., 2011. Seismic Reservoir Characterization in Resource Shale Plays: Stress Analysis and Sweet Spot Discrimination. The Leading Edge, 30(7): 758–764. https://doi.org/10.1190/1.3609090

    Article  Google Scholar 

  16. Walker, C., Ulrych, T. J., 1983. Autoregressive Recovery of the Acoustic Impedance. Geophysics, 48(10): 1338–1350. https://doi.org/10.1190/1.1441414

    Article  Google Scholar 

  17. Yilmaz, Ö., 2001. Seismic Data Analysis. Society of Exploration Geophysicists, Tulsa. 1809. https://doi.org/10.1190/1.9781560801580

    Google Scholar 

  18. Yin, X. Y., Liu, X. J., Zong, Z. Y., 2015. Pre-Stack Basis Pursuit Seismic Inversion for Brittleness of Shale. Petroleum Science, 12(4): 618–627. https://doi.org/10.1007/s12182-015-0056-3

    Article  Google Scholar 

  19. Yuan, S. Y., Wang, S. X., Luo, C. M., et al., 2015. Simultaneous Multitrace Impedance Inversion with Transform-Domain Sparsity Promotion. Geophysics, 80(2): R71–R80. https://doi.org/10.1190/geo2014-0065.1

    Article  Google Scholar 

  20. Zhang, F. C., Dai, R. H., Liu, H. Q., 2014. Seismic Inversion Based on L1-Norm Misfit Function and Total Variation Regularization. Journal of Applied Geophysics, 109: 111–118. https://doi.org/10.1016/j.jappgeo.2014.07.024

    Article  Google Scholar 

  21. Zhang, J., Liu, H. S., Tong, S. Y., et al., 2015. Estimation of Elastic Parameters Using Two-Term Fatti Elastic Impedance Inversion. Journal of Earth Science, 26(4): 556–566. https://doi.org/10.1007/s12583-015-0564-5

    Article  Google Scholar 

  22. Zhang, R., Sen, M. K., Srinivasan, S., 2013. A Prestack Basis Pursuit Seismic Inversion. Geophysics, 78(1): R1–R11. https://doi.org/10.1190/geo2011-0502.1

    Article  Google Scholar 

  23. Zong, Z.-Y., Yin, X.-Y., Zhang, F., et al., 2012. Reflection Coefficient Equation and Pre-Stack Seismic Inversion with Young’s Modulus and Poisson Ratio. Chinese Journal of Geophysics, 55(11): 3786–3794. https://doi.org/10.6038/j.issn.0001-5733.2012.11.025 (in Chinese with English Abstract)

    Google Scholar 

  24. Zong, Z.-Y., Yin, X.-Y., Wu, G. C., 2013. Elastic Impedance Parameterization and Inversion with Young’s Modulus and Poisson’s Ratio. Geophysics, 78(6): N35–N42. https://doi.org/10.1190/geo2012-0529.1

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Nos. 61775030, 61571096, 41301460, 61362018, and 41274127), and the key projects of Hunan Provincial Department of Education (No. 16A174). The authors thank the referees for their valuable suggestions. The authors also thank Chengdu Jingshi petroleum Technology Co., Ltd for providing us with the field data. The final publication is available at Springer via https://doi.org/10.1007/s12583-017-0905-7.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Zhenming Peng.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, S., Peng, Z. & Wu, H. Prestack Multi-Gather Simultaneous Inversion of Elastic Parameters Using Multiple Regularization Constraints. J. Earth Sci. 29, 1359–1371 (2018). https://doi.org/10.1007/s12583-017-0905-7

Download citation

Key words

  • elastic parameter
  • pre-stack inversion
  • multi-gather
  • regularization