Density-sensitivity analysis about prestack multi-parameter inversion based on the exact Zoeppritz equation

Guo Qiang1 ZHANG Hongbing1 CAO Chenghao2 HAN Feilong1 SHANG Zuoping3

(1.College of Earth Science and Engineering,Hohai University, Nanjing, Jiangsu Province, China 210098)
(2.Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China 100029)
(3.College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu Province, China 210098)

【Abstract】The prestack seismic inversion based on the exact Zoeppritz equation and its approximations has been widely adopted but complicated problems remain. Multi-parameter inversion results are unstable, especially for the parameter of density. We develop an inversion method by constructing a new objective function which includes the edge-preserving regularization and soft constraints based on Markov random domain. We apply the fast simulated annealing algorithm to solve the nonlinear optimization problem based on the exact Zoeppritz equation. The numerical results indicate that the density is insensitive to angle variation within small incidence angle range, but it makes more contribution to the reflectivity magnitude variation. The test results on 2-D synthetic data demonstrate that a satisfactory inverted density result can be achieved within small incidence angles with the proposed approach. The field data inverted results provide detailed stratigraphic information well matched with the logging data over most parts.

【Keywords】 prestack multi-parameter inversion; density sensitivity; the exact Zoeppritz equation; edge-preserved regularization; Markov random domain;


【Funds】 National Natural Science Foundation of China (41374116, 41674113) Research Project of China National Offshore Oil Corporation (CNOOC-KJ125 ZDXM 07 LTD NFGC 2014-04)

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    [1] Yang Wencai. 地球物理反演的理论与方法. Beijing: Geological Publishing House of China, 1997 (in Chinese).

    [2] Virieux J, Operto S. An overview of full-waveform inversion in exploration geophysics. Geophysics, 2009, 74 (6): WCC1–WCC26.

    [3] Tarantola A, Valette B. Generalized nonlinear inverse problems solved using the least squares criterion. Review of Geophysics and Space Physics, 1982, 20 (2): 219–232.

    [4] Bae H S, Pyun S, Chung W et al. Frequency-domain acoustic-elastic coupled waveform inversion using the Gauss-Newton conjugate gradient method. Geophysical Prospecting, 2012, 60 (3): 413–432.

    [5] Yao Yao. Improvement on nonlinear geophysical inversion simulated annealing. Chinese Journal of Geophysics, 1995, 38 (5): 643–650 (in Chinese).

    [6] Zhang Linbin, Yao Zhenxing, Ji Chen et al. Fast simulated annealing algorithm and its application. OGP, 1997, 32 (5): 654–660 (in Chinese).

    [7] Zhang H, Shang Z, Yang C. A non-linear regularized constrained impedance inversion. Geophysical Prospecting, 2007, 55 (6): 819–833.

    [8] Chiappa F, Mazzotti A. Estimation of petrophysical parameters by linearized inversion of angle domain pre-stack data. Geophysical Prospecting, 2009, 57 (3): 413–426.

    [9] Down J E. Seismic Paramter Estimation from AVO Inversion [D]. University of Calgary, Canada, 2005.

    [10] Tian Jun, Wu Guochen, Zong Zhaoyun. Robust threeterm AVO inversion and uncertainty analysis. OGP, 2013, 48 (3): 443–449 (in Chinese).

    [11] Aki K, Richards P G. Quantitative Seismology: Theory and Methods. W. H. Freeman and Co., 1980.

    [12] Shuey R T. A simplification of the Zoeppritz equations. Geophysics, 1985, 50 (4): 609–614.

    [13] Fatti J L, Smith G C, Vail P J et al. Detection of gas in sandstone reservoirs using AVO analysis: A 3-D seismic case history using the Geostack technique. Geophysics, 1994, 59 (9): 1362–1376.

    [14] Deng Wei, Yin Xingyao, Zong Zhaoyun et al. Highorder nonlinear AVO inversion based on estimated inverse operator. OGP, 2016, 51 (5): 955–964 (in Chinese).

    [15] Zhi L X, Chen S Q, Li X Y. Amplitude variation with angle inversion using the exact Zoeppritz equations—Theory and methodology. Geophysics, 2016, 81 (2): N1–N15.

    [16] Huang Handong, Wang Yanchao, Guo Fei et al. High precision prestack inversion algorithm based on Zoeppritz equations. OGP, 2013, 48 (5): 740–749 (in Chinese).

    [17] Chemingui N, Biondi B. Seismic data reconstruction by inversion to common offset. Geophysics, 2002, 67 (5): 1575–1585.

    [18] Ghosh S K. Limitations on impedance inversion of band-limited reflection data. Geophysics, 2000, 65 (3): 951–957.

    [19] А. Н. Тихонов, В. Я. Арсенин; translated by Wang Bingchen. 不适定问题的解法. Beijing: Geological Publishing House of China, 1979 (in Chinese).

    [20] Sen M K, Roy I G. Computation of differential seismograms and iteration adaptive regularization in prestack waveform inversion. Geophysics, 2003, 68 (6): 2026–2039.

    [21] Zhang Fengqi, Jin Zhijun, Sheng Xiujie et al. Bayesian prestack three-term inversion with soft low-frequency constraint. OGP, 2016, 51 (5): 965–975 (in Chinese).

    [22] Zhang Hongbing, Shang Zuoping, Yang Changchun. Estimation of regular parameters for the impedance inversion. Chinese Journal of Geophysics, 2005, 48 (1): 181–188 (in Chinese).

    [23] Zhang H, Shang Z, Yang C. Adaptive reconstruction method of impedance model with absolute and relative constraints. Journal of Applied Geophysics, 2009, 67 (2): 114–124.

    [24] Yan Z, Gu H. Non-linear prestack seismic inversion with global optimization using an edge-preserving smoothing filter. Geophysical Prospecting, 2013, 61 (4): 747–760.

    [25] Kabir N, Crider R, Ramkhelawan R et al. Can hydrocarbon saturation be estimated using density contrast parameter? CSEG Recorder, 2006, 31 (6): 31–37.

    [26] Zong Z, Yin X, Wu G. AVO inversion and poroelasticity with P-and S-wave moduli. Geophysics, 2012, 77 (6): N17–N24.

    [27] Zong Z, Yin X, Wu G. Elastic impedance parameterization and inversion with Young’s modulus and Poisson’s ratio. Geophysics, 2013, 78 (6): N35–N42.

    [28] Liang Lifeng, Zhang Hongbing, Dan Zhiwei et al. Prestack density inversion using the Fatti equation constrained by the P- and S-wave impedance and density. Applied Geophysics, 2017, 14 (1): 133–141.

    [29] Charbonnier P, Blanc-Féraud L, Aubert G. Deterministic edge-preserving regularization in computed imaging. IEEE Transactions on Image Processing, 1997, 6 (2): 298–311.

    [30] Geman D, Yang C. Nonlinear image recovery with halfquadratic regularization. IEEE Transactions on Image Processing, 1995, 4 (7): 932–946.

    [31] Huang Handong, Zhang Ruwei, Shen Guoqiang et al. Study of prestack elastic parameter consistency inversion methods. Applied Geophysics, 2011, 8 (4): 311–318.

This Article


CN: 13-1095/TE

Vol 52, No. 06, Pages 1218-1225+1120

December 2017


Article Outline


  • 1 Introduction
  • 2 Principles
  • 3 Density sensitivity analysis
  • 4 Synthetic data test
  • 5 Real data test
  • 6 Conclusions and discussions
  • References