Basis pursuit inversion for Young’s modulus and Poisson’s ratio

LIU Chang1,2,3,4 LI Chao5 ZHU Zhenyu5 CHEN Guojun1

(1.Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, Gansu Province, China 730000)
(2.China United Coalbed Methane Corporation Ltd., Beijing, China 100011)
(3.Unconventional Oil and Gas Branch, CNOOC, Beijing, China 100011)
(4.University of Chinese Academy of Sciences, Beijing, China 100049)
(5.Research Institute, CNOOC, Beijing, China 100028)
【Knowledge Link】Young’s modulus; Poisson’s ratio

【Abstract】Based on the basis pursuit theory, this paper develops an approach to directly invert Young’s modulus and Poisson’s ratio with the prestack seismic data. First, based on the approximate equation of Zoeppritz equation and the relationship between elastic parameters, a linear approximate equation of the seismic reflection coefficient is derived, which contains Young’s modulus, Poisson’s ratio, and density. Thereafter, Young’s modulus and Poisson’s ratio are directly inverted with the prestack seismic data based on the basis pursuit. Model constraints are added to objective functions of the basis pursuit inversion to improve the stability. Both model tests and field data applications show that the proposed approach can stably estimate Young’s modulus and Poisson’s ratio from seismic data.

【Keywords】 Young’s modulus; Poisson’s ratio; prestack inversion; basis pursuit;


【Funds】 National Science and Technology Major Project (2016zx05026-007-05)

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    [1] Backus M M, Chen R L. Flat spot exploration [J]. Geophysical Prospecting, 1975, 23 (3): 533–577.

    [2] Shuey R T. A simplification of the Zoeppritz equa-tions [J]. Geophysics, 1985, 50 (4): 609–614.

    [3] Connolly P. Elastic impedance [J]. The Leading Edge, 1999, 18 (4): 438–452.

    [4] Gray D. Bridging the gap: Using AVO to detect changes in fundamental elastic constants [C]. SEG Technical Program Expanded Abstracts, 1999, 18: 852–855.

    [5] Russell B H, Hedlin K, Hilterman F J, et al. Fluid-property discrimination with AVO: A Biot-Gassmann perspective [J]. Geophysics, 2003, 68 (1): 29–39.

    [6] Sena A, Castillo G, Chesser K, et al. Seismic reservoir characterization in resource shale plays: stress analysis and sweet spot discrimination [J]. The Leading Edge, 2011, 30 (7): 758–764.

    [7] LI Meng, LIU Zhen, LIU Minzhu, et al. Impedance inversion based on small-angle stacking seismic data [J]. Oil Geophysical Prospecting, 2018, 53 (6): 1291–1298 (in Chinese).

    [8] Debeye H W J, Riel P V. Lp-norm deconvolution [J]. Geophysical Prospecting, 1990, 38 (4): 381–403.

    [9] Amaldi E, Kann V. On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems [J]. Theoretical Computer Science, 1998, 209 (1): 237–260.

    [10] Nguyen T H. High Resolution Seismic Reflectivity Inversion [D]. University of Houston, Houston, 2008.

    [11] ZHANG Fanchang, LI Chuanhui, YIN Xingyao. Delta fringe line recognition based on seismic matching pursuit instantaneous spectral characteristics [J]. Oil Geo-physical Prospecting, 2012, 47 (1): 82–88 (in Chinese).

    [12] LIU Xiaojing, YIN Xingyao, WU Guochen, et al. Pre-stack seismic inversion based on orthogonal matching pursuit algorithm [J]. Oil Geophysical Prospecting, 2015, 56 (5): 925–935 (in Chinese).

    [13] Zhang R, Castagna J. Seismic sparse-layer reflectivity inversion using basis pursuit decomposition [J]. Geophysics, 2011, 76 (6): R147–R158.

    [14] Zhang R, Sen M K, Srinivasan S. A prestack basis pursuit seismic inversion [J]. Geophysics, 2013, 78 (1): R1–R11.

    [15] Theune U, Jensås I ∅, Eidsvik J. Analysis of prior models for a blocky inversion of seismic AVA data [J]. Geophysics, 2010, 75 (3): C25–C35.

    [16] Zhang R, Sen M K, Srinivasan S. Multi-trace basis pursuit inversion with spatial regularization [J]. Journal of Geophysics and Engineering, 2013, 10 (3): 1–6.

    [17] WANG Hailong, QU Yongqiang, ZHANG Qiaofeng, et al. Tight-sand reservoir prediction in the deep Shahezi formation, Songliao Basin [J]. Oil Geophysical Prospecting, 2017, 52 (S2): 129–134 (in Chinese).

    [18] NIU Cong, ZHANG Yiming, WANG Di, et al. Prediction of high-quality reservoir characteristics and distribution in the area LA [J]. Oil Geophysical Prospecting, 2017, 52 (3): 591–598 (in Chinese).

    [19] Bork J, and Wood L. Seismic interpretation of sonic logs [C]. SEG Technical Program Expanded Abstracts, 2001, 20: 510–513.

    [20] Santosa F, Symes W W. Linear inversion of band-limited reflection seismograms [J]. SIAM Journal on Scientific and Statistical Computing, 1986, 7 (4): 1307–1330.

    [21] Tibshirani R. Regression shrinkage and selection via the Lasso [J]. Journal of the Royal Statistical Society: Series B (Methodological), 1996, 58 (1): 267–288.

    [22] Donoho D L. For most large underdetermined systems of linear equations the minimal L1-norm solution is also the sparsest solution [J]. Communications on Pure and Applied Mathematics, 2006, 59 (6): 797–829.

    [23] Candès E J, Romberg J K, Tao T. Stable signal reco-very from incomplete and inaccurate measurements [J]. Communications on Pure and Applied Mathema-tics, 2006, 59 (8): 1207–1223.

    [24] Pérez D, Velis D, Sacchi M. High-resolution prestack seismic inversion using a hybrid FISTA least-squares strategy [J]. Geophysics, 2013, 78 (5): R185–R195.

    [25] Birgin E G. Inexact spectral projected gradient methods on convex sets [J]. SIMA Journal of Numerical Analysis, 2003, 23 (4): 539–559.

This Article


CN: 13-1095/TE

Vol 54, No. 06, Pages 1310-1315+1175

December 2019


Article Outline



  • 0 Introduction
  • 1 Methodology
  • 2 Inversion methods
  • 3 Model trial
  • 4 Application examples
  • 5 Conclusion
  • References