Side-by-side Chinese-English

基于混合快速共轭梯度法的有限差分对比源反演

王豆豆1,2 王守东2 邹少峰1 高艳霞1 刘晗1

(1.中国石化石油物探技术研究院, 江苏南京 211103)
(2.中国石油大学(北京)油气资源与探测国家重点实验室, 北京 102249)

【摘要】有限差分对比源反演(FDCSI)是一种解决逆散射问题的方法,该方法在反演中背景模型保持不变,只进行一次全正演计算,减少了计算量。FDCSI将逆散射问题转化为优化问题,采用常规共轭梯度法优化目标泛函,但收敛速度较慢,影响反演效率。为此,在研究频率域声波方程有限差分对比源反演方法的基础上,提出了基于混合快速共轭梯度法的有限差分对比源反演方法,提高了反演效率。混合快速共轭梯度法是在快速迭代收缩阈值算法基础上改进得到的优化方法,该方法适用于有限差分对比源反演,在不增加单次迭代计算量的基础上加速目标泛函收敛,保证了对比源反演算法的快速稳定收敛。

【关键词】 逆散射;对比源反演;频率域声波方程;快速迭代收缩阈值算法;混合快速共轭梯度法;

【DOI】

【基金资助】 国家科技重大专项“不同缝洞储集体地震识别与预测技术”(2016ZX05014-001); 国家科技重大专项“宽方位地震数据规则化与有效信号增强方法研究与应用”(2016ZX05024-001-004);

Finite-difference contrast source inversion based on hybrid fast conjugate gradient method

WANG Doudou1,2 WANG Shoudong2 ZOU Shaofeng1 GAO Yanxia1 LIU Han1

(1.SINOPEC Geophysical Research Institute, Nanjing, Jiangsu Province, China 211103)
(2.State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (Beijing), Beijing, China 102249)

【Abstract】Finite-difference contrast source inversion (FDCSI) is a solution to inverse scattering. The background model remains unchanged in the inversion, and forward modeling is performed for only one time; this reduces the workload of computation. FDCSI translates the problem of inverse scattering into that of optimization. The cost function is optimized with the conjugate gradient method, which suffers from a low convergence rate and low efficiency. After the study of FDCSI based on acoustic wave equation in frequency domain, we develop a FDCSI algorithm based on a hybrid fast conjugate gradient method to improve the efficiency of inversion. The hybrid fast conjugate gradient method is modified from the fast iterative shrinkage-thresholding algorithm and is feasible for FDCSI. The cost function could converge quickly without more computation in a single iteration; this guarantees fast and robust convergence of FDCSI.

【Keywords】 inverse scattering; contrast source inversion; acoustic wave equation in frequency domain; fast iterative shrinkage-thresholding algorithm; hybrid fast conjugate gradient method;

【DOI】

【Funds】 National Science and Technology Major Project of China (2016ZX05014-001); National Science and Technology Major Project of China (2016ZX05024-001-004);

Download this article
    References

    [1] Tarantola A. A strategy for nonlinear elastic inversion of seismic reflection data [J]. Geophysics, 1986, 51 (5): 1893–1903.

    [2] Pratt R G, Worthington M H. Inverse theory applied to multisource cross-hole tomography: Part 1, Acoustic wave-equation method [J]. Geophysical Prospecting, 1990, 38 (3): 287–310.

    [3] LI Haishan, YANG Wuyang, YONG Xueshan. Three-dimensional full waveform inversion based on the first-order velocity-stress acoustic wave equation [J]. Oil Geophysical Prospecting, 2018, 53 (4): 730–736 (in Chinese).

    [4] Choi Y, Shin C, Min D J, et al. Efficient calculation of the steepest descent direction for source-independent seismic waveform inversion: an amplitude approach [J]. Journal of Computational Physics, 2005, 208: 455–468.

    [5] Jang U, Min D J, Shin C. Comparison of scaling methods for waveform inversion [J]. Geophysical Prospecting, 2009, 57 (1): 49–59.

    [6] Chi B, Dong L, Liu Y. Full waveform inversion method using envelope objective function without low frequency data [J]. Journal of Applied Geophysics, 2014, 109: 36–46.

    [7] Pratt R G. Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model [J]. Geophysics, 1999, 64 (3): 888–901.

    [8] Kamei R, Pratt R G, Tsuji T. Misfit functions in Laplace–Fourier domain waveform inversion, with application to wide-angle ocean bottom seismograph data [J]. Geophysical Prospecting, 2014, 62 (5): 1054–1074.

    [9] Pratt R G, Shin C, Hick G J. Gauss–Newton and full Newton methods in frequency space seismic waveform inversion [J]. Geophysical Journal International, 1998, 133 (2): 341–362.

    [10] Brossier R, Operto S, Virieux J. Seismic imaging of complex onshore structures by 2D elastic frequency domain full waveform inversion [J]. Geophysics, 2009, 74 (6): WCC105–WCC118.

    [11] Métivier L, Bretaudeau F, Brossier R, et al. Full waveform inversion and the truncated Newton method: quantitative imaging of complex subsurface structures [J]. Geophysical Prospecting, 2014, 62 (6): 1353–1375.

    [12] Kim W K, Min D J. A new parameterization for frequency-domain elastic full waveform inversion for VTI media [J]. Journal of Applied Geophysics, 2014, 109: 88–110.

    [13] van den Berg P M, Ralph E K. A contrast source inversion method [J]. Inverse Problems, 1997, 13 (6): 1607–1620.

    [14] Tarek M H, Michael L O. Simultaneous nonlinear reconstruction of two-dimensional permittivity and conductivity [J]. Radio Science, 1994, 29 (4): 1101–1118.

    [15] van Dongen, Koen W A, William M D. A full vectorial contrast source inversion scheme for 3D acoustic imaging of both compressibility and density profiles [J]. Journal of the Acoustical Society of America, 2007, 121: 1538–1549.

    [16] Wang S D, Wu R S, Liu Y F. The contrast source inversion for reflection seismic data [C]. Extended Abstracts of 78th EAGE Conference and Exhibition, 2016, 01540.

    [17] Abubakar, Hu W, van den Berg P M, et al. A finite-difference contrast source inversion method [J]. Inverse Problems, 2008, 24 (6): 065004–065020.

    [18] Abubakar, Hu W, Tarek M H, et al. Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data [J]. Geophysics, 2009, 74 (6): WCC47–WCC58.

    [19] Abubakar, Pan G, Li M, et al. Three-dimensional seismic full-waveform inversion using the finite-difference contrast source inversion method [J]. Geophysical Prospecting, 2011, 59 (5): 874–888.

    [20] Han B, He Q, Chen Y, et al. Seismic waveform inversion using the finite-difference contrast source inversion method [J]. Journal of Applied Mathematics, 2014, 109: 1–11.

    [21] He Q, Han B, Chen Y, et al. Application of the finite-difference contrast source inversion method to multi-parameter reconstruction using seismic full-waveform data [J]. Journal of Applied Geophysics, 2016, 124: 4–16.

    [22] DUAN Xiaoliang, ZHAI Hongyu, WANG Yibo, et al. Effect of stratigraphic attenuation on inverse-scattering seismic velocity inversion [J]. Chinese Journal of Geophysics, 2016, 59 (10): 3788–3797 (in Chinese).

    [23] Beck A, Teboulle M. A fast iterative shrinkage-thresholding algorithm for linear inverse problems [J]. SIAM Journal on Imaging Sciences, 2009, 2 (1): 183–202.

    [24] Chambolle A, Dossal C. On the convergence of the iterates of the “fast iterative shrinkage/thresholding algorithm” [J]. Journal of Optimization Theory and Applications, 2015, 166 (3): 968–982.

    [25] CHEN Shaoli, YANG Min. An improved fast iterative shrinkage-thresholding algorithm with variable step size [J]. Computer Technology and Development, 2017, 27 (10): 69–73 (in Chinese).

    [26] ZHANG Guangzhi, SUN Changlu, PAN Xinpeng, et al. Fast conjugate gradient method for frequency domain acoustic wave full waveform inversion [J]. Oil Geophysical Prospecting, 2016, 51 (4): 730–737 (in Chinese).

    [27] Jo C H, Shin C S, Suh J H. An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator [J]. Geophysics, 1996, 61 (2): 529–537.

    [28] DONG Shiqi, HAN Liguo, HU Yong, et al. Acoustic equation high-accuracy modeling in the frequency domain based on MCPML absorbing boundary [J]. Oil Geophysical Prospecting, 2018, 53 (1): 47–54 (in Chinese).

    [29] CHENG Jingwang, LYU Xiaochun, GU Hanming, et al. Full waveform inversion with Cauchy distribution in the frequency domain [J]. Oil Geophysical Prospecting, 2014, 49 (5): 940–945 (in Chinese).

    [30] Polyak B T. The conjugate gradient method in extremal problems [J]. USSR Computational Mathematics & Mathematical Physics, 1969, 9 (4): 94–112.

    [31] Sirgue L, Pratt R G. Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies [J]. Geophysics, 2004, 69 (1): 231–248.

This Article

ISSN:1000-7210

CN: 13-1095/TE

Vol 55, No. 02, Pages 351-359+231

April 2020

Downloads:0

Share
Article Outline

Abstract

  • 0 Introduction
  • 1 Idea of FDCSI
  • 2 HFCG method
  • 3 Model tests
  • 4 Conclusion
  • References