The generalized over-relaxation iterative method for Lippmann-Schwinger equation and its convergence

被引：0
作者：
Xu Y. [1 ]
Sun J. [1 ]
Shang Y. [1 ]
Meng X. [1 ]
Wei P. [1 ]
机构：
[1] College of Geo-exploration Science and Technology, Jilin University, Changchun
来源：
Acta Geophysica Sinica | 2021年 / 64卷 / 01期
关键词：
Integral equation; Over-relaxation iteration; Seismic modeling; Wave scattering;
D O I：
10.6038/cjg2021O0105
中图分类号：
学科分类号：
摘要：
To overcome the shortcomings of the traditional Born scattering series, which is only applicable to weak scattering and short-range propagation, we introduce a generalized over-relaxation iterative method for the Lippmann-Schwinger equation from the optical theory. It is a numerical simulation method for strong scattering to solve forward modeling and inversion problems of strong optical scattering. The applicability and convergence characteristics of the over-relaxation method under the condition of seismic reflection were analyzed in this work. Results show that (1) compared with scattering series renormalisation, the over-relaxation method has a more solid mathematics basis. (2) The over-relaxation method can effectively overcome the shortcomings of the Born series and obtain numerical simulation results equivalent to that of the finite-difference method. And (3) under the condition of seismic reflection, the over-relaxation method can be used to fully solve the problem of strong scattering. © 2021, Science Press. All right reserved.
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页码：249 / 262
页数：13
相关论文
共 36 条
  • [1] Achenbach J D, Gautesen A K, McMaken H., Ray Methods for Waves in Elastic Solids: with Applications to Scattering by Cracks, (1982)
  • [2] Aki K, Richards P G., Quantitative Seismology: Theory and Methods, 2, (1980)
  • [3] Bing Q, Sun Z Q, Han F X, Et al., Review on the seismic wave ray tracing: methods, classification, developmental present and trend, Progress in Geophysics, 35, 2, pp. 536-547, (2020)
  • [4] Cao J, Chen J B, Cao S H., Studies on iterative algorithms for modeling of frequency-domain wave equation based on multi-grid precondition, Chinese Journal of Geophysics, 58, 3, pp. 1002-1012, (2015)
  • [5] Cerveny V., Seismic Ray Theory, (2001)
  • [6] Chertock G., Convergence of iterative solutions to integral equations for sound radiation, Quarterly of Applied Mathematics, 26, 2, pp. 268-272, (1968)
  • [7] Coyle J, Monk P., The finite element approximation of scattering in a layered medium, Analytical and Computational Methods in Scattering and Applied Mathematics, 417, pp. 67-84, (2000)
  • [8] Fu L Y., Seismogram synthesis for piecewise heterogeneous media, Geophysical Journal International, 150, 3, pp. 800-808, (2002)
  • [9] Fu L Y, Mu Y G, Yang H J., Forward problem of nonlinear Fredholm integral equation in reference medium via velocity-weighted wavefield function, Geophysics, 62, 2, pp. 650-656, (1997)
  • [10] Fu L Y, Wu R S., Infinite boundary element absorbing boundary for wave propagation simulations, Geophysics, 65, 2, pp. 596-602, (2000)
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