none 10.1190/geo2020-0411.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 122695443 5981 2026041612394669400 10.1190 2026-04-16T16:39:58Z 2020-12-24T12:11:12Z 21 Geophysics 0016-8033 1942-2156 03 01 2021 86 2 Xingguo Huang Jilin University 1 , College of Instrumentation and Electrical Engineering, and Key Lab of Geo-Exploration Instrumentation (Ministry of Education), Changchun 130026, China. E-mail: xingguo.huang19@gmail.com (corresponding author). http://orcid.org/0000-0001-9719-6297 Stewart Greenhalgh Swiss Federal Institute of Technology (ETH) Zurich 2 , Institute of Geophysics, Department of Earth Sciences, 8092 Zurich, Switzerland. E-mail: gstewart@retired.ethz.ch . ABSTRACT We have developed a finite-difference iterative solver of the Helmholtz equation for seismic modeling and inversion in the frequency domain. The iterative solver involves the shifted Laplacian operator and two-level preconditioners. It is based on the application of the preconditioners to the Krylov subspace stabilized biconjugate gradient method. A critical factor for the iterative solver is the introduction of a new preconditioner into the Krylov subspace iteration method to solve the linear equation system resulting from the discretization of the Helmholtz equation. This new preconditioner is based on a reformulation of an integral equation-based convergent Born series for the Lippmann-Schwinger equation to an equivalent differential equation. We have determined that our iterative solver combined with the novel preconditioner when incorporated with the finite-difference method accelerates the convergence of the Krylov subspace iteration method for frequency-domain seismic wave modeling. A comparison of a direct solver, a one-level Krylov subspace iterative solver, and our two-level iterative solver verified the accuracy and accelerated convergence of the new scheme. Extensive tests in full-waveform inversion demonstrate the solver’s applicability to such problems. 02 23 2021 03 01 2021 T107 T116 1 10.1190/crossmark-policy library.seg.org true 2020-06-24 2020-12-07 2020-12-08 2021-02-23 10.1190/geo2020-0411.1 https://pubs.geoscienceworld.org/geophysics/article/86/2/T107/594902/A-finite-difference-iterative-solver-of-the https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/86/2/T107/5264488/geo-2020-0411.1.pdf https://pubs.geoscienceworld.org/seg/geophysics/article-pdf/86/2/T107/5264488/geo-2020-0411.1.pdf https://pubs.geoscienceworld.org/geophysics/article/86/2/t107/594902/a-finite-difference-iterative-solver-of-the Quantitative seismology: Theory and methods Aki 1980 0045-7825 Computer Methods in Applied Mechanics and Engineering Amestoy 184 501 2000 10.1016/S0045-7825(99)00242-X Multifrontal parallel distributed symmetric and unsymmetric solvers 0021-9991 Journal of Computational Physics Belonosov 345 330 2017 10.1016/j.jcp.2017.05.026 An 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