Skip to main content
Top

2019 | OriginalPaper | Chapter

Parallelization Strategy for Wavefield Simulation with an Elastic Iterative Solver

Authors : Mikhail Belonosov, Vladimir Cheverda, Victor Kostin, Dmitry Neklyudov

Published in: Supercomputing

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We present a parallelization strategy for our novel iterative method to simulate elastic waves in 3D land inhomogeneous isotropic media via MPI and OpenMP. The unique features of the solver are the preconditioner developed to assure fast convergence of the Krylov-type iteration method at low time frequencies and the way to calculate how the forward modeling operator acts on a vector. We successfully benchmark the accuracy of our solver against the exact solution and compare it to another iterative solver. The quality of the parallelization is justified by weak and strong scaling analysis. Our modification allows simulation in big models including a modified 2.5D Marmousi model comprising 90 million cells.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Albanese, C., Gilblom, K.: This oil major has a supercomputer the size of a soccer field. Bloomberg, 18 January 2018 Albanese, C., Gilblom, K.: This oil major has a supercomputer the size of a soccer field. Bloomberg, 18 January 2018
2.
go back to reference Aminzadeh, F., Brac, J., Kuntz, T.: 3-D Salt and Overthrust Models. SEG/EAGE Modelling Series, no. 1. SEG Book Series, Tulsa, Oklahoma (1997) Aminzadeh, F., Brac, J., Kuntz, T.: 3-D Salt and Overthrust Models. SEG/EAGE Modelling Series, no. 1. SEG Book Series, Tulsa, Oklahoma (1997)
3.
go back to reference Aki, K., Richards, P.G.: Quantitative Seismology, Theory and Methods, vol. 1. W.H. Freeman and Co., San Francisco (1980) Aki, K., Richards, P.G.: Quantitative Seismology, Theory and Methods, vol. 1. W.H. Freeman and Co., San Francisco (1980)
4.
5.
go back to reference Belonosov, M., Dmitriev, M., Kostin, V., Neklyudov, D., Tcheverda, V.: An iterative solver for the 3D Helmholtz equation. J. Comput. Phys. 345, 330–344 (2017)MathSciNetCrossRef Belonosov, M., Dmitriev, M., Kostin, V., Neklyudov, D., Tcheverda, V.: An iterative solver for the 3D Helmholtz equation. J. Comput. Phys. 345, 330–344 (2017)MathSciNetCrossRef
6.
go back to reference Berenger, J.P.: Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 127, 363–379 (1996)MathSciNetCrossRef Berenger, J.P.: Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 127, 363–379 (1996)MathSciNetCrossRef
7.
go back to reference Darbas, M., Louer, F.: Analytic preconditioners for the iterative solution of elastic scattering problems. HAL, hal-00839653, pp. 1–32 (2013) Darbas, M., Louer, F.: Analytic preconditioners for the iterative solution of elastic scattering problems. HAL, hal-00839653, pp. 1–32 (2013)
8.
go back to reference Erlangga, Y.A., Nabben, R.: On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian. Electron. Trans. Numer. Anal. 31, 403–424 (2008)MathSciNetMATH Erlangga, Y.A., Nabben, R.: On a multilevel Krylov method for the Helmholtz equation preconditioned by shifted Laplacian. Electron. Trans. Numer. Anal. 31, 403–424 (2008)MathSciNetMATH
9.
go back to reference Etienne, V., Tonellot, T., Thierry, P., Berthoumieux, V., Andreolli, C.: Optimization of the seismic modeling with the time-domain finite-difference method. In: 84th Annual International Meeting, SEG, Expanded Abstracts, pp. 3536–3540 (2014) Etienne, V., Tonellot, T., Thierry, P., Berthoumieux, V., Andreolli, C.: Optimization of the seismic modeling with the time-domain finite-difference method. In: 84th Annual International Meeting, SEG, Expanded Abstracts, pp. 3536–3540 (2014)
12.
go back to reference Kostin, V., Lisitsa, V., Reshetova, G., Tcheverda, V.: Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media. J. Comput. Phys. 281, 669–689 (2015)MathSciNetCrossRef Kostin, V., Lisitsa, V., Reshetova, G., Tcheverda, V.: Local time-space mesh refinement for simulation of elastic wave propagation in multi-scale media. J. Comput. Phys. 281, 669–689 (2015)MathSciNetCrossRef
13.
go back to reference Kostin, V., Neklyudov, D., Tcheverda, V., Belonosov, M., Dmitriev, M.: 3D elastic frequency-domain iterative solver for full-waveform inversion. In: 86th Annual International Meeting, SEG, Expanded Abstracts, pp. 3825–3829 (2016) Kostin, V., Neklyudov, D., Tcheverda, V., Belonosov, M., Dmitriev, M.: 3D elastic frequency-domain iterative solver for full-waveform inversion. In: 86th Annual International Meeting, SEG, Expanded Abstracts, pp. 3825–3829 (2016)
14.
go back to reference Kostin, V., Solovyev, S., Liu, H., Bakulin, A.: HSS cluster-based direct solver for acoustic wave equation. In: 87th Annual International Meeting, SEG, Expanded Abstracts, pp. 4017–4021 (2017) Kostin, V., Solovyev, S., Liu, H., Bakulin, A.: HSS cluster-based direct solver for acoustic wave equation. In: 87th Annual International Meeting, SEG, Expanded Abstracts, pp. 4017–4021 (2017)
15.
go back to reference Li, Y., Metivier, L., Brossier, R., Han, B., Virieux, J.: 2D and 3D frequency-domain elastic wave modeling in complex media with a parallel iterative solver. Geophysics 80, T101–T118 (2015)CrossRef Li, Y., Metivier, L., Brossier, R., Han, B., Virieux, J.: 2D and 3D frequency-domain elastic wave modeling in complex media with a parallel iterative solver. Geophysics 80, T101–T118 (2015)CrossRef
16.
go back to reference Lisitsa, V., Tcheverda, V., Botter, C.: Combination of discontinuous Galerkin method with finite differences for simulation of elastic wave. J. Comput. Phys. 311, 142–157 (2016)MathSciNetCrossRef Lisitsa, V., Tcheverda, V., Botter, C.: Combination of discontinuous Galerkin method with finite differences for simulation of elastic wave. J. Comput. Phys. 311, 142–157 (2016)MathSciNetCrossRef
17.
go back to reference Operto, S., Virieux, J., Amestoy, P., L’Excellent, J., Giraud, L., Hadj, H.: 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: a feasibility study. Geophysics 72, SM195–SM211 (2007)CrossRef Operto, S., Virieux, J., Amestoy, P., L’Excellent, J., Giraud, L., Hadj, H.: 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: a feasibility study. Geophysics 72, SM195–SM211 (2007)CrossRef
18.
go back to reference Pissarenko, D., Reshetova, G., Tcheverda, V.: 3D finite-difference synthetic acoustic log in cylindrical coordinates: parallel implementation. J. Comput. Appl. Math. 234(6), 1766–1772 (2010)MathSciNetCrossRef Pissarenko, D., Reshetova, G., Tcheverda, V.: 3D finite-difference synthetic acoustic log in cylindrical coordinates: parallel implementation. J. Comput. Appl. Math. 234(6), 1766–1772 (2010)MathSciNetCrossRef
19.
go back to reference Pratt, R.G.: Seismic waveform inversion in the frequency domain, Part 1: theory and verification in a physical scale model. Geophysics 64, 888–901 (1999)CrossRef Pratt, R.G.: Seismic waveform inversion in the frequency domain, Part 1: theory and verification in a physical scale model. Geophysics 64, 888–901 (1999)CrossRef
20.
go back to reference Rizzuti, G., Mulder, W.A.: A multigrid-based iterative solver for the frequency-domain elastic wave equation. In: 77th EAGE Conference and Exhibition, Expanded Abstracts, pp. 1–4 (2015) Rizzuti, G., Mulder, W.A.: A multigrid-based iterative solver for the frequency-domain elastic wave equation. In: 77th EAGE Conference and Exhibition, Expanded Abstracts, pp. 1–4 (2015)
21.
go back to reference Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003)CrossRef Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. SIAM, Philadelphia (2003)CrossRef
22.
go back to reference Sirgue, L., Etgen, J., Albertin, U., Brandsberg-Dahl, S.: System and method for 3D frequency domain waveform inversion based on 3D time-domain forward modeling. U. S. Patent, 11/756,384 (2007) Sirgue, L., Etgen, J., Albertin, U., Brandsberg-Dahl, S.: System and method for 3D frequency domain waveform inversion based on 3D time-domain forward modeling. U. S. Patent, 11/756,384 (2007)
23.
go back to reference Sonneveld, P., van Gijzen, M.B.: IDR(s): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations. SIAM J. Sci. Comput. 31, 1035–1062 (2008)MathSciNetCrossRef Sonneveld, P., van Gijzen, M.B.: IDR(s): a family of simple and fast algorithms for solving large nonsymmetric systems of linear equations. SIAM J. Sci. Comput. 31, 1035–1062 (2008)MathSciNetCrossRef
24.
go back to reference Symes, W.W.: Migration velocity analysis and waveform inversion. Geophys. Prospect. 56(6), 765–790 (2008)CrossRef Symes, W.W.: Migration velocity analysis and waveform inversion. Geophys. Prospect. 56(6), 765–790 (2008)CrossRef
25.
go back to reference Van Der Vorst, H.A.: BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992)MathSciNetCrossRef Van Der Vorst, H.A.: BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 13(2), 631–644 (1992)MathSciNetCrossRef
26.
go back to reference Virieux, J.: Seismic wave modeling for seismic imaging. Lead. Edge 28, 538–544 (2009)CrossRef Virieux, J.: Seismic wave modeling for seismic imaging. Lead. Edge 28, 538–544 (2009)CrossRef
27.
go back to reference Wang, S.V., de Hoop, M., Xia, J., Li, X.S.: Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3-D anisotropic media. Geophys. J. Int. 191, 346–366 (2012)CrossRef Wang, S.V., de Hoop, M., Xia, J., Li, X.S.: Massively parallel structured multifrontal solver for time-harmonic elastic waves in 3-D anisotropic media. Geophys. J. Int. 191, 346–366 (2012)CrossRef
Metadata
Title
Parallelization Strategy for Wavefield Simulation with an Elastic Iterative Solver
Authors
Mikhail Belonosov
Vladimir Cheverda
Victor Kostin
Dmitry Neklyudov
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-05807-4_28

Premium Partner