Skip to main content

Data-Based Choice of the Training Dataset for the Numerical Dispersion Mitigation Neural Network

  • Conference paper
  • First Online:
Supercomputing (RuSCDays 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13708))

Included in the following conference series:

  • 746 Accesses

Abstract

The main way that numerical error in seismic modeling manifests itself is through numerical dispersion brought on by coarse grids. Refining the mesh has the potential to minimize it, but doing so will result in an unacceptably high computational cost. Numerical Dispersion Mitigation network (NDM-net), a new technique that was recently created, is applied to the full dataset computed using a coarse mesh after the network has been trained using a relatively small number of seismograms that were previously computed using a fine mesh. The creation of the training dataset is the component of the procedure that requires the greatest computation. Therefore, reducing the quantity of precomputed seismograms may help the approach perform better as a whole. In this article, we describe a method for building the training dataset so that the difference between it and the full dataset does not go above the allowed limit.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Ainsworth, M.: Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. J. Comput. Phys. 198(1), 106–130 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Billette, F., Brandsberg-Dahl, S.: The 2004 BP velocity benchmark. In: 67-th EAGE Conference and Exibition, p. B035. EAGE (2005)

    Google Scholar 

  3. Blanch, J., Robertsson, J., Symes, W.: Modeling of a constant Q: methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique. Geophysiscs 60(1), 176–184 (1995)

    Article  Google Scholar 

  4. Gadylshin, K., Lisitsa, V., Gadylshina, K., Vishnevsky, D., Novikov, M.: Machine learning-based numerical dispersion mitigation in seismic modelling. In: Gervasi, O., et al. (eds.) ICCSA 2021. LNCS, vol. 12949, pp. 34–47. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-86653-2_3

    Chapter  Google Scholar 

  5. Kaur, H., Fomel, S., Pham, N.: Overcoming numerical dispersion of finite-difference wave extrapolation using deep learning. In: SEG Technical Program Expanded Abstracts, pp. 2318–2322 (2019). https://doi.org/10.1190/segam2019-3207486.1

  6. Koene, E.F.M., Robertsson, J.O.A., Broggini, F., Andersson, F.: Eliminating time dispersion from seismic wave modeling. Geophys. J. Int. 213(1), 169–180 (2017)

    Article  Google Scholar 

  7. Kragh, E., Christie, P.: Seismic repeatability, normalized RMS, and predictability. Lead. Edge 21(7), 640–647 (2002)

    Article  Google Scholar 

  8. Kragh, E., Laws, R.: Rough seas and statistical deconvolution. Geophys. Prospect. 54(4), 475–485 (2006)

    Article  Google Scholar 

  9. Levander, A.R.: Fourth-order finite-difference P-SV seismograms. Geophysics 53(11), 1425–1436 (1988)

    Article  Google Scholar 

  10. Lisitsa, V., Vishnevskiy, D.: Lebedev scheme for the numerical simulation of wave propagation in 3D anisotropic elasticity. Geophys. Prospect. 58(4), 619–635 (2010). https://doi.org/10.1111/j.1365-2478.2009.00862.x

    Article  Google Scholar 

  11. Lisitsa, V.: Dispersion analysis of discontinuous Galerkin method on triangular mesh for elastic wave equation. Appl. Math. Model. 40, 5077–5095 (2016). https://doi.org/10.1016/j.apm.2015.12.039

    Article  MathSciNet  MATH  Google Scholar 

  12. Lisitsa, V., Kolyukhin, D., Tcheverda, V.: Statistical analysis of free-surface variability’s impact on seismic wavefield. Soil Dyn. Earthq. Eng. 116, 86–95 (2019)

    Article  Google Scholar 

  13. Masson, Y.J., Pride, S.R.: Finite-difference modeling of Biot’s poroelastic equations across all frequencies. Geophysics 75(2), N33–N41 (2010)

    Article  Google Scholar 

  14. Mittet, R.: Second-order time integration of the wave equation with dispersion correction procedures. Geophysics 84(4), T221–T235 (2019)

    Article  Google Scholar 

  15. Ronneberger, O., Fischer, P., Brox, T.: U-net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, A.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28http://lmb.informatik.uni-freiburg.de/Publications/2015/RFB15a

    Chapter  Google Scholar 

  16. Saenger, E.H., Gold, N., Shapiro, S.A.: Modeling the propagation of the elastic waves using a modified finite-difference grid. Wave Motion 31, 77–92 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Siahkoohi, A., Louboutin, M., Herrmann, F.J.: The importance of transfer learning in seismic modeling and imaging. Geophysics 84, A47–A52 (2019). https://doi.org/10.1190/geo2019-0056.1

    Article  Google Scholar 

  18. Vishnevsky, D.M., Solovyev, S.A., Lisitsa, V.V.: Numerical simulation of wave propagation in 3D elastic media with viscoelastic formations. Lobachevskii J. Math. 41(8), 1603–1614 (2020)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The algorithm of optimal dataset construction was developed by Vadim Lisitsa, using the NKS-30T cluster of the Siberian Supercomputer Center, Dmitry Vishnevsky performed seismic modeling, while Kseniia Gadylshina carried out numerical experiments for NDM-net training with the help of RSCF grant number 22-11-00004. NDM-net hyperparameters were tuned by Kirill Gadylshin with the help of the grant for young scientists MK-3947.2021.1.5.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vadim Lisitsa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gadylshin, K., Lisitsa, V., Gadylshina, K., Vishnevsky, D. (2022). Data-Based Choice of the Training Dataset for the Numerical Dispersion Mitigation Neural Network. In: Voevodin, V., Sobolev, S., Yakobovskiy, M., Shagaliev, R. (eds) Supercomputing. RuSCDays 2022. Lecture Notes in Computer Science, vol 13708. Springer, Cham. https://doi.org/10.1007/978-3-031-22941-1_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-22941-1_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22940-4

  • Online ISBN: 978-3-031-22941-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics