DOI: https://doi.org/10.26089/NumMet.v24r215

Training data set construction based on the Hausdorff metric for numerical dispersion mitigation neural network in seismic modelling

Authors

  • Kseniia A. Gadylshina
  • Dmitry M. Vishnevsky
  • Kirill G. Gadylshin
  • Vadim V. Lisitsa

Keywords:

seismograms numerical modelling
numerical dispersion
deep learning
teaching dataset creation

Abstract

The article outlines a strategy for constructing a training data set for a numerical dispersion mitigation network (NDM-net), consisting in the calculation of the full set of seismograms by the finite difference method on a coarse grid and the calculation of the training sample using a fine grid. The training dataset is a small set of seismograms with a certain spatial distribution of wave field sources. After training, the NDM-net allows approximating low-quality coarse-grid seismograms into seismograms with a smaller sampling step. Optimization of the process of constructing a representative training dataset of seismograms is based on minimizing the Hausdorff metric between the training sample and the full set of seismograms. The use of the NDM-net makes it possible to reduce time costs when calculating wave fields on a fine grid.


Published

2023-05-15

Issue

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Kseniia A. Gadylshina

Dmitry M. Vishnevsky

Kirill G. Gadylshin

LLC RN-BashNIPIneft
• Expert

Vadim V. Lisitsa


References

  1. V. Kostin, V. Lisitsa, G. Reshetova, and V. Tcheverda, “Local Time-Space Mesh Refinement for Simulation of Elastic Wave Propagation in Multi-Scale Media,” J. Comput. Phys. 281, 669-689 (2015).
    doi 10.1016/j.jcp.2014.10.047.
  2. E. H. Saenger, N. Gold, and S. A. Shapiro, “Modeling the Propagation of Elastic Waves Using a Modified Finite-Difference Grid,” Wave Motion 31 (1), 77-92 (2000).
    doi 10.1016/S0165-2125(99)00023-2.
  3. J. O. Blanch, J. O. A. Robertsson, and W. W. Symes, “Modeling of a Constant Q: Methodology and Algorithm for an Efficient and Optimally Inexpensive Viscoelastic Technique,” Geophysics 60 (1), 176-184 (1995).
    doi 10.1190/1.1443744.
  4. Y. J. Masson and S. R. Pride, “Finite-Difference Modeling of Biot’s Poroelastic Equations across all Frequencies,” Geophysics 75 (2), N33-N41 (2010).
    doi 10.1190/1.3332589.
  5. V. Lisitsa, D. Kolyukhin, and V. Tcheverda, “Statistical Analysis of Free-Surface Variability’s Impact on Seismic Wavefield,” Soil Dyn. Earthq. Eng. 116, 86-95 (2019).
    doi 10.1016/j.soildyn.2018.09.043.
  6. I. Tarrass, L. Giraud, and P. Thore, “New Curvilinear Scheme for Elastic Wave Propagation in Presence of Curved Topography,” Geophys. Prospect. 59 (5), 889-906 (2011).
    doi 10.1111/j.1365-2478.2011.00972.x.
  7. Y. Liu, “Optimal Staggered-Grid Finite-Difference Schemes Based on Least-Squares for Wave Equation Modelling,” Geophys. J. Int. 197 (2), 1033-1047 (2014).
    doi 10.1093/gji/ggu032.
  8. M. Käser, M. Dumbser, J. Puente, and H. Igel, “An Arbitrary High-Order Discontinuous Galerkin Method for Elastic Waves on Unstructured Meshes -- III. Viscoelastic Attenuation,” Geophys. J. Int. 168 (1), 224-242 (2007).
    doi 10.1111/j.1365-246X.2006.03193.x.
  9. V. Lisitsa, V. Tcheverda, and C. Botter, “Combination of the Discontinuous Galerkin Method with Finite Differences for Simulation of Seismic Wave Propagation,” J. Comput. Phys. 311, 142-157 (2016).
    doi 10.1016/j.jcp.2016.02.005.
  10. M. Ainsworth, “Dispersive and Dissipative Behaviour of High Order Discontinuous Galerkin Finite Element Methods,” J. Comput. Phys. 198 (1), 106-130 (2004).
    doi 10.1016/j.jcp.2004.01.004.
  11. V. Lisitsa, “Dispersion Analysis of Discontinuous Galerkin Method on Triangular Mesh for Elastic Wave Equation,” Appl. Math. Model. 40 (7-8), 5077-5095 (2016).
    doi 10.1016/j.apm.2015.12.039.
  12. A. Pleshkevich, D. Vishnevskiy, and V. Lisitsa, “Sixth-Order Accurate Pseudo-Spectral Method for Solving One-Way Wave Equation,” Appl. Math. Comput. 359, 34-51 (2019).
    doi 10.1016/j.amc.2019.04.029.
  13. E. F. M. Koene, J. O. A. Robertsson, F. Broggini, and F. Andersson, “Eliminating Time Dispersion from Seismic Wave Modeling,” Geophys. J. Int. 213 (1), 169-180 (2018).
    doi 10.1093/gji/ggx563.
  14. R. Mittet, “Second-Order Time Integration of the Wave Equation with Dispersion Correction Procedures,” Geophysics 84 (4), T221-T235 (2019).
    doi 10.1190/geo2018-0770.1.
  15. A. Siahkoohi, M. Louboutin, and F. J. Herrmann, “The Importance of Transfer Learning in Seismic Modeling and Imaging,” Geophysics 84 (6), A47-A52 (2019).
    doi 10.1190/geo2019-0056.1.
  16. H. Kaur, S. Fomel, and N. Pham, “Overcoming Numerical Dispersion of Finite-Difference Wave Extrapolation Using Deep Learning,” SEG Tech. Program Expand. Abstr. 2019, 2318-2322 (2019).
    doi 10.1190/segam2019-3207486.1.
  17. K. A. Gadylshina, V. V. Lisitsa, D. M. Vishnevsky, and K. G. Gadylshin, “Deep Neural Network Reducing Numerical Dispersion for Post-Processing of Seismic Modeling Results,” Russ. J. Geophys. Technol. No. 1, 99-109 (2022).
    doi 10.18303/2619-1563-2022-1-99.
  18. K. Gadylshin, D. Vishnevsky, K. Gadylshina, and V. Lisitsa, “Numerical Dispersion Mitigation Neural Network for Seismic Modeling,” Geophysics 87 (3), T237-T249 (2022).
    doi 10.1190/geo2021-0242.1.
  19. A. R. Levander, “Fourth-Order Finite-Difference P-SV Seismograms,” Geophysics 53 (11), 1425-1436 (1988).
    doi 10.1190/1.1442422.
  20. O. Ronneberger, P. Fischer, and T. Brox, “U-Net: Convolutional Networks for Biomedical Image Segmentation,” in Lecture Notes in Computer Science (Springer, Cham, 2015), Vol. 9351, pp. 234-241.
    doi 10.1007/978-3-319-24574-4_28.
  21. F. Collino and C. Tsogka, “Application of the Perfectly Matched Absorbing Layer Model to the Linear Elastodynamic Problem in Anisotropic Heterogeneous Media,” Geophysics 66 (1), 294-307 (2001).
    doi 10.1190/1.1444908.
  22. R. Martin, D. Komatitsch, and A. Ezziani, “An Unsplit Convolutional Perfectly Matched Layer Improved at Grazing Incidence for Seismic Wave Propagation in Poroelastic Media,” Geophysics 73 (4), T51-T61 (2008).