Abstract
We present an approach to construct the training dataset for the numerical dispersion mitigation network (NDM-net). The network is designed to suppress numerical error in the simulated seismic wavefield. The training dataset is the wavefield simulated using a fine grid, thus almost free from the numerical dispersion. Generation of the training dataset is the most computationally intense part of the algorithm, thus it is important to reduce the number of seismograms used in the training dataset to improve the efficiency of the NDM-net. In this work, we introduce the discrepancy between seismograms and construct the dataset, so that the discrepancy between the dataset and any seismogram is below the prescribed level.
V.L. developed the algorithm of optimal dataset construction under the support of RSF grant no. 22-11-00004. D.V. performed seismic modeling using NKS-30T cluster of the Siberian Supercomputer Center under the support of RSF grant no. 22-21-00738. Kseniia Gadylshina performed numerical experiments on NDM-net training under the support of the RSF grant no. 19-77-20004. Kirill Gadylshin optimized the NDM-net hyperparameters under the support of the grant for young scientists MK-3947.2021.1.5.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ainsworth, M.: Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods. J. Comput. Phys. 198(1), 106–130 (2004)
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)
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
Kaser, M., Dumbser, M., Puente, J.D.l., Igel, H.: An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes III. Viscoelastic attenuation. Geophys. J. Int. 168(1), 224–242 (2007). https://doi.org/10.1111/j.1365-246X.2006.03193.x
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
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)
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)
Levander, A.R.: Fourth-order finite-difference P-SV seismograms. Geophysics 53(11), 1425–1436 (1988)
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
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)
Lisitsa, V., Tcheverda, V., Botter, C.: Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation. J. Comput. Phys. 311, 142–157 (2016)
Liu, Y.: Optimal staggered-grid finite-difference schemes based on least-squares for wave equation modelling. Geophys. J. Int. 197(2), 1033–1047 (2014)
Masson, Y.J., Pride, S.R.: Finite-difference modeling of Biot’s poroelastic equations across all frequencies. Geophysics 75(2), N33–N41 (2010)
Mittet, R.: Second-order time integration of the wave equation with dispersion correction procedures. Geophysics 84(4), T221–T235 (2019)
Pleshkevich, A., Vishnevskiy, D., Lisitsa, V.: Sixth-order accurate pseudo-spectral method for solving one-way wave equation. Appl. Math. Comput. 359, 34–51 (2019)
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_28
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)
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
Tarrass, I., Giraud, L., Thore, P.: New curvilinear scheme for elastic wave propagation in presence of curved topography. Geophys. Prospect. 59(5), 889–906 (2011). https://doi.org/10.1111/j.1365-2478.2011.00972.x
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Gadylshin, K., Lisitsa, V., Gadylshina, K., Vishnevsky, D. (2022). Optimization of the Training Dataset for Numerical Dispersion Mitigation Neural Network. In: Gervasi, O., Murgante, B., Misra, S., Rocha, A.M.A.C., Garau, C. (eds) Computational Science and Its Applications – ICCSA 2022 Workshops. ICCSA 2022. Lecture Notes in Computer Science, vol 13378. Springer, Cham. https://doi.org/10.1007/978-3-031-10562-3_22
Download citation
DOI: https://doi.org/10.1007/978-3-031-10562-3_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-10561-6
Online ISBN: 978-3-031-10562-3
eBook Packages: Computer ScienceComputer Science (R0)