Abstract
We present an original approach to improving seismic modelling performance by applying deep learning techniques to mitigate numerical error. In seismic modelling, a series of several thousand simulations are required to generate a typical seismic dataset. These simulations are performed for different source positions (equidistantly distributed) at the free surface. Thus, the output wavefields that corresponded to the nearby sources are relatively similar, sharing common peculiarities. Our approach suggests simulating wavefields using finite differences with coarse enough discretization to reduce the computational complexity of seismic modelling. After that, solutions for 1 to 10 percents of source positions are simulated using fine discretizations to obtain the training dataset, which is used to train the deep neural network to remove numerical error (numerical dispersion) from the coarse-grid simulated wavefields. Later the network is applied to the entire dataset. Our experiments illustrate that the suggested algorithm in the 2D case significantly (up to ten times) speeds up seismic modelling.
K. Gadylshin and V. Lisitsa—are grateful to Mathematical Center in Akademgorodok, the agreement with Ministry of Science and High Education of the Russian Federation number 075-15-2019-1613 for the financial support. MN is supported by the Agency of the Precedent of Russian Federation, grant no. MK-3947.2021.1.5.
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References
Baldassari, C., Barucq, H., Calandra, H., Diaz, J.: Numerical performances of a hybrid local-time stepping strategy applied to the reverse time migration. Geophys. Prospect. 59(5), 907–919 (2011). https://doi.org/10.1111/j.1365-2478.2011.00975.x
Chen, G., Song, L., Liu, L.: 3D numerical simulation of elastic wave propagation in discrete fracture network rocks. Pure Appl. Geophys. 176(12), 5377–5390 (2019)
Cohen, G. (ed.): Metodes numeriques d’ordre eleve pour les ondes en regime transitoire. INRIA (1994). in French
Collino, F., Tsogka, C.: Application of the perfectly matched layer absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media. Geophysics 66, 294–307 (2001)
Gadylshin, K., Silvestrov, I., Bakulin, A.: Inpainting of local wavefront attributes using artificial intelligence for enhancement of massive 3-D prestack seismic data. Geophys. J. Int. 223, 1888–1898 (2020)
Guo, X., Li, W., Iorio, F.: Convolutional neural networks for steady flow approximation. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD ’16, San Francisco, CA, USA, pp. 481–490 (2016). https://doi.org/10.1145/2939672.2939738
Hicks, G.: Arbitrary source and receiver positioning in finite-difference schemes using kaiser windowed sinc functions. Geophysics 67(1), 156–165 (2002)
Kaser, M., Dumbser, M.: An arbitrary high-order discontinuous galerkin method for elastic waves on unstructured meshes - i. the two-dimensional isotropic case with external source terms. Geophys. J. Int. 166(2), 855–877 (2006)
Koene, E., Robertsson, J.: Removing numerical dispersion artifacts from reverse time migration and full-waveform inversion, pp. 4143–4147 (2017)
Kragh, E., Christie, P.: Seismic repeatability, normalized rms, and predictability. Lead. Edge 21(7), 640–647 (2002)
Levander, A.R.: Fourth-order finite-difference p-sv seismograms. Geophysics 53(11), 1425–1436 (1988)
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)
Martin, G.S., Wiley, R., Marfurt, K.J.: Marmousi2: an elastic upgrade for marmousi. Lead. Edge 25(2), 156–166 (2006)
Moczo, P., Kristek, J., Vavrycuk, V., Archuleta, R.J., Halada, L.: 3D heterogeneous staggered-grid finite-differece modeling of seismic motion with volume harmonic and arithmetic averagigng of elastic moduli and densities. Bull. Seismol. Soc. Am. 92(8), 3042–3066 (2002)
Moseley, B., Nissen-Meyer, T., Markham, A.: Deep learning for fast simulation of seismic waves in complex media. Solid Earth 11, 1527–1549 (2020)
Ronneberger, O., Fischer, P., Brox, T.: U-Net: convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., Wells, W.M., Frangi, Al.F. (eds.) MICCAI 2015. LNCS, vol. 9351, pp. 234–241. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24574-4_28
Shokin, Y., Yanenko, N.: Method of Differential Approximation. Application to Gas Dynamics. Nauka, Novosibirsk (1985). in Russian
Virieux, J.: P-sv wave propagation in heterogeneous media: velocity-stress finite-difference method. Geophysics 51(4), 889–901 (1986)
Virieux, J., Calandra, H., Plessix, R.E.: A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging. Geophys. Prospect. 59(5), 794–813 (2011). https://doi.org/10.1111/j.1365-2478.2011.00967.x
Vishnevsky, D., Lisitsa, V., Tcheverda, V., Reshetova, G.: Numerical study of the interface errors of finite-difference simulations of seismic waves. Geophysics 79(4), T219–T232 (2014)
Xu, Z., et al.: Time-dispersion filter for finite-difference modeling and reverse time migration, pp. 4448–4452 (2017)
Zhu, J., Ren, M., Liao, Z.: Wave propagation and diffraction through non-persistent rock joints: an analytical and numerical study. Int. J. Rock Mech. Mining Sci. 132, 104362 (2020)
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Gadylshin, K., Lisitsa, V., Gadylshina, K., Vishnevsky, D., Novikov, M. (2021). Machine Learning-Based Numerical Dispersion Mitigation in Seismic Modelling. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_3
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