Rapid Seismic Traveltime Modeling Using Deep Neural Operator

References

1. Cao, Q., Goswami, S. and Karniadakis, G.E. [2023] LNO: Laplace neural operator for solving differential equations.arXiv preprint arXiv:2303.10528.
   [Google Scholar]
2. Chen, T. and Chen, H. [1995] Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems.IEEE transactions on neural networks, 6(4), 911–917.
   [Google Scholar]
3. Fomel, S., Luo, S. and Zhao, H. [2009] Fast sweeping method for the factored eikonal equation.Journal of Computational Physics, 228(17), 6440–6455.
   [Google Scholar]
4. Goswami, S., Bora, A., Yu, Y. and Karniadakis, G.E. [2022] Physics-informed neural operators.arXiv preprint arXiv:2207.05748.
   [Google Scholar]
5. Haghighat, E., bin Waheed, U. and Karniadakis, G. [2024] En-DeepONet: An enrichment approach for enhancing the expressivity of neural operators with applications to seismology.Computer Methods in Applied Mechanics and Engineering, 420, 116681.
   [Google Scholar]
6. Khosro Anjom, E., Vaccarino, F. and Socco, L.V. [2024] Machine learning for seismic exploration: Where are we and how far are we from the holy grail?Geophysics, 89(1), WA157–WA178.
   [Google Scholar]
7. Krebes, E. [2004] Seismic forward modeling.CSEG Recorder, 30, 28–39.
   [Google Scholar]
8. Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A. and Anandkumar, A. [2020] Fourier neural operator for parametric partial differential equations.arXiv preprint arXiv:2010.08895.
   [Google Scholar]
9. Lu, L., Jin, P., Pang, G., Zhang, Z. and Karniadakis, G.E. [2021] Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.Nature machine intelligence, 3(3), 218–229.
   [Google Scholar]
10. Sethian, J.A. [1999] Fast marching methods.SIAM review, 41(2), 199–235.
    [Google Scholar]
11. Smith, J.D., Azizzadenesheli, K. and Ross, Z.E. [2020] Eikonet: Solving the eikonal equation with deep neural networks.IEEE Transactions on Geoscience and Remote Sensing, 59(12), 10685–10696.
    [Google Scholar]
12. Tripura, T. and Chakraborty, S. [2023] Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems.Computer Methods in Applied Mechanics and Engineering, 404, 115783.
    [Google Scholar]
13. Waheed, U., Haghighat, E., Alkhalifah, L., Song, C. and Hao, Q. [2021] PINNeik: Eikonal solution using physics-informed neural networks.Computers & Geosciences, 155, 104833.
    [Google Scholar]
14. Waheed, U.b. and Alkhalifah, T. [2017] A fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization.Geophysics, 82(6), WB1–WB8.
    [Google Scholar]