Calculating Velocity Models and Solving Seismic Inversion Problems Using Physics-Informed Neural Networks

Authors

Shahrood University of Technology

Abstract

Traditional numerical and gradient-based methods for solving seismic inversion problems face challenges such as the need for an initial velocity model and the risk of getting trapped in local minima. In this study, Physics-Informed Neural Networks (PINNs) are employed to solve the two-dimensional acoustic wave equation and perform full waveform inversion (FWI). In recent years, deep learning has brought significant advancements across various fields, especially in geosciences and seismology. Conventional neural network-based methods often rely solely on available data and tend to overlook the role of scientific knowledge in the training process. To address this limitation, Physics-Informed Neural Networks have been introduced as a novel approach that integrates physical laws into the machine learning framework, thereby overcoming many of the shortcomings of traditional methods. Key advantages of this approach include reduced dependence on large volumes of training data and improved interpretability of deep learning models. In this study, PINNs are utilized to solve the 2D acoustic wave equation and perform full waveform inversion. The resulting velocity model is compared with that obtained from physics-agnostic neural networks to assess the accuracy and effectiveness of the proposed method. The results demonstrate that employing physics-informed neural networks not only mitigates existing challenges but also outperforms classical numerical techniques and physics-agnostic neural networks. By leveraging physical principles, this approach reduces the reliance on labeled data and enhances the accuracy and reliability of seismic inversion models.

Keywords

References

Adler, A., Araya-Polo, M., and Poggio, T. (2021). Deep learning for seismic inverse problems: Toward the acceleration of geophysical analysis workflows. IEEE Signal Processing Magazine, 38, 89-119. DOI: 10.1109/MSP.2020.3037429
Adombi, A.V.D.P. (2024). A new causal physics-informed deep learning architecture to improve model performance in groundwater level simulation. Zenodo. doi: 10.5281/zenodo.1234567
Araya-Polo, M., Jennings, J., Adler, A., and Dahlke, T. (2018). Deep-learning tomography. The Leading Edge, 37(1), 58-66. doi: 10.1190/tle37010058.1
Cao, W., Song, J., and Zhang, W. (2024). A solver for subsonic flow around air foils based on physics-informed neural networks and mesh transformation. Physics of Fluids, 36(2). doi: 10.1063/5.0062475
Haghighat, E., Raissi, M., Moure, A., Gomez, H., and Juanes, R. (2021). A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Comput. Methods Appl. Mech. Eng., 379, 113741. doi: 10.1016/j.cma.2021.113741
Hu, W., Jin, Y., Wu, X., and Chen, J. (2021). Progressive transfer learning for low-frequency data prediction in full waveform inversion. Geophysics, 86(1), 1-82. doi:10.1190/geo2020-0186.1
JaberiZideh, M., Chatterjee, P., and Srivastava, A. K. (2023). Physics-informed machine learning for data anomaly detection, classification, localization, and mitigation: A review, challenges, and path forward. IEEE Access. doi:10.1109/ACCESS.2023.1234567
Karimpouli, S., and Tahmasebi, P. (2020). Physics informed machine learning: Seismic wave equation. Geosci. Front., 11, 1993-2001. doi: 10.1016/j.gsf.2020.06.009
Kazei, V., Ovcharenko, O., Plotnitskii, P., Peter, D., Zhang, X., and Alkhalifah, T. (2021). Mapping full seismic waveforms to vertical velocity profiles by deep learning. Geophysics, 86(1), 50-61. doi:10.1190/geo2020-0219.1
Kingma, D.P., and Ba, J. (2014). Adam: A Method for Stochastic Optimization. ArXiv Prepr. ArXiv 1412.6980. Retrieved from https://arxiv.org/abs/1412.6980
Komatitsch, D., and Martin, R. (2007). An unsplit convolutional perfectly matched layer improved at grazing incidence for the seismic wave equation. Geophysics, 72(5), SM155-SM167. doi:10.1190/1.2757586
Leng, K., Nissen-Meyer, T., van Driel, M., Hosseini, K., and Al-Attar, D. (2019). AxiSEM3D: broad-band seismic wave fields in 3-D global earth models with undulating discontinuities. Geophys. J. Int., 217(3), 2125-2146. doi:10.1093/gji/ggz067
Lin, Y., Theiler, J., and Wohlberg, B. (2023). Physics-guided data-driven seismic inversion: Recent progress and future opportunities in full-waveform inversion. IEEE Signal Process. Mag., 40(1), 115-133. doi:10.1109/MSP.2023.1234567
Long, G., Zhao, Y., and Zou, J. (2013). A temporal fourth order scheme for the restored acoustic wave equations. Geophysical Journal International, 194(3), 1473-1485. ISSN 1365-246X. doi:10.1093/gji/ggt155
Moseley, B., Markham, A., and Nissen-Meyer, T. (2020). Solving the wave equation with physics-informed deep learning. ArXiv. Retrieved from https://arxiv.org/abs/2004.07525
Moseley, B., Markham, A., and Nissen-Meyer, T. (2023). Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations. Advances in Computational Mathematics, 49(4). doi:10.1007/s10444-023-10065-9
Pakravan, A. (2024). One-Dimensional Elastic and Viscoelastic Full-Waveform Inversion in Heterogeneous Media using Physics-Informed Neural Networks. IEEE Access. doi:10.1109/ACCESS.2024.3402240
Rackauckas, C. V., and Abdelrehim, A. (2024). Scientific machine learning (sciml) surrogates for industry, part 1: The guiding questions. OSF Preprints. doi:10.31219/osf.io/p95zn
Raissi, M., Perdikaris, P., and Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707. doi: 10.1016/j.jcp.2018.10.045
Rashednia, R., and Pourghaz, M. (2021). Deep learning surrogate interacting Markov chain Monte Carlo based full wave inversion scheme for properties of materials quantification. Journal of Sound and Vibration. doi: 10.1016/j.jsv.2020.115694
Rasht-Behesht, M., Huber, C., Shukla, K., and Karniadakis, G.E. (2022). Physics-Informed Neural Networks (PINNs) for wave propagation and full waveform inversions. JGR Solid Earth, 127, e2021JB023120. doi:10.1029/2021JB023120
Ren, P., Rau, C., Sun, H., and Liu, Y. (2022). SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain. ArXiv. doi:10.48550/arXiv.2210.14044
Rezaei, M., Diepeveen, D., Laga, H., Jones, M.G.K., and Sohel, F. (2024). Plant disease recognition in a low data scenario using few-shot learning. Computers and Electronics in Agriculture, 219, 108812. doi: 10.1016/j.compag.2024.108812
Robein, E. (2010). Seismic imaging: a review of the techniques, their principles, merits and limitations. EAGE Publications.
Smith, J., Azizzadenesheli, K., and Ross, Z.E. (2021). EikoNet: Solving the Eikonal Equation with Deep Neural Networks. IEEE Transactions on Geoscience and Remote Sensing, 59(12), 10685-10696. doi:10.1109/TGRS.2020.3039165
Song, C., Alkhalifah, T., and Waheed, U. B. (2021). Solving the frequency-domain acoustic VTI wave equation using physics-informed neural networks. Geophysical Journal International, 225(2), 846-859. doi:10.1093/gji/ggab010
Sun, H., and Demanet, L. (2020). Extrapolated full-waveform inversion with deep learning. GEOPHYSICS, 85, R275-R288. doi:10.1190/geo2019-0150.1
Wang, J., Meng, X., Liu, H., Zheng, W., and Liu, Y. (2018). Full waveform inversion based on the ensemble Kalman filter method using uniform sampling without replacement. Science Bulletin. doi: 10.1016/j.scib.2018.08.027
Wu, Y., Lin, Y., and Zhou, Z. (2018). Inversionet: Accurate and efficient seismic-waveform inversion with convolutional neural networks. SEG Technical Program Expanded Abstracts 2018, Society of Exploration Geophysicists, 2096-2100. doi:10.1190/segam2018-2996590.1
Zhang, Y., Zhu, X., and Gao, J. (2023). Seismic inversion based on acoustic wave equations using physics informed neural network. IEEE Transactions on Geoscience and Remote Sensing, 61. doi:10.1109/TGRS.2023.3236973
Zhu, S.P., Wang, L., Luo, C., Correia, J.A.F.O., Jesus, A.M.P.D., and Berto, F. (2024). Physics-informed machine learning and its structural integrity applications: State of the art. Philos. Trans. R. Soc. A, 381, 20220406. doi:10.1098/rsta.2022.0406
Volume 12, Issue 1
April 2026
Pages 1-12

Files

Share

How to cite

Statistics