1887

Abstract

Summary

Traveltimes corresponding to both compressional and shear waves are needed for many applications in seismology ranging from seismic imaging to earthquake localization. Since the behavior of shear waves in anisotropic media is considerably more complicated than the isotropic case, accurate traveltime computation for shear waves in anisotropic media remains a challenge. Ray tracing methods are often used to compute qSV wave traveltimes but they become unstable around triplication points and, therefore, we often use the weak anisotropy approximation. Here, we employ the emerging paradigm of physics-informed neural networks to solve transversely isotropic eikonal equation for the qSV wave that otherwise are not easily solvable using conventional finite difference methods. By minimizing a loss function formed by imposing the validity of eikonal equation, we train a neural network to produce traveltime solutions that are consistent with the underlying equation. Through tests on synthetic models, we show that the method is capable of producing accurate qSV wave traveltimes even at triplication points and works for arbitrary strength of medium anisotropy.

Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.202112541
2021-10-18
2025-11-08
Loading full text...

Full text loading...

References

  1. Fomel, S., Ying, L. and Song, X.
    [2013] Seismic wave extrapolation using lowrank symbol approximation. Geophysical Prospecting, 61(3): 526–536.
    [Google Scholar]
  2. Garotta, R.
    [1999] Shear waves from acquisition to interpretation. Society of Exploration Geophysicists.
    [Google Scholar]
  3. Haghighat, E. and Juanes, R.
    [2021] SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks. Computer Methods in Applied Mechanics and Engineering, 373, 113552.
    [Google Scholar]
  4. Han, S., Zhang, W. and Zhang, J.
    [2017] Calculating qP-wave traveltimes in 2-D TTI media by highorder fast sweeping methods with a numerical quartic equation solver. Geophysical Journal International, 210(3): 1560–1569.
    [Google Scholar]
  5. Huang, G., Luo, S., Deng, J. and Vavrycuk, V.
    [2020] Traveltime Calculations for qP, qSV, and qSH Waves in Two-Dimensional Tilted Transversely Isotropic Media. Journal ofGeophysical Research: Solid Earth, 125(8), e2019JB018868.
    [Google Scholar]
  6. Jagtap, A.D., Kawaguchi, K. and Em Karniadakis, G.
    [2020] Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks. Proceedings ofthe Royal SocietyA, 476(2239), 20200334.
    [Google Scholar]
  7. Padhi, A. and Willis, M.
    [2019] Accurate quasi-SV traveltimes in 3D transversely isotropic media with vertical axis of symmetry using a high-order fast-sweeping-based eikonal solver. In: SEG Technical Program Expanded Abstracts 2019, Society of Exploration Geophysicists, 3879–3883.
    [Google Scholar]
  8. Song, C., Alkhalifah, T. and Waheed, U.
    [2020] Solving the acoustic VTI wave equation using physics-informed neural networks. arXiv preprint arXiv:2008.01865.
    [Google Scholar]
  9. Vavrycuk, V.
    [2001] Ray tracing in anisotropic media with singularities. Geophysical Journal International, 145265–276.
    [Google Scholar]
  10. Waheed, U., Haghighat, E., Alkhalifah, T., Song, C. and Hao, Q.
    [2020] Eikonal solution using physics-informed neural networks. arXiv preprint arXiv:2007.08330.
    [Google Scholar]
/content/papers/10.3997/2214-4609.202112541
Loading
/content/papers/10.3997/2214-4609.202112541
Loading

Data & Media loading...

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error