1887

Abstract

Summary

Since the original algorithm by John Vidale in 1988 to numerically solve the isotropic eikonal equation, there has been tremendous progress on the topic addressing an array of computational challenges, including improvement of the solution accuracy, incorporation of surface topography, the addition of accurate physics by accounting for anisotropy/attenuation in the medium, and speeding up computations. Despite these advances, these algorithms have no mechanism to carry information gained by solving one problem to the next. Moreover, these approaches may breakdown for certain complex forms of the eikonal equation, requiring simplification of the equations to estimate approximate solutions. Therefore, we seek an alternate approach to address these challenges holistically. We propose an algorithm based on the emerging paradigm of physics-informed neural network to solve different forms of the eikonal equation. We show how transfer learning can be used to speed up computations by utilizing information gained from prior solutions. Such an approach makes the implementation of eikonal solvers much simpler and puts us on a much faster path to progress. The method paves the pathway to solving complex forms of the eikonal equation that have remained unsolved using conventional algorithms or solved using some approximation techniques at best.

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/content/papers/10.3997/2214-4609.202210613
2022-06-06
2023-02-03
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References

  1. Breuß, M., Cristiani, E., Gwosdek, P. and Vogel, O. [2011] An adaptive domain-decomposition technique for parallelization of the fast marching method. Applied Mathematics and Computation, 218(1), 32–44.
    [Google Scholar]
  2. Detrixhe, M., Gibou, F. and Min, C. [2013] A parallel fast sweeping method for the Eikonal equation. Journal of Computational Physics, 237, 46–55.
    [Google Scholar]
  3. Grechka, V., De La Pena, A., Schisselé-Rebel, E., Auger, E. and Roux, P.F. [2015] Relative location of microseismicity. Geophysics, 80(6), WC1–WC9.
    [Google Scholar]
  4. Haghighat, E. and Juanes, R. [2021] SciANN: A Keras/TensorFlow wrapper for scientifc computations and physics-informed deep learning using artifcial neural networks. Computer Methods in Applied Mechanics and Engineering, 373, 113552.
    [Google Scholar]
  5. Hole, J. and Zelt, B. [1995] 3-D fnite-difference refection traveltimes. Geophysical Journal International, 121(2), 427–434.
    [Google Scholar]
  6. Lan, H. and Zhang, Z. [2013] A high-order fast-sweeping scheme for calculating first-arrival travel times with an irregular surface. Bulletin of the Seismological Society of America, 103(3), 2070–2082.
    [Google Scholar]
  7. Lawton, D.C. [1989] Computation of refraction static corrections using first-break traveltime differences. Geophysics, 54(10), 1289–1296.
    [Google Scholar]
  8. Rickett, J. and Fomel, S. [1999] A second-order fast marching eikonal solver. Stanford Exploration Project Report, 100, 287–293.
    [Google Scholar]
  9. Sethian, J.A. and Popovici, A.M. [1999] 3-D traveltime computation using the fast marching method. Geophysics, 64(2), 516–523.
    [Google Scholar]
  10. Sethian, J.A. and Vladimirsky, A. [2003] Ordered upwind methods for static Hamilton–Jacobi equations: Theory and algorithms. SIAM Journal on Numerical Analysis, 41(1), 325–363.
    [Google Scholar]
  11. Vidale, J. [1988] Finite-difference calculation of travel times. Bulletin of the Seismological Society of America, 78(6), 2062–2076.
    [Google Scholar]
  12. Waheed, U., Yarman, C.E. and Flagg, G. [2015] An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media. Geophysics, 80(3), C49–C58.
    [Google Scholar]
  13. Zhang, Y.T., Zhao, H.K. and Qian, J. [2006] High order fast sweeping methods for static Hamilton– Jacobi equations. Journal of Scientifc Computing, 29(1), 25–56.
    [Google Scholar]
  14. Zhao, H. [2005] A fast sweeping method for eikonal equations. Mathematics of computation, 74(250), 603–627.
    [Google Scholar]
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