Novosibirsk State University Journal of Information Technologies
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ISSN 2410-0420 (Online), ISSN 1818-7900 (Print)

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Parallel algorithm of three-dimensional eikonal solver for seismic applications
Aleksandr Alekseyevich Nikitin, Aleksandr Sergeyevich Serdyukov, Anton Albertovich Duchkov

Trofimuk Institute of Petroleum Geology and geophysics SB RAS
Novosibirsk State University

UDC code: 004.021:550.34

Solution to the eikonal equation is used in seismic problems to determine first arrival travel times of seismic waves. In this paper we present a new parallel algorithm of the eikonal equation solution based on the Fast Sweeping Method (FSM). The algorithm achieves higher efficiency compared to existing parallel implementations of FSM due to optimization of CPU cache use.

Key Words
Eikonal equation, Parallel algorithm, Fast sweeping method, Exploration seismology, Forward traveltime problem, Fast sweeping method

How to cite:
Nikitin A. A., Serdyukov A. S., Duchkov A. A. Parallel algorithm of three-dimensional eikonal solver for seismic applications // Vestnik NSU Series: Information Technologies. - 2015. - Volume 13, Issue No 3. - P. 19-28. - ISSN 1818-7900. (in Russian).

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1. Cerveny V. Seismic ray theory. Cambridge University Press, 2005.
2. Sethian J. A. Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge University Press, 1999. Vol. 3.
3. Runborg O. Mathematical models and numerical methods for high frequency waves // Communications in Computational Physics. 2007. Vol. 2, № 5. Р. 827–880.
4. Crandall M. G., Lions P. L. Viscosity solutions of Hamilton-Jacobi equations // Transactions of the American Mathematical Society. 1983. Vol. 277, № 1. Р. 1–42.
5. Yilmaz Ö. Seismic data analysis. Society of Exploration Geophysicists, 2001.
6. Vidale J. Finite-difference calculation of travel times // Bulletin of the Seismological Society of America. 1988. Vol. 78, № 6. Р. 2062–2076.
7. Podvin P., Lecomte I. Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools // Geophysical Journal International. 1991. Vol. 105, № 1. Р. 271–284.
8. Sethian J. A. A fast marching level set method for monotonically advancing fronts // Proceedings of the National Academy of Sciences. 1996. Vol. 93, № 4. Р. 1591–1595.
9. Hassouna S. M., Farag A. A. Multistencils fast marching methods: A highly accurate solution to the eikonal equation on cartesian domains // IEEE Transactions on Pattern Analysis and Machine Intelligence. 2007. Vol. 29, № 9. Р. 1563–1574.
10. Kim S. An O(N) Level Set Method for Eikonal Equations // SIAM Journal on Scientific Computing. 2001. Vol. 22, № 6. Р. 2178–2193.
11. Zhao H. A fast sweeping method for eikonal equations // Mathematics of computation. 2005. Vol. 74, № 250. Р. 603–627.
12. Zhang Y. T., Zhao H. K., Qian J. High order fast sweeping methods for static Hamilton – Jacobi equations // Journal of Scientific Computing. 2006. Vol. 29, № 1. Р. 25–56.
13. Zhao H. Parallel implementations of the fast sweeping method // Journal of Computational Mathematics. 2007. Vol. 25, № 4. Р. 421–429.
14. Detrixhe M., Gibou F., Min C. A parallel fast sweeping method for the Eikonal equation // Journal of Computational Physics. 2013. Vol. 237. Р. 46–55.
15. Rouy E., Tourin A. A viscosity solutions approach to shape-from-shading // SIAM Journal on Numerical Analysis. 1992. Vol. 29, № 3. Р. 867–884.

Publication information
Main title Vestnik NSU Series: Information Technologies, Volume 13, Issue No 3 (2015).
Parallel title: Novosibirsk State University Journal of Information Technologies Volume 13, Issue No 3 (2015).

Key title: Vestnik Novosibirskogo gosudarstvennogo universiteta. Seriâ: Informacionnye tehnologii
Abbreviated key title: Vestn. Novosib. Gos. Univ., Ser.: Inf. Tehnol.
Variant title: Vestnik NGU. Seriâ: Informacionnye tehnologii

Year of Publication: 2015
ISSN: 1818-7900 (Print), ISSN 2410-0420 (Online)
Publisher: Novosibirsk State University Press
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