Abstract
We have developed and tested a new Eikonal first-arrival forward model scheme by combining a fast marching method (FMM) algorithm, an upwind Eikonal solver scheme first described by Sethian and Popovici in 1996, with a more accurate but less robust Eikonal scheme described by Vidale in 1990 as a finite difference method (VFD) in order to produce a robust forward model based in FMM, with application of VFD schemes for refinement of computed model times (FMM-VFD). The developed model was tested through a uniform velocity base case, and the Southern California Earthquake Center (SCEC) Harvard Velocity Model (CVM-H) of upper crust including the sedimentary basin under Los Angeles, CA. Its performance was evaluated by measuring error at different grid sizes against a set of reference times generated by an independent model. In comparison against first-order FMM (FMM-O1), second-order FMM (FMM-O2), and an improved FMM scheme known as factored FMM (FMM-F) against a set of generated reference times, FMM-VFD error was found to be significantly lower than first- and second-order FMM, and competitive with FMM-F, outperforming it in the presented scenarios.
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Code Availability
Code used in this study is freely available at https://github.com/abatchev/FMM-VFD.
Change history
16 April 2021
A Correction to this paper has been published: https://doi.org/10.1007/s10596-020-10022-1
References
Sethian, J.: Fast-marching level-set methods for three-dimensional photolithography development. Proc. SPIE 2726 optical microlithography IX (1996)
Sethian, J., Popovici, A.M.: Three-dimensional traveltime computation using the fast marching method. 67th Ann. Internat. Mtg, Soc. of Expl. Geophys., pp. 1778–1781 https://library.seg.org/doi/abs/10.1190/1.1444558 (1997)
Sethian, J.: Fast marching methods. SIAM Rev. 41(2), 199–235 (1999)
Vidale, J.: Finite-difference calculation of traveltimes in three dimensions. Geophysics 55(5), 521–526 (1990)
SCEC Community Velocity Model -Harvard (CVM-H) v4.0. https://scec.usc.edu/scecpedia/CVM-H
Fomel, S., Luo, S., Zhao, H.: Fast sweeping method for the factored eikonal equation. J. Comput. Phys. 228(17), 6440–6455 (2009)
Treister, E., Haber, E.: A fast marching algorithm for the factored eikonal equation. J. Comput. Phys. 324, 210–225 (2016)
Klimes, L., Kvasnicka, M.: 3-D network ray tracing. Geophys. J. Int. 116, 726–738 (1994)
Moser, T.J.: Shortest path calculation of seismic rays. Geophysics 56(1), 59–67 (1991)
Abatchev, Z.: Development of Specialized Nonlinear Inversion Algorithms, Basis Functions, Eikonal Solvers, and Their Integration for Use in Joint Seismic and Gravitational Tomographic Inversion, University of California, Los Angeles Phd Thesis. https://escholarship.org/uc/item/22q7c2vf (2019)
Sibson, R.: A brief description of natural neighbor interpolation. In: Barnett, V. (ed.) Interpolating Multivariate Data, pp 21–36. Chichester, Wiley (1981)
Park, S.W., et al.: Discrete Sibson interpolation. IEEE Trans. Visual. Comput. Graphics 12(2) (2006)
Baer, M., Kradolfer, U.: An automatic phase picker for local and teleseismic events. Bulletin of the Seismological Society of America 77(4), 1437–1445 (1987)
Withers, M., et al.: A comparison of select trigger algorithms for automated global seis- mic phase and event detection. Bull. Seismol. Soc. Am. 88(1), 95–106 (1998)
Eikonalfm Python module https://github.com/kevinganster/eikonalfm/
Sedgewick, W.: Algorithms, vol. 4, pp 315–319. Addison Wesley, Boston (2011)
Chacon, V.: Fast two-scale methods for Eikonal equations. SIAM J. Sci. Comput. 34(2) (2012)
Yang, J., Stern, F.: A highly scalable massively parallel fast marching method for the Eikonal equation. J. Comput. Phys. 332, 333–62 (2017)
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Abatchev, Z., Binder, G. & Davis, P. Development of efficient and robust Eikonal solver variants for first-arrival seismic modeling. Comput Geosci 25, 1437–1453 (2021). https://doi.org/10.1007/s10596-020-10010-5
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DOI: https://doi.org/10.1007/s10596-020-10010-5