An upwind fast sweeping scheme for calculating seismic wave first‐arrival travel times for models with an irregular free surface

References

1. AlkhalifahT. and FomelS.2001. Implementing the fast marching eikonal solver: spherical versus Cartesian coordinates. Geophysical Prospecting49, 165–178.
   [Google Scholar]
2. AlkhalifahT.2002. Traveltime computation with the linearized eikonal equation in anisotropic media. Geophysical Prospecting50(4), 373–382.
   [Google Scholar]
3. AltonK. and MitchellI.M.2008. Fast marching methods for stationary Hamilton–Jacobi equations with axis‐aligned anisotropy. SIAM Journal on Numerical Analysis47, 363–385.
   [Google Scholar]
4. AppeloD. and PeterssonN.2009. A stable finite difference method for the elastic wave equation on complex geometries with free surfaces. Communications in Computational Physics5, 84–107.
   [Google Scholar]
5. BadalJ., DuttaU., SerónF. and BiswasN.2004. Three‐dimensional imaging of shear wave velocity in the uppermost 30 m of the soil column in Anchorage, Alaska. Geophysical Journal International158, 983–997.
   [Google Scholar]
6. BakS., McLaughlinJ. and RenziD.2010. Some improvements for the fast sweeping method. SIAM Journal on Scientific Computing32(5), 2853–2874.
   [Google Scholar]
7. CaoS. and GreenhalghS.1994. Finite‐difference solution of the eikonal equation using an efficient, first‐arrival wavefront tracking scheme. Geophysics59, 632–643.
   [Google Scholar]
8. ČervenýV.2001. Seismic Ray Theory. Cambridge University Press.
   [Google Scholar]
9. CoppensF.2006. First arrival picking on common‐offset trace collections for automatic estimation of static corrections. Geophysical Prospecting33, 1212–1231.
   [Google Scholar]
10. DellingerJ.1991. Anisotropic seismic wave propagation. PhD thesis, Stanford University, USA.
    [Google Scholar]
11. DellingerJ. and SymesW.1997. Anisotropic finite‐difference traveltimes using a Hamilton‐Jacobi solver. 67th SEG annual international meeting, Expanded Abstracts, 1786–1789.
12. FomelS., LuoS. and ZhaoH.2009. Fast sweeping method for the factored eikonal equation. Journal of Computational Physics228, 6440–6455.
    [Google Scholar]
13. FornbergB.1988. The pseudo‐spectral method: accurate representation in elastic wave calculations. Geophysics53, 625–637.
    [Google Scholar]
14. GrayS.H. and MayW.P.1994. Kirchhoff migration using eikonal equation traveltimes. Geophysics59, 810–817.
    [Google Scholar]
15. HestholmS. and RuudB.1994. 2D finite‐difference elastic wave modeling including surface topography. Geophysical Prospecting42, 371–390.
    [Google Scholar]
16. HestholmS. and RuudB.1998. 3‐D finite‐difference elastic wave modeling including surface topography. Geophysics63, 613–622.
    [Google Scholar]
17. HoleJ.1992. Nonlinear high‐resolution three‐dimensional seismic traveltime tomography. Journal of Geophysical Research: Solid Earth97, 6553–6562.
    [Google Scholar]
18. HuangJ.‐W. and BellefleurG.2012. Joint transmission and reflection traveltime tomography using the fast sweeping method and the adjoint‐state technique. Geophysical Journal International188, 570–582.
    [Google Scholar]
19. KaoC.Y., OsherS. and QianJ.2004. Lax‐Friedrichs sweeping scheme for static Hamilton‐Jacobi equations. Journal of Computational Physics196, 367–391.
    [Google Scholar]
20. KaoC.Y., OsherS. and TsaiY.H.2005. Fast sweeping methods for static Hamilton‐Jacobi equations. SIAM Journal on Numerical Analysis42, 2612–2632.
    [Google Scholar]
21. KaoC.Y., OsherS. and QianJ.2008. Legendre‐transform‐based fast sweeping methods for static Hamilton‐Jacobi equations on triangulated meshes. Journal of Computational Physics227, 10209–10225.
    [Google Scholar]
22. KennettB. and EngdahlE.1991. Traveltimes for global earthquake location and phase identification. Geophysical Journal International105, 429–465.
    [Google Scholar]
23. KimmelR. and SethianJ.A.1998. Computing geodesic paths on manifolds. Proceedings of the National Academy of Sciences95, 8431–8435.
    [Google Scholar]
24. LanH. and ZhangZ.2011. Three‐dimensional wave‐field simulation in heterogeneous transversely isotropic medium with irregular free surface. Bulletin of the Seismological Society of America101(3), 1354–1370.
    [Google Scholar]
25. LanH. and ZhangZ.2012. Seismic wave field modeling in media with fluid‐filled fractures and surface topography. Applied Geophysics9, 301–312.
    [Google Scholar]
26. LanH. and ZhangZ.2013a. Topography‐dependent eikonal equation and its solver for calculating first‐arrival traveltimes with an irregular surface. Geophysical Journal International193(2), 1010–1026.
    [Google Scholar]
27. LanH. and ZhangZ.2013b. A high‐order fast‐sweeping scheme for calculating first‐arrival traveltimes with an irregular surface. Bulletin of the Seismological Society of America103(3), 2070–2082.
    [Google Scholar]
28. LanH., ChenJ., ZhangZ. and LiuY.2014. Reverse time migration from irregular surface by flattening surface topography. Tectonophysics627, 26–37.
    [Google Scholar]
29. LanH., ChenJ., ZhangZ., LiuY., ZhaoJ. and ShiR.2016. Application of the perfectly matched layer in seismic wavefield simulation with an irregular free surface. Geophysical Prospecting64, 112–128.
    [Google Scholar]
30. LawtonD.C.1989. Computation of refraction static corrections using first‐break traveltime differences. Geophysics54, 1289–1296.
    [Google Scholar]
31. LelièvreP.G., FarquharsonC.G. and HurichC.A.2010. Computing first‐arrival seismic traveltimes on unstructured 3‐D tetrahedral grids using the Fast Marching Method. Geophysical Journal International184(2), 885–896.
    [Google Scholar]
32. LuoS. and QianJ.2011. Factored singularities and high‐order Lax‐Friedrichs sweeping schemes for point‐source traveltimes and amplitudes. Journal of Computational Physics230, 4742–4755.
    [Google Scholar]
33. MaT. and ZhangZ.2014a. Calculating ray paths for first‐arrival traveltimes using a topography‐dependent eikonal equation solver. Bulletin of the Seismological Society of America104(3), 1501–1517.
    [Google Scholar]
34. MaT. and ZhangZ.2014b. A model expansion criterion for treating surface topography in ray path calculations using the eikonal equation. Journal of Geophysics and Engineering11(2), 1–9.
    [Google Scholar]
35. MorelliA. and DziewonskiA.M.1987. Topography of the core‐mantle boundary and lateral homogeneity of the liquid core. Nature325, 678–683.
    [Google Scholar]
36. NielsenP., IfF., BergO. and SkovgaardO.1994. Using the pseudospectral method on curved grid for 2D acoustic forward modeling. Geophysical Prospecting43, 321–341.
    [Google Scholar]
37. Officer, C.B.1974. Introduction to Theoretical Geophysics, Springer‐Verlag, New York.
    [Google Scholar]
38. PengD., OsherS., MerrimanB. and ZhaoH.K.1999. The geometry of Wulff crystal shapes and its relations with Riemann problems. In: Nonlinear Partial Differential Equations (Evanston, IL, 1998), pp. 251–303. Providence, RI: American Mathematical Society.
    [Google Scholar]
39. PiromalloC. and MorelliA.1998. P‐wave propagation heterogeneity and earthquake location in the Mediterranean region. Geophysical Journal International135, 232–254.
    [Google Scholar]
40. PodvinP. and LecomteI.1991. Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. Geophysical Journal International105, 271–284.
    [Google Scholar]
41. PšenčíkI. and FarraV.2005. First‐order ray tracing for qPwaves in inhomogeneous, weakly anisotropic media. Geophysics70, D65–D75.
    [Google Scholar]
42. QianJ. and SymesW.W.2002. Finite‐difference quasi‐P travel‐times for anisotropic media. Geophysics67, 147–155.
    [Google Scholar]
43. QianJ., ZhangY.T. and ZhaoH.K.2007a. Fast sweeping methods for eikonal equations on triangular meshes. SIAM Journal on Numerical Analysis45, 83–107.
    [Google Scholar]
44. QianJ., ZhangY.T. and ZhaoH.K.2007b. A fast sweeping method for static convex Hamilton‐Jacobi equations. Journal of Computational Physics31, 237–271.
    [Google Scholar]
45. QinF., LuoY., OlsenK.B., CaiW. and SchusterG.T.1992. Finite‐difference solution of the eikonal equation along expanding wavefronts. Geophysics57(3), 478–487.
    [Google Scholar]
46. RawlinsonN. and SambridgeM.2005. The fast marching method: an effective tool for tomographic imaging and tracking multiple phases in complex layered media. Exploration Geophysics36, 341–350.
    [Google Scholar]
47. SethianJ.A. and PopoviciA.M.1999. Three dimensional traveltimes computation using the Fast Marching Method. Geophysics64, 516–523.
    [Google Scholar]
48. SethianJ.A. and VladimirskyA.2000. Fast methods for the Eikonal and related Hamilton–Jacobi equations on unstructured meshes. Proceedings of the National Academy of Sciences97, 5699–5703.
    [Google Scholar]
49. SethianJ.A. and VladimirskyA.2001. Ordered upwind methods for static Hamilton–Jacobi equations. Proceedings of the National Academy of Sciences98, 11069–11074.
    [Google Scholar]
50. SunJ., SunZ. and HanF.2011. A finite difference scheme for solving the eikonal equation including surface topography. Geophysics76, T53–T63.
    [Google Scholar]
51. SymesW., VersteegR., SeiA. and TranQ.H.1994. Kirchhoff simulation migration and inversion using finite‐difference travel‐times and amplitudes. Annual Report, The Rice Inversion Project (http://www. trip. caam. rice. edu/). Rice University.
    [Google Scholar]
52. TaillandierC., NobleM., ChaurisH. and CalandraH.2009. First‐arrival traveltime tomography based on the adjoint state method. Geophysics74(6), WCB1–WCB10.
    [Google Scholar]
53. TessmerE. and KosloffD.1994. 3‐D elastic modeling with surface topography by a Chebyshev spectral method. Geophysics59, 464–473.
    [Google Scholar]
54. TessmerE.T., KosloffD. and BehleA.1992. Elastic wave propagation simulation in the presence of surface topography. Geophysical Journal International108, 621–632.
    [Google Scholar]
55. TsaiY.R., ChengL.T., OsherS. and ZhaoH.2003. Fast sweeping algorithms for a class of Hamilton‐Jacobi equations. SIAM Journal on Numerical Analysis41(2), 673–694.
    [Google Scholar]
56. Van TrierJ. and SymesW.W.1991. Upwind finite‐difference calculation of traveltimes. Geophysics56, 812–821.
    [Google Scholar]
57. VersteegR.1994. The Marmousi experience: velocity model determination on a synthetic complex data set. The Leading Edge13(9), 927–936.
    [Google Scholar]
58. VidaleJ.E.1988. Finite‐difference calculation of traveltimes. Bulletin of the Seismological Society of America78, 2062–2076.
    [Google Scholar]
59. WaheedU., AlkhalifahT. and WangH.2015a. Efficient traveltime solution of the acoustic TI eikonal equation. Journal of Computational Physics282, 62–76.
    [Google Scholar]
60. WaheedU., YarmanC.E. and FlaggG.2015b. An iterative, fast‐sweeping‐based eikonal solver for 3D tilted anisotropic media. Geophysics80(3), C49–C58.
    [Google Scholar]
61. XiongT., ZhangM., ZhangY.‐T. and ShuC.‐W.2010. Fast sweeping fifth order WENO scheme for static Hamilton‐Jacobi equations with accurate boundary treatment. Journal of Scientific Computing45, 514–536.
    [Google Scholar]
62. XuT., ZhangZ., GaoE., XuG. and SunL.2010. Segmentally iterative ray tracing in complex 2D and 3D heterogeneous block models. Bulletin of the Seismological Society of America100, 841–850.
    [Google Scholar]
63. XuT., XuG., GaoE., LiY., JiangX. and LuoK.2006. Block modeling and segmentally iterative ray tracing in complex 3D media. Geophysics71, T41–T51.
    [Google Scholar]
64. XuT., LiF., WuZ., WuC., GaoE., ZhouB.et al. 2014. A successive three‐point perturbation method for fast ray tracing in complex 2D and 3D geological model. Tectonophysics627, 72–81.
    [Google Scholar]
65. ZhangW. and ChenX.2006. Traction image method for irregular free surface boundaries in finite difference seismic wave simulation. Geophysical Journal International167, 337–353.
    [Google Scholar]
66. ZhangY.T., ZhaoH.K. and QianJ.2006. High order fast sweeping methods for static Hamilton‐Jacobi equations. Journal of Scientific Computing29, 25–56.
    [Google Scholar]
67. ZhangZ., BaiZ., KlempererS.L., TianX., TianX., XuT.et al. 2013. Crustal structure across northeastern Tibet from wide‐angle seismic profiling: constraints on the Caledonian Qilian orogeny and its reactivation. Tectonophysics606, 140–159.
    [Google Scholar]
68. ZhaoH.2005. A fast sweeping method for eikonal equations. Mathematics of Computation74603–628.
    [Google Scholar]
69. ZhaoA., ZhangZ. and TengJ.2004. Minimum traveltime tree algorithm for seismic ray tracing: improvement in efficiency. Journal of Geophysics and Engineering1(4), 245–251.
    [Google Scholar]