1887
Volume 50, Issue 2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

ABSTRACT

This paper presents a first-arrival tomography incorporating a fast sweeping method (FSM) solving the factored eikonal equation (factored FSM). The traveltime calculation method plays a significant role in velocity inversion. However, for a point source condition, all finite-difference based eikonal solvers suffer from the source singularity problem. Numerical error caused by source singularity will propagate from the source to all computational domains, and makes traveltimes inaccurate. A FSM solving the factored eikonal equation can deal with the source singularity problem very well. Therefore, a first-arrival tomography is developed by incorporating 2D and 3D factored FSMs to provide more accurate traveltimes in velocity inversion. For comparison, an open source package is used to invert the same data set. It incorporates the traveltime calculation algorithms and . Traveltime accuracy tests show that factored FSM can generate more accurate traveltimes than FSM, and . Numerical and field data tests show that inversion with factored FSM can acquire much better tomograms than inversion with and . Therefore, it is worthwhile using a more accurate traveltime computation method in velocity inversion.

© 2019 Australian Society of Exploration Geophysics
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2019-03-04
2026-01-17

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References

  1. Ajo-Franklin, J. B., J. A. Urban, and J. M. Harris 2006 Using resolution-constrained adaptive meshes for traveltime tomography. Journal of Seismic Exploration14: 371–92.
     [Google Scholar]
  2. Aki, K., and W. H. K. Lee 1976 Determination of three-dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes: 1. A homogeneous initial model. Journal of Geophysical Research81: 4381–99. DOI:10.1029/JB081i023p04381.
     [Google Scholar]
  3. Benz, H. M., B. A. Chouet, P. B. Dawson, J. C. Lahr, and R. A. Page 1996 Three-dimensional P and S wave velocity structure of Redoubt Volcano, Alaska. Journal of Geophysical Research: Solid Earth101, no. B4: 8111–28. DOI:10.1029/95JB03046.
     [Google Scholar]
  4. Bergman, B., A. Tryggvason, and C. Juhlin 2004 High-resolution seismic traveltime tomography incorporating static corrections applied to a till-covered bedrock environment. Geophysics69, no. 4: 1082–90. DOI:10.1190/1.1778250.
     [Google Scholar]
  5. Calvert, A. J., and M. A. Fisher 2001 Imaging the Seattle Fault Zone with high-resolution seismic tomography. Geophysical Research Letters28: 2337–40. DOI:10.1029/2000GL012778.
     [Google Scholar]
  6. Cerveny, V. 2001 Seismic ray theory. Cambridge: Cambridge University Press, DOI:10.1115/1.1508173.
  7. Cheng, N., and L. House 1996 Minimum traveltime calculation in 3-D graph theory. Geophysics61: 1895–8. DOI:10.1190/1.1444104.
     [Google Scholar]
  8. Engdahl, E. R., R. V. D. Hilst, and R. Buland 1998 Global teleseismic earthquake relocation with improved travel times and procedures for depth determination. Bulletin of the Seismological Society of America88, no. 3: 722–43.
     [Google Scholar]
  9. Ettrich, N., and D. Gajewski 1996 Wave front construction in smooth media for prestack depth migration. Pure and Applied Geophysics148, no. 3: 481–502. DOI:10.1007/BF00874576.
     [Google Scholar]
  10. Fischer, R., and J. M. Lees 1993 Shortest path ray tracing with sparse graphs. Geophysics58, no. 7: 987–96. DOI:10.1190/1.1443489.
     [Google Scholar]
  11. Fomel, S., S. T. Luo, and H. K. Zhao 2009 Fast sweeping method for the factored eikonal equation. Journal of Computational Physics228, no. 17: 6440–55. DOI:10.1016/j.jcp.2009.05.029.
     [Google Scholar]
  12. Han, S., W. Zhang, and J. Zhang 2017 Calculating qP-wave travel times in 2D TTI media by high-order fast sweeping method with a numerical quartic equation solver. Geophysical Journal International210, no. 3: 1560–69. DOI:10.1093/gji/ggx236.
     [Google Scholar]
  13. Huang, G. N., B. Zhou, H. X. Li, and D. C. Nobes 2017 Seismic traveltime inversion based on tomographic equation without integral terms. Computer & Geosciences104: 29–34. DOI:10.1016/j.cageo.2017.04.002.
     [Google Scholar]
  14. Huang, G. N., B. Zhou, H. X. Li, H. Zhang, and Z. L. Li 2014 2D seismic reflection tomography in strongly anisotropic media. Journal of Geophysics and Engineering11: 1–8. DOI:10.1088/1742-2132/11/6/065012.
     [Google Scholar]
  15. Hole, J. A., and B. C. Zelt 1995 3-D finite-difference reflection traveltimes. Geophysical Journal International121: 427–34. DOI:10.1111/j.1365-246X.1995.tb05723.x.
     [Google Scholar]
  16. Kennett, B. L. N., E. R. Engdahl, and R. Buland 1995 Constraints on seismic velocities in the Earth from traveltimes. Geophysical Journal International122: 108–24. DOI:10.1111/j.1365-246X.1995.tb03540.x.
     [Google Scholar]
  17. Kim, S., and R. Cook 1999 3-D traveltime computation using second-order ENO scheme. Geophysics64: 1867–76. DOI:10.1190/1.1444693.
     [Google Scholar]
  18. Kissling, E., W. L. Ellsworth, D. Eberhart-Phillips, and U. Kradolfer 1994 Initial reference models in local earthquake tomography. Journal of Geophysical Research: Solid Earth99, no. B10: 19635–46. DOI:10.1029/93JB03138.
     [Google Scholar]
  19. Lambare, G., P. S. Lucio, and A. Hanyga 1996 Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of a ray field. Geophysical Journal International125: 584–98. DOI:10.1111/j.1365-246X.1996.tb00021.x.
     [Google Scholar]
  20. Lees, J. M. 1992 The magma system of Mount St. Helens non-linear high-resolution P-wave tomography. Journal of Volcanology and Geothermal Research53: 103–16. DOI:10.1016/0377-0273(92)90077-Q.
     [Google Scholar]
  21. Lees, J. M., and R. S. Crosson 1989 Tomographic inversion for three-dimensional velocity structure at Mount St. Helens using earthquake data. Journal of Geophysical Research94, no. B5: 5716–28. DOI:10.1029/JB094iB05p05716.
     [Google Scholar]
  22. Leidenfrost, A., N. Ettrich, D. Gajewski, and D. Kosloff 1999 Comparison of six different methods for calculating travel times. Geophysical Prospecting47: 269–97. DOI:10.1046/j.1365-2478.1999.00124.x.
     [Google Scholar]
  23. Liu, Y. Z., K. Y. Ding, and L. G. Dong 2010 The dependence of first-arrival travel time tomography on initial model. Oil Geophysical Prospecting45, no. 4: 502–11.
     [Google Scholar]
  24. Luo, S. T., and J. L. Qian 2011 Factored singularities and high-order Lax-Friedrichs sweeping schemes for point-source traveltimes and amplitudes. Journal of Computational Physics230: 4742–55. DOI:10.1016/j.jcp.2011.02.043.
     [Google Scholar]
  25. Luo, S., and J. Qian 2012 Fast sweeping methods for factored anisotropic eikonal equations: Multiplicative and additive factors. Journal of Scientific Computing52: 360–82. DOI:10.1007/s10915-011-9550-y.
     [Google Scholar]
  26. Marti, D., R. Carbonell, and I. Flecha 2008 High-resolution seismic characterization in an urban area: Subway tunnel construction in Barcelona, Spain. Geophysics73, no. 2: B41–50. DOI:10.1190/1.2832626.
     [Google Scholar]
  27. Moser, T. J. 1991 Shortest path calculation of seismic rays. Geophysics56, no. 1: 59–67. DOI:10.1190/1.1442958.
     [Google Scholar]
  28. Nakanishi, I., and K. Yamaguchi 1986 A numerical experiment of nonlinear image reconstruction from first-arrival times for two-dimensional island arc structure. Journal of Physics of the Earth34: 195–201. DOI:10.4294/jpe1952.34.195.
     [Google Scholar]
  29. Nolet, G. 2008 A breviary of seismic tomography imaging the interior of the Earth and Sun. Cambridge: Cambridge University Press, DOI:10.1121/1.3203995.
  30. Podvin, P., and I. Lecomte 1991 Finite difference computation of traveltimes in very contrasted velocity models: A massively parallel approach and its associated tools. Geophysical Journal International105: 271–84. DOI:10.1111/j.1365-246X.1991.tb03461.x.
     [Google Scholar]
  31. Phillips, W. S., and M. C. Fehler 1991 Traveltime tomography: A comparison of popular methods. Geophysics56, no. 10: 1639–49. DOI:10.1190/1.1442974.
     [Google Scholar]
  32. Qian, J., and W. W. Symes 2001 Paraxial eikonal solvers for anisotropic quasi-P travel times. Journal of Computational Physics173: 256–78. DOI:10.1006/jcph.2001.6875.
     [Google Scholar]
  33. Qian, J., and W. W. Symes 2002a Finite-difference quasi-P traveltimes for anisotropic media. Geophysics67: 147–55. DOI:10.1190/1.1451438.
     [Google Scholar]
  34. Qian, J., and W. W. Symes 2002b An adaptive finite-difference method for traveltimes and amplitudes. Geophysics67, no. 1: 167–76. DOI:10.1190/1.1451472.
     [Google Scholar]
  35. Qin, F. H., Y. Luo, and K. B. Olsen 1992 Finite-difference solution of the eikonal equation along expanding wavefronts. Geophysics57, no. 3: 478–87. DOI:10.1190/1.1443263.
     [Google Scholar]
  36. Rawlinson, N., and S. Fishwick 2012 Seismic structure of the southeast Australian lithosphere from surface and body wave tomography. Tectonophysics572-573: 111–22. DOI:10.1016/j.tecto.2011.11.016.
     [Google Scholar]
  37. Sethian, J., and M. Popovici 1999 3-D traveltime computation using the fast-marching method. Geophysics64, no. 2: 516–23. DOI:10.1190/1.1444558.
     [Google Scholar]
  38. Toomey, D. R., S. C. Solomon, and G. M. Purdy 1994 Tomographic imaging of the shallow crustal structure of the East Pacific Rise at 9° 30′N. Journal of Geophysical Research: Solid Earth99, no. B12: 24135–57. DOI:10.1029/94JB01942.
     [Google Scholar]
  39. Tryggvason, A., and B. Bergman 2006 A traveltime reciprocity discrepancy in the Podvin & Lecomte time3d finite difference algorithm. Geophysical Journal International165: 432–5. DOI:10.1111/j.1365-246X.2006.02925.x.
     [Google Scholar]
  40. Tryggvason, A., S. T. Rognvaldsson, and O. G. Flovenz 2002 Three-dimensional imaging of the P- and S-wave velocity structure and earthquake locations beneath southwest Iceland. Geophysical Journal International151: 848–66. DOI:10.1046/j.1365-246X.2002.01812.x.
     [Google Scholar]
  41. Tryggvason, A., C. Schmelzbach, and C. Juhlin 2009 Traveltime tomographic inversion with simultaneous static corrections — well worth the effort. Geophysics74, no. 6: WCB25–33. DOI:10.1190/1.3240931.
     [Google Scholar]
  42. Tsai, Y. H., L. T. Cheng, S. Osher, and H. K. Zhao 2003 Fast sweeping algorithms for a class of Hamilton-Jacobi equations. SIAM Journal on Numerical Analysis41, no. 2: 673–94. DOI:10.1137/S0036142901396533.
     [Google Scholar]
  43. Van Trier, J., and W. W. Symes 1991 Upwind finite-difference calculation of travel times. Geophysics56, no. 6: 812–21. DOI:10.1190/1.1443099.
     [Google Scholar]
  44. Vesnaver, A. L., F. Accaino, G. Bohm, and G. D. Moro 2003 Time-lapse tomography. Geophysics68, no. 3: 815–23. DOI:10.1190/1.1581034.
     [Google Scholar]
  45. Vidale, J. 1988 Finite-difference calculation of travel times. Bulletin of the Seismological Society of America78, no. 6: 2062–76.
     [Google Scholar]
  46. Vidale, J. 1990 Finite-difference calculation of traveltimes in three dimensions. Geophysics55, no. 5: 521–6. DOI:10.1190/1.1442863.
     [Google Scholar]
  47. Vinje, V., K. Astebol, E. Iversen, and H. Gjoystdal 1999 3-D ray modeling by wavefront construction in open models. Geophysical Prospecting64: 1912–19. DOI:10.1190/1.1444697.
     [Google Scholar]
  48. Vinje, V., E. Iversen, and H. Gjoystdal 1993 Traveltime and amplitude estimation using wavefront construction. Geophysics58: 1157–66. DOI:10.1190/1.1443499.
     [Google Scholar]
  49. Waheed, U., and T. Alkhalifah 2017 A fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization. Geophysics82, no. 6: WB1–8. DOI:10.1190/geo2016-0712.1.
     [Google Scholar]
  50. Yordkayhun, S., A. Tryggvason, B. Norden, C. Juhlin, and B. Bergman 2009 3D seismic travel time tomography imaging of the shallow subsurface at the CO2SINK project site, Ketzin, Germany. Geophysics74, no. 1: G1–15. DOI:10.1190/1.3026553.
     [Google Scholar]
  51. Zelt, C. A., A. Azaria, and A. Levander 2006 3D seismic refraction traveltime tomography at a groundwater contamination site. Geophysics71: H67–78. DOI:10.1190/1.2258094.
     [Google Scholar]
  52. Zhao, H. K. 2005 A fast sweeping method for eikonal equations. Mathematics of Computation74, no. 250: 603–28. DOI:10.1.1.153.6742.
     [Google Scholar]
  53. Zhou, H. W. 2006 First-break vertical seismic profiling tomography for Vinton Salt Dome. Geophysics71, no. 3: U29–36. DOI:10.1190/1.2192970.
     [Google Scholar]
  54. Zhou, B., and S. A. Greenhalgh 2006 Raypath and traveltime computations for 2D transversely isotropic media with dipping symmetry axes. Exploration Geophysics37, no. 2: 150–9. DOI:10.1071/EG06150.
     [Google Scholar]
  55. Zhou, B., C. Sinadinovski, and S. A. Greenhalgh 1992 Non-linear inversion travel-time tomography: Imaging high-contrast inhomogeneities. Exploration Geophysics23, no. 2: 459–64. DOI:10.1071/EG992459.
     [Google Scholar]
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First-arrival tomography with fast sweeping method solving the factored eikonal equation
Exploration Geophysics 50, 144 (2019); https://doi.org/10.1080/08123985.2019.1577110
/content/journals/10.1080/08123985.2019.1577110
/content/journals/10.1080/08123985.2019.1577110
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  • Article Type: Research Article
Keyword(s): factored eikonal equation; fast sweeping method; seismic tomography

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