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Numerical modeling of Gaussian beam propagation and diffraction in inhomogeneous media based on the complex eikonal equation

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Języki publikacji
EN
Abstrakty
EN
Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss–Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.
Czasopismo
Rocznik
Strony
497--508
Opis fizyczny
Bibliogr. 53 poz.
Twórcy
autor
  • Previously Institute of Geophysical and Geochemical Exploration (IGGE), Chinese Academy of Geological Sciences (CAGS), Langfang, China
  • Present Address: Department of Earth Science, University of Bergen, Bergen, Norway
autor
  • Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 610031, China
Bibliografia
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  • 2. Babich VM, Kirpichnikova NJ (1974) Boundary layer method in diffraction problems. Leningrad University Press, Leningrad (in Russian)
  • 3. Babich VM, Kirpichnikova NJ (1980) Boundary layer method in diffraction problems. Springer, Berlin
  • 4. Berczynski P, Kravtsov YA (2004) Theory for Gaussian beam diffraction in 2D inhomogeneous medium, based on the eikonal form of complex geometrical optics. Phys Lett A 331:265–268
  • 5. Berczynski P, Kravtsov YA (2005) Gaussian beam diffraction in inhomogeneous media: solution in the frame of complex geometrical optics. Proc SPIE 5949:280–292
  • 6. Berczynski P, Bliokh KY, Kravtsov YA, Stateczny A (2006) Diffraction of Gaussian beam in 3D smoothly inhomogeneous media: eikonal-based complex geometrical optics approach. J Opt Soc Am A 23:1442–1451
  • 7. Born M, Wolf E (1980) Principles of Optics, 6th edn. Pergamon Press, Oxford
  • 8. Bouteiller LP, Benjemaa M, Métivier L, Virieux J (2017) An accurate discontinuous Galerkin method for solving point-source eikonal equation in 2-D heterogeneous anisotropic media. Geophys J Int 212(3):1498–1522
  • 9. Carter HW (1972) Electromagnetic field of a Gaussian beam with an elliptical cross section. JOSA 62:1195–1201
  • 10. Červený V (1983) Synthetic body wave seismograms for laterally varying layered structures by the Gaussian beam method. Geophys J Int 73:389–426
  • 11. Červenỳ V (2001) Seismic ray theory. Oxford University Press, Oxford
  • 12. Červenỳ V, Popov MM, Psencık I (1982) Computation of wavefields in inhomogeneous-media Gaussian-beam approach. Geophys J R Astron Soc 70:109–128
  • 13. Deschamps AG (1971) Gaussian beam as a bundle of complex rays. Electron Lett 7:684–685
  • 14. Egorchenkov RA, Kravtsov YA (2000) Numerical realization of complex geometrical optics method. Radiophys Quantum Electron 43:512–517
  • 15. Egorchenkov RA, Kravtsov YA (2001) Complex ray tracing algorithms with application to optical problems. J Opt Soc Am A 18:650–656
  • 16. Felsen BL (1976) Evanescent waves. J Opt Soc Am 66:751–760
  • 17. Felsen BL (1984) Geometrical theory of diffraction, evanescent waves, complex rays, and Gaussian beams. Geophys J R Astron Soc 79:77–88
  • 18. Goldsmith PF (1998) Quasioptical systems: gaussian beam quasioptical propagation and applications, chapman and hall series on microwave technology and techniques. Institute of Electrical and Electronics Engineers, New York
  • 19. Gray SH (2005) Gaussian beam migration of common-shot records. Geophysics 70:S71–S77
  • 20. Hao Q, Alkhalifah T (2017) An acoustic eikonal equation for attenuating orthorhombic media. Geophysics 82(4):1–96
  • 21. Heyman E, Felsen LB (1989) Complex-source pulsed beam fields. J Opt Soc Am A 6:806–817
  • 22. Heyman E, Felsen LB (2001) Gaussian beam and pulsed beam dynamics: complex source and complex spectrum formulations within and beyond paraxial asymptotics. J Opt Soc Am A 18:1588–1611
  • 23. Hill NR (1990) Gaussian beam migration. Geophysics 55:1416–1428
  • 24. Hill NR (2001) Prestack Gaussian-beam depth migration. Geophysics 66:1240–1250
  • 25. Huang X, Greenhalgh S (2018) Linearized formulations and approximate solutions for the complex eikonal equation in orthorhombic media and applications of complex seismic traveltime. Geophysics 83:C115–C136
  • 26. Huang X, Sun H, Sun J (2016a) Born modeling for heterogeneous media using the Gaussian beam summation based Green’s function. J Appl Geophys 131:191–201
  • 27. Huang X, Sun J, Sun Z (2016b) Local algorithm for computing complex travel time based on the complex eikonal equation. Phys Rev E 93:043307
  • 28. Huang X, Sun J, Sun Z, Wang Q (2016c) A method for the computation of the complex traveltime based on the complex eikonal equation and the modified fast marching method. Oil Geophys Prospect 51(6):1109–1118 (in Chinese with English Abstract)
  • 29. Keller JB, Streifer W (1971) Complex rays with an application to Gaussian beams. J Opt Soc Am 61:40–43
  • 30. Klimes L (2006) Common-ray tracing and dynamic ray tracing for S waves in a smooth elastic anisotropic medium. Stud Geophys Geod 50:449–461
  • 31. Klimes L (2009) System of two Hamilton-Jacobi equations for complex-valued travel time. In: Seismic waves in complex 3-D structures, Report 19. Department of Geophysics, Charles University, Prague, pp 157–171
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  • 33. Kravtsov AY (1967) Complex rays and complex caustics. Radiophys Quantum Electron 10:719–730
  • 34. Kravtsov YA, Forbes GW, Asatryan AA (1999) Theory and applications of complex rays, in vol. 39 of progress in optics series. Elsevier, Amsterdam
  • 35. Li S, Fomel S, Vladimirsky A (2011) Improving wave-equation fidelity of Gaussian beams by solving the complex eikonal equation. In: SEG annual meeting, San Antonio, Texas, USA
  • 36. Magnanini R, Talenti AG (1999) On complex solutions to a 2-D eikonal equation. Part one: qualitative properties. Contemp Math 283:203–229
  • 37. Magnanini R, Talenti AG (2002) On complex solutions to a 2D eikonal equation. Part two: existence theorems. SIAM J Math Anal 34:805–835
  • 38. Magnanini R, Talenti AG (2003) On complex–valued solutions to a two-dimensional eikonal equation II. Existence theorems. Soc Ind Appl Math 34:805–835
  • 39. Magnanini R, Talenti AG (2006) On complex solutions to a 2D eikonal equation. Part three: analysis of a Backlund transformation. Appl Anal 85:249–276
  • 40. Magnanini R, Talenti AG (2009) On complex solutions to a 2D eikonal. Part four: continuation past a caustic. Milan J Math 77:1–66
  • 41. Permitin GV, Smirnov AI (1996) Quasioptics of smoothly inhomogeneous isotropic media. J Exp Theor Phys 82:395–402
  • 42. Poli E, Pereverzev GV, Peeters AG, Bornatici M (2001) EC beam tracing in fusion plasmas. Fusion Eng Des 53:9–21
  • 43. Popov MM (1981) A new method of computing wave fields in the high-frequency approximation, zapiski nauchnykh seminarov leningradskogo otdeleniya matematicheskogo instituta im. V. A. Steklova AN SSSR 104, 195–216 (translated in J Sov Math 20, 1869–1882 1982)
  • 44. Popov MM (1982) A new method of computation of wavefields using Gaussian beams. Wave Motion 4:85–97
  • 45. Popov MM, Semtchenok NM, Popov PM (2010) Depth migration by the Gaussian beam summation method. Geophysics 75:S81–S93
  • 46. Porter BM, Bucker PH (1987) Gaussian beam tracing for computing ocean acoustic fields. J Acoust Soc Am 82:1349–1359
  • 47. Sethian JA (1996) A fast marching level set method for monotonically advancing fronts. Proc Natl Acad Sci USA 93:1591–1595
  • 48. Sethian JA (1999) Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science. Cambridge University Press, Cambridge
  • 49. Shin SY, Felsen LB (1977) Lateral shifts of totally reflected Gaussian beams. Radio Sci 12:551–564
  • 50. Sun JG, Sun ZQ, Han FX (2011) A finite difference scheme for solving the eikonal equation including surface topography. Geophysics 76:T53–T63
  • 51. Waheed U, Alkhalifah T, Wang H (2015) Efficient traveltime solutions of the acoustic TI eikonal equation. J Comput Phys 282:62–76
  • 52. Wang WD, Deschamps GA (1974) Application of complex ray tracing to scattering problems. Proc IEEE 62(1974):1541–1551
  • 53. Wu RS (1985) Gaussian beams, complex rays, and the analytic extension of the Green’s function in smoothly inhomogeneous media. Geophys J Int 83:93–110
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7e71c17f-f8e9-41d1-88fd-74e2cf582d7e
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