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

Huang, X.; Sun, H.

doi:10.1007/s11600-018-0154-x

Powiadomienia systemowe

Sesja wygasła!
Sesja wygasła!

Artykuł - szczegóły

Tytuł artykułu

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

Autorzy

Huang X. , Sun H.

Wybrane pełne teksty z tego czasopisma

https://www.springer.com/journal/11600

Identyfikatory

DOI

10.1007/s11600-018-0154-x

Warianty tytułu

Języki publikacji

Abstrakty

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.

Słowa kluczowe

wave propagation finite difference method FMM gaussian beam modeling complex eikonal equation

propagacja fal metoda różnic skończonych FMM

Wydawca

Instytut Geofizyki PAN
Springer

Czasopismo

Acta Geophysica

Rocznik

2018

Tom

Vol. 66, no. 4

Strony

497--508

Opis fizyczny

Bibliogr. 53 poz.

Twórcy

autor

Huang X.

xingguo.huang19@gmail.com

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

Sun H.

sunhui@swjtu.edu.cn

Faculty of Geosciences and Environmental Engineering, Southwest Jiaotong University, Chengdu 610031, China

Bibliografia

1. Babich VM (1968) Eigenfunctions, concentrated in the vicinity of closed geodesic. In: Babich VM (ed) Mathematical problems in wave propagation theory. Seminars in mathematics, vol 9. V.A. Steklov Mathematical Institute, Nauka, Leningrad, pp 15–63 (in Russian)
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
32. Klimeš M, Klimeš L (2011) Perturbation expansion of complex valued traveltime along real-valued reference rays. Geophys J Int 186:751–759
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