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A new acoustic traveltime approximation for attenuating transversely isotropic media

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Języki publikacji
EN
Abstrakty
EN
Attenuation is one of the most important quantities in describing seismic wave propagation, which is also anisotropic because of the dispersion relationship between the seismic wave and the symmetry direction. Transverse isotropic media with titled symmetry-axis (TTI) is a widespread approximation of the Earth’s surface. For 2D TTI attenuating media, we frstly use the acoustic assumption to simplify the exact eikonal equation for the complex-valued quasi P-wave traveltime. Then we design a perturbation method to obtain the new approximation by solving the acoustic attenuating eikonal equation of TTI media and use Shanks transform to increase precision. Compared with former studies, the new approximation considers the symmetryaxis angles of the media as a factor, which will improve its robustness. The approximation is tested in several medium to demonstrate its efectiveness. The energy velocity which derived by the steepest-descent method is used to calculate the exact complex-valued traveltime. We test the accuracy of the approximations developed with and without Shanks transform in the following. Finally, we discussed the possibility to apply this approximation to the methods like fast marching methods.
Czasopismo
Rocznik
Strony
1611--1621
Opis fizyczny
Bibliogr. 34 poz.
Twórcy
autor
  • College of Geo-Exploration Science and Technology, Jilin University, Changchun, China
autor
  • College of Geo-Exploration Science and Technology, Jilin University, Changchun, China
Bibliografia
  • 1. Aki K, Richards PG (2002) Quantitative seismology, 2nd edn. University Science Books
  • 2. Alkhalifah T (1998) Acoustic approximations for seismic processing in transversely isotropic media. Geophysics 63:623–631. https://doi.org/10.1190/1.1444361
  • 3. Alkhalifah T (2000) An acoustic wave equation for anisotropic media. Geophysics 65:1239–1250. https://doi.org/10.1190/1.1444815
  • 4. Alkhalifah T (2011) Scanning anisotropy parameters in complex media. Geophysics 76(2):U13–U22. https://doi.org/10.1190/1.3553015
  • 5. Alkhalifah T & Sava P (2010) Migration velocity analysis using a transversely isotropic medium with tilt normal to the reflector dip. Eage Conference and Exhibition - Workshops and Fieldtrips
  • 6. Amodei D, Keers H, Vasco W, Johnson L (2006) Computation of uniform wave forms using complex rays. Phys Rev E 73:1–14
  • 7. Audebert F, Pettenati A, and Dirks V (2006) Tti anisotropic depth migration-which tilt estimate should we use? In: 68th EAGE conference and exhibition incorporating SPE EUROPEC 2006
  • 8. Bender CM, Orszag SA (1978) Advanced mathematical methods for scientists and engineers. McGraw-Hill
  • 9. Ben-Menahem A, Singh SJ (1981) Seismic waves and sources. Springer
  • 10. Carcione JM (2015) Wave fields in real media: Theory and numerical simulation of wave propagation in anisotropic, anelastic, porous and electromagnetic media: Handbook of Geophysical exploration, 3rd edn. Elsevier
  • 11. Červený V (2001) Seismic ray theory. Cambridge University Press, Cambridge
  • 12. Červený V, Pšenčík I (2005) Plane waves in viscoelastic anisotropic media—I. Theory. Geophys J Int 161:197–212. https://doi.org/10.1111/j.1365-246X.2005.02589.x
  • 13. Červený V, Pšenčík I (2006) Energy flux in viscoelastic anisotropic media. Geophys J Int 166:1299–1317. https://doi.org/10.1111/j.1365-246X.2006.03057.x
  • 14. Červený V, Pšenčík I (2009) Perturbation Hamiltonians in heterogeneous anisotropic weakly dissipative media. Geophys J Int 178:939–949. https://doi.org/10.1111/j.1365-246X.2009.04218.x
  • 15. Chapman SJ, Lawry JMH, Ockendon JR, Tew RH (1999) On the theory of complex rays. SIAM Rev 41:417–509. https://doi.org/10.1137/S0036144599352058
  • 16. Fedorov FI (1968) Theory of elastic waves in crystals. Springer
  • 17. Gajewski D, Pšenčík I (1992) Vector wavefields for weakly attenuating anisotropic media by the ray method. Geophysics 57:27–38. https://doi.org/10.1190/1.1443186
  • 18. Hanyga A, Seredyňska M (2000) Ray tracing in elastic and viscoelastic media. Pure Appl Geophys 157:679–717. https://doi.org/10.1007/PL00001114
  • 19. Hao Q, Alkhalifah T (2017a) An acoustic eikonal equation for attenuating orthorhombic media. Geophysics 82:WA67–WA81
  • 20. Hao Q, Alkhalifah T (2017b) An acoustic eikonal equation for attenuating transversely isotropic media with a vertical symmetry axis. Geophysics 82:C9–C20
  • 21. Klimeš M, Klimeš L (2011) Perturbation expansion of complex-valued traveltime along real-valued reference rays. Geophys J Int 186:751–759. https://doi.org/10.1111/j.1365-246X.2011.05054.x
  • 22. Kravtsov YA, Forbes GW, Asatryan AA (1999) Theory and applications of complex rays. In: Wolf E (ed) Progress in optics, pp. 1–62. Elsevier
  • 23. Luo S, Qian J (2012) Fast sweeping methods for factored anisotropic eikonal equations: multiplicative and additive factors. J Sci Comput 52:360–382. https://doi.org/10.1007/s10915-011-9550-y
  • 24. Sethian JA (1996) A fast marching level set method for monotonically advancing fronts. Proc Natl Acad Sci USA 93:1591–1595. https://doi.org/10.1073/pnas.93.4.1591
  • 25. Sethian JA, Vladimirsky A (2001) Ordered upwind methods for static Hamilton–Jacobi equations. Proc Natl Acad Sci 98:11069–11074. https://doi.org/10.1073/pnas.201222998
  • 26. Thomsen L (1986) Weak elastic anisotropy. Geophysics 51:1954–1966. https://doi.org/10.1190/1.1442051
  • 27. Thomson CJ (1997) Complex rays and wave packets for decaying signals in inhomogeneous, anisotropic and anelastic media. Stud Geophys Geod 41:345–381. https://doi.org/10.1023/A:1023359401107
  • 28. Vavryčuk V (2007) Ray velocity and ray attenuation in homogeneous anisotropic viscoelastic media. Geophysics 72(6):D119–D127. https://doi.org/10.1190/1.2768402
  • 29. Vavryčuk V (2010) Behavior of rays at interfaces in anisotropic viscoelastic media. Geophys J Int 181:1665–1677
  • 30. Vidale JE (1988) Finite-difference calculation of travel times. Bull Seismol Soc Am 78:2062–2076
  • 31. Vidale JE (1990) Finite-difference calculation of traveltimes in three dimensions. Geophysics 55:521–526. https://doi.org/10.1190/1.1442863
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Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-f3d79b8f-e70b-4f55-bc5b-5882b68ac895
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