Equivalent time‐average and effective medium for periodic layers

References

1. BackusG.E.1962. Long‐wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research67, 4427–4440.
   [Google Scholar]
2. BambergerA., ChaventG., HemonCh. and LaillyP.1982. Inversion of normal incidence seismograms. Geophysics47, 757–770.
   [Google Scholar]
3. BanikN.C., LercheI. and ShueyR.T.1985a. Stratigrafic filtering, Part I: Derivation of the O'Doherty‐Anstey formula. Geophysics50, 2768–2774.
   [Google Scholar]
4. BanikN.C., LercheI., ResnikJ.R. and ShueyR.T.1985b. Stratigrafic filtering, Part II: Model spectra. Geophysics50, 2775–2783.
   [Google Scholar]
5. BrekhovskikhL.M.1960. Waves in Layered Medi. Academic Press.
   [Google Scholar]
6. CarcioneJ.M., KosloffD. and BehleA.1991. Long‐wave anisotropy in stratified media: A numerical test. Geophysics56, 245–254.
   [Google Scholar]
7. CarcioneJ.M.2001. Wavefields in Real Media: Wave Ppropagation in Anisotropic, Anelastic and Porous Media . Pergamon .
   [Google Scholar]
8. CvetichM. and PicmanL.1981. Scattering states for a finite chain in one Dimension. Journal of Physics Part A General14, 379–382.
   [Google Scholar]
9. GradshteinI.S. and RyzhikI.M.1995. Tables of Integrals, Series and Products , fifth edition. Academic Press.
   [Google Scholar]
10. GriffithsD.J. and SteinkeC.A.2001. Waves in locally periodic media. American Journal of Physics69, 137–154.
    [Google Scholar]
11. HelbigK.1984. Anisotropy and dispersion in periodically layered media. Geophysics49, 364–373.
    [Google Scholar]
12. HovemJ.M.1995. Acoustic waves in finely layered media. Geophysics60, 1217–1221.
    [Google Scholar]
13. MarionD. and CoudinP.1992. From ray to effective medium theories in stratified media: An experimental study. 62nd SEG meeting, New Orleans, Louisiana, USA, Expanded Abstract, 1341–1343.
14. MarionD., MukerjiT. and MavkoG.1994. Scale effects on velocity dispersion: From ray to effective theories in stratified media. Geophysics59, 1613–1619.
    [Google Scholar]
15. MorletJ., AtensG., FourgeauE. and GiardD.1982a. Wave propagation and sampling theory – Part I: Complex signal and scattering in multilayered media. Geophysics47, 203–221.
    [Google Scholar]
16. MorletJ., AtensG., FourgeauE. and GiardD.1982b. Wave propagation and sampling theory – Part II: Sampling theory and complex waves. Geophysics47, 222–236.
    [Google Scholar]
17. O'DohertyR.F. and AnsteyN.A.1971. Reflections on amplitudes. Geophysical Prospecting19, 430–458.
    [Google Scholar]
18. SchoenbergerM. and LevinF.K.1974. Apparent attenuation due to intrabed multiples. Geophysics39, 278–291.
    [Google Scholar]
19. ShapiroS.A., HubralP. and UrsinB.1996. Reflectivity/transmissivity for one dimensional inhomogeneous random elastic media: Dynamic‐equivalent medium approach. Geophysical Journal International126, 184–196.
    [Google Scholar]
20. StovasA. and ArntsenB.2003. Low frequency waves in finely layered media. 65th EAGE meeting, Stavanger, Norway.
21. StovasA. and UrsinB.2003. Reflection and transmission responses of layered transversely isotropic visco‐elastic media. Geophysical Prospecting51, 447–477.
    [Google Scholar]
22. UrsinB.1983. Review of elastic and electromagnetic wave propagation in horizontally layered media. Geophysics48, 1063–1081.
    [Google Scholar]
23. M.Bernabini
    UrsinB.1987. The plane‐wave reflection and transmission response of a vertically inhomogeneous acoustic medium. In: Deconvolution and Inversion (eds M.Bernabini , P.Carrion , G.Jacovitti , F.Rocca , S.Treitel and M.Worthington ), pp. 189–207. Blackwell Scientific Publishers.
    [Google Scholar]
24. UrsinB. and StovasA.2002. Reflection and transmission responses of layered isotropic visco‐elastic media. Geophysics67, 307–323.
    [Google Scholar]
25. WuH., SprungD.W.L. and MartorellJ.1993. Periodic quantum wires and their quasi‐one‐dimensional nature. Journal of Physics D26, 798–803.
    [Google Scholar]