1887
Volume 57, Issue 5
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Many tasks in geophysics and acoustics require estimation of mode velocities in cylindrically layered media. For example, acoustic logging or monitoring in open and cased boreholes need to account for radial inhomogeneity caused by layers inside the borehole (sand screen, gravel pack, casing) as well as layers outside (cement, altered and unaltered formation layers). For these purposes it is convenient to study a general model of cylindrically layered media with inner fluid layer and free surface on the outside. Unbounded surrounding media can be described as a limiting case of this general model when thickness of the outer layer is infinite. At low frequencies such composite media support two symmetric modes called Stoneley (tube) and plate (extensional) wave. Simple expressions are obtained for these two mode velocities valid at zero frequency. They are written in a general form using elements of a propagator matrix describing axisymmetric waves in the entire layered composite. This allows one to apply the same formalism and compute velocities for ‐layered composites as well as anisotropic pipes. It is demonstrated that the model of periodical cylindrical layers is equivalent to a homogeneous radially transversely isotropic media when the number of periods increases to infinity, whereas their thickness goes to zero. Numerical examples confirm good validity of obtained expressions and suggest that even small number of periods may already be well described by equivalent homogeneous anisotropic media.

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2008-12-15
2019-12-09
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References

  1. AchenbachJ.D.1970. Field equations governing the mechanical behavior of layered circular cylinders. AIAA Journal8, 1445–1452.
    [Google Scholar]
  2. BakulinA., SidorovA., KashtanB. and JaaskelainenM.2008. Real‐time completion monitoring with acoustic waves. Geophysics73, E15–E33.
    [Google Scholar]
  3. BackusG.E.1962. Long‐wave elastic anisotropy produced by horizontal layering. Journal of Geophysical Research67, 4427–4440.
    [Google Scholar]
  4. DelGrosso V.A.1971. Analysis of multimode acoustic propagation in liquid cylinders with realistic boundary conditions application to sound speed and absorbtion measurements. Acustica24, 299–311.
    [Google Scholar]
  5. EwingW.M., JardetzkyW.S. and PressF.1957. Elastic Waves in Layered Media . McGraw‐Hill. ISBN 0070198608.
    [Google Scholar]
  6. HillR.1963. Elastic properties of reinforced solids: some theoretical principles. Journal of the Mechanics and Physics of Solids11, 357–372.
    [Google Scholar]
  7. KarpfingerF., GurevichB. and BakulinA.2007. Computing borehole modes with spectral method. 77th SEG meeting, San Antonio, Texas , USA , Expanded Abstracts, 333–337.
  8. LafleurL.D. and ShieldsF.D.1995. Low‐frequency propagation modes in a liquid‐filled elastic tube waveguide. Journal of the Acoustic Society of America97, 1437.
    [Google Scholar]
  9. LoveA.E.H.1944. A Treatise on the Mathematical Theory of Elasticity . Dover, New York . ISBN 0486601749.
    [Google Scholar]
  10. NorrisA.N.1990. The speed of a tube wave. Journal of the Acoustic Society of America87, 414–417.
    [Google Scholar]
  11. PetrashenG., MolotkovL. and KrauklisP.1985. Waves in Layered Isotropic Elastic Media II . Nauka, Leningrad , Russia (in Russian).
    [Google Scholar]
  12. WhiteJ.E.1983. Underground Sound . Elsevier. ISBN 0444421394.
    [Google Scholar]
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