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    Tube wave signatures in cylindrically layered poroelastic media computed with spectral method

    Access Status
    Open access via publisher
    Authors
    Karpfinger, F.
    Gurevich, Boris
    Valero, H.
    Bakulin, Andrey
    Sinha, B.
    Date
    2010
    Type
    Journal Article
    
    Metadata
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    Citation
    Karpfinger, Florian and Gurevich, Boris and Valero, Henri-Pierre and Bakulin, Andrey and Sinha, Bikash. 2010. Tube wave signatures in cylindrically layered poroelastic media computed with spectral method. Geophysical Journal International. 183 (2): pp. 1005-1013.
    Source Title
    Geophysical Journal International
    DOI
    10.1111/j.1365-246X.2010.04773.x
    ISSN
    0956540X
    School
    Department of Exploration Geophysics
    URI
    http://hdl.handle.net/20.500.11937/26521
    Collection
    • Curtin Research Publications
    Abstract

    This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered.

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