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    Acoustic anisotropic wavefields through perturbation theory

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    Type
    Article
    Authors
    Alkhalifah, Tariq Ali cc
    KAUST Department
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Seismic Wave Analysis Group
    Date
    2013-09
    Permanent link to this record
    http://hdl.handle.net/10754/575816
    
    Metadata
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    Abstract
    Solving the anisotropic acoustic wave equation numerically using finite-difference methods introduces many problems and media restriction requirements, and it rarely contributes to the ability to resolve the anisotropy parameters. Among these restrictions are the inability to handle media with η<0 and the presence of shear-wave artifacts in the solution. Both limitations do not exist in the solution of the elliptical anisotropic acoustic wave equation. Using perturbation theory in developing the solution of the anisotropic acoustic wave equation allows direct access to the desired limitation-free solutions, that is, solutions perturbed from the elliptical anisotropic background medium. It also provides a platform for parameter estimation because of the ability to isolate the wavefield dependency on the perturbed anisotropy parameters. As a result, I derive partial differential equations that relate changes in the wavefield to perturbations in the anisotropy parameters. The solutions of the perturbation equations represented the coefficients of a Taylor-series-type expansion of the wavefield as a function of the perturbed parameter, which is in this case η or the tilt of the symmetry axis. The expansion with respect to the symmetry axis allows use of an acoustic transversely isotropic media with a vertical symmetry axis (VTI) kernel to estimate the background wavefield and the corresponding perturbation coefficients. The VTI extrapolation kernel is about one-fourth the cost of the transversely isotropic model with a tilt in the symmetry axis kernel. Thus, for a small symmetry axis tilt, the cost of migration using a first-order expansion can be reduced. The effectiveness of the approach was demonstrated on the Marmousi model.
    Citation
    Alkhalifah, T. (2013). Acoustic anisotropic wavefields through perturbation theory. GEOPHYSICS, 78(5), WC41–WC50. doi:10.1190/geo2012-0391.1
    Publisher
    Society of Exploration Geophysicists
    Journal
    GEOPHYSICS
    ISBN
    9781629937908
    DOI
    10.1190/geo2012-0391.1
    ae974a485f413a2113503eed53cd6c53
    10.1190/geo2012-0391.1
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