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    The TTI slowness surface approximation

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    Type
    Article
    Authors
    Stovas, A.
    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
    2012-05-25
    Online Publication Date
    2012-05-25
    Print Publication Date
    2011-01
    Permanent link to this record
    http://hdl.handle.net/10754/575676
    
    Metadata
    Show full item record
    Abstract
    The relation between the vertical and horizontal slownesses, better known as the dispersion relation, for a transversely isotropic media with titled symmetry axis {left parenthesis, less than bracket}TTI{right parenthesis, greater than bracket} requires solving a quartic polynomial, which does not admit a practical explicit solution to be used, for example, in downward continuation. Using a combination of perturbation theory with respect to the anelliptic parameter and Shanks transform to improve the accuracy of the expansion, we develop an explicit formula for the dispersion relation that is highly accurate for all practical purposes. It also reveals some insights into the anisotropy parameter dependency of the dispersion relation including the low impact that the anelliptic parameter has on the vertical placement of reflectors for small tilt in the symmetry angle. © 2011 Society of Exploration Geophysicists.
    Publisher
    Society of Exploration Geophysicists
    Journal
    SEG Technical Program Expanded Abstracts 2011
    DOI
    10.1190/1.3627651
    ae974a485f413a2113503eed53cd6c53
    10.1190/1.3627651
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program

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