On a new approach to frequency sounding of layered media

    Authors

    A. Tamasan;A. Timonov

    Comments

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    Abbreviated Journal Title

    Numer. Funct. Anal. Optim.

    Keywords

    asymptotic expansions; Cauchy problem; frequency sounding; inverse; problem; Riccati equation; INVERSE SCATTERING; EQUATION; LINE; Mathematics, Applied

    Abstract

    Frequency sounding of layered media is modeled by a hyperbolic problem. Within the framework of this model, we formulate an inverse problem. Applying the Laplace transform and introducing the impedance function, the latter is first reduced to the inverse boundary value problem for the Riccati equation and then to the Cauchy problem for a first-order quadratic equation. The advantage of such transformations is that the quadratic equation does not contain an unknown coefficient. For a specific class of data, it is shown that the Cauchy problem is uniquely solvable. Based on the asymptotic behavior of solutions to both the Riccati and quadratic equations, a stable reconstruction algorithm is constructed. Its feasibility is demonstrated in computational experiments.

    Journal Title

    Numerical Functional Analysis and Optimization

    Volume

    29

    Issue/Number

    3-4

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    470

    Last Page

    486

    WOS Identifier

    WOS:000255986300013

    ISSN

    0163-0563

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