Title

On A New Approach To Frequency Sounding Of Layered Media

Keywords

Asymptotic expansions; Cauchy problem; Frequency sounding; Inverse problem; Riccati equation

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.

Publication Date

3-1-2008

Publication Title

Numerical Functional Analysis and Optimization

Volume

29

Issue

3-4

Number of Pages

470-486

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1080/01630560802001023

Socpus ID

46249096648 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/46249096648

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