Title
On a new approach to frequency sounding of layered media
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
ISSN
0163-0563
Recommended Citation
"On a new approach to frequency sounding of layered media" (2008). Faculty Bibliography 2000s. 1047.
https://stars.library.ucf.edu/facultybib2000/1047
Comments
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