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
Copyright Status
Unknown
Socpus ID
46249096648 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/46249096648
STARS Citation
Tamasan, Alexandru and Timonov, Alexandre, "On A New Approach To Frequency Sounding Of Layered Media" (2008). Scopus Export 2000s. 10650.
https://stars.library.ucf.edu/scopus2000/10650