We consider the exact iterative algorithm for solution of the direct and inverse scattering problems in 1D inhomogeneous half-space using piecewise-constant approximation of the constitutive parameter profiles (e.g., refractive index). A novel modification of the Gelfand–Levitan equation is derived for solution of the inverse scattering problem. Numerical examples are given and the effects related to a finite frequency band of the sounding pulse are discussed.
Similar content being viewed by others
References
K. Aki and P. G.Richards, Quantitative Seismology: Theory and Methods, Freeman, San Francisco (1980).
B. M. Levitan, The Sturm–Liouville Inverse Problems [in Russian], Nauka, Moscow (1984).
V. A. Marchenko, The Sturm–Liouville Operators and Their Applications [in Russian], Naukova Dumka, Kiev (1977).
E.A. Robinson, IEEE, 70, No. 9, 153 (1982).
L. A. Molotkov, Matrix Method in the Theory of Wave Propagation in Layered Elastic and Liquid Media [in Russian], Nauka, Leningrad (1984).
L. M. Brekhovskikh, Waves in Layered Media, Academic Press, New York (1980).
G.Mavko, T.Mukerji, and J.Dvorkin, The Rock Physics Handbook. Tools for Seismic Analysis in Porous Media, Cambridge Univ. Press (1998).
J. M.Maweu and G. F. Margrave, CREWES Res. Rep., 19, 1 (2007).
O. G.Kut’ina and A. B.Kut’in, The Tracking of Seismic Boundaries [in Russian], Nedra, Moscow (1993).
A. G. Byakov, I. F.Glumov, L. I.Kogan, et al., Wide-Angle Deep Seismic Profiling of the Water-Basin Bottom, Part 1 [in Russian], Nauka, Moscow (2001).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 53, No. 7, pp. 481–492, July 2010.
Rights and permissions
About this article
Cite this article
Skulkin, S.P., Turchin, V.I. Characteristics of exact retrieval of the structure of plane-stratified media using reflected and transmitted pulse signals. Radiophys Quantum El 53, 432–442 (2010). https://doi.org/10.1007/s11141-010-9240-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11141-010-9240-x