Wave field in a layer with a linear background profile and multiscale random irregularities

Abstract

The paper addresses the problem of determining the field of a reflected wave in a multiscale inhomogeneous medium, which consists of a background deterministic large-scale irregularity and multiscale random irregularities with scales both larger and smaller than the wavelength. A layer with a linear permittivity profile is taken as the background irregularity. The small-scale irregularities are responsible for wide-angle scattering including backscattering. The first approximation of the perturbation theory is used to account for scattering from these irregularities. As the zero approximation and Green’s function in determining the field backscattered by small-scale irregularities, we utilize the integral representation of the field, obtained in our earlier work by combining the method of double weighted Fourier transform (DWFT) and the Fock proper-time method. Asymptotic methods are used to reduce the sevenfold integral representation of a field to lower-order integrals. Conditions for validity of such representations are obtained. Formulas of the frequency coherence functions of waves reflected and backscattered from the turbulent plasma layer are given. The paper presents the results of the simulation of pulse sounding of a randomly inhomogeneous reflecting plasma layer demonstrating the effect of large-scale irregularities on backscattering by small-scale irregularities.

KEYWORDS:

• Propagation
• random media
• volume scattering
• backscattering
• reflected wave
• asymptotic methods

Acknowledgements

The author is very grateful to O. A. Kulish for help in preparing the English version of the manuscript. I am also grateful to two anonymous reviewers and the editor V.U. Zavorotny for their valuable comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was funded by the Russian Foundation for Basic Research within the framework of the research project No. 19-05-00185 with the support of the Ministry of Higher Education and Science of the Russian Federation (Government assignment No. FZZE-2020-0017).