Unified theory of scattering of congugate wave fields by a localized object

Scattering theory is the basis of methods for the theoretical study of the interaction of radiation of various physical nature (acoustic, electromagnetic, elastic waves) and matter. The section of scattering theory devoted to the development of methods for solving the solution of the direct scattering problem — the problem of the interaction of a wave field with heterogeneities of a heterogeneous medium, is the basis of mathematical modeling methods in various fields of knowledge: propagation of acoustic waves in the ocean and atmosphere (scattering on the distribution of salinity, on the accumulation of discharged and condensed clouds of water droplets); propagation of seismic waves in solid earth (scattering by fluctuations and discrete inclusions of matter); flaw detection of engineering structures (scattering of waves by defects in solid materials); study of the response of composite materials to external influences. The section of scattering theory that studies the solution of the inverse scattering problem (ORR) — the problem of restoring the structure of the object under study by the wave field scattered by it, is the basis of methods for remote study of objects whose direct study is impossible: medical and technical tomography; exploration and additional exploration of mineral deposits; nondestructive testing of the structure of building and other structures, and much, much more. Scattering theory finds great applications in optics and, of course, in quantum physics, where it first appeared. In the most general case, the process of scattering of the wave field by the object under study, the characteristic dimensions of which are comparable to or less than the length of the incident field, can be characterized from an energy point of view as an extinction process: extinction = scattering + absorption. Thus, part of the energy of the field incident on the obstacle when interacting with the object is dissipated in space, and part is absorbed by the material of the object. The absorption of field energy is significant in the case when the wavelength of the primary field is significantly less than the characteristic size of the object under study, that is, in the case of a high-frequency field. In the case when the length of the incident field is comparable or significantly larger than the characteristic size of the object under study, the absorption processes are insignificant extinction is reduced to pure scattering. In this article, the mathematical formalism of the scattering theory for the case of pure scattering is extended to the case of scattering of a conjugate wave field by a solitary scattering object in a polar medium.

Surnev V. B. Unified theory of scattering of congugate wave fields by a localized object. MIAB. Mining Inf. Anal. Bull. 2022;(11-2):63-72. [In Russ]. DOI: 10.25018/0236_149 3_2022_112_0_63.

V.B. Surnev, Dr. Sci. (Phys. Mathem.), Head of Chair, Ural State Mining University, 620144, Ekaterinburg, Russia, e-mail: sournev@mail.ru, sournev@yandex.ru, ORCID ID: 0000-0001-6534-6668.

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