Direct and inverse scattering in the time domain for a dissipative wave equation. Part 1: Scattering operators
(1986) In Journal of Mathematical Physics 27(6). p.1667-1682- Abstract
- This is the first part of a series of papers devoted to direct and inverse scattering of transient waves in lossy inhomogeneous media. The medium is assumed to be stratified, i.e., it varies only with depth. The wave propagation is modeled in an electromagnetic case with spatially varying permittivity and conductivity. The objective in this first paper is to analyze properties of the scattering operators (impulse responses) for the medium and to introduce the reader to the inverse problem, which is the subject of the second paper in this series. In particular, imbedding equations for the propagation operators are derived and the corresponding equations for the scattering operators are reviewed. The kernel representations of the propagation... (More)
- This is the first part of a series of papers devoted to direct and inverse scattering of transient waves in lossy inhomogeneous media. The medium is assumed to be stratified, i.e., it varies only with depth. The wave propagation is modeled in an electromagnetic case with spatially varying permittivity and conductivity. The objective in this first paper is to analyze properties of the scattering operators (impulse responses) for the medium and to introduce the reader to the inverse problem, which is the subject of the second paper in this series. In particular, imbedding equations for the propagation operators are derived and the corresponding equations for the scattering operators are reviewed. The kernel representations of the propagation operators are shown to have compact support in the time variable. This property implies that transmission and reflection data can be extended from one round trip to arbitrary time intervals. The compact support of the propagator kernels also restricts the admissible set of transmission kernels consistent with the model employed in this paper. Special cases of scattering and propagation kernels that can be expressed in closed form are presented. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1038394
- author
- Kristensson, Gerhard LU and Krueger, Robert J
- publishing date
- 1986
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 27
- issue
- 6
- pages
- 1667 - 1682
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:36549093112
- ISSN
- 0022-2488
- DOI
- 10.1063/1.527083
- language
- English
- LU publication?
- no
- id
- fa192c7b-0a93-4231-99e3-2839dd24f96b (old id 1038394)
- alternative location
- http://link.aip.org/link/?JMAPAQ/27/1667/1
- date added to LUP
- 2016-04-04 09:31:08
- date last changed
- 2021-04-11 03:24:24
@article{fa192c7b-0a93-4231-99e3-2839dd24f96b,
abstract = {{This is the first part of a series of papers devoted to direct and inverse scattering of transient waves in lossy inhomogeneous media. The medium is assumed to be stratified, i.e., it varies only with depth. The wave propagation is modeled in an electromagnetic case with spatially varying permittivity and conductivity. The objective in this first paper is to analyze properties of the scattering operators (impulse responses) for the medium and to introduce the reader to the inverse problem, which is the subject of the second paper in this series. In particular, imbedding equations for the propagation operators are derived and the corresponding equations for the scattering operators are reviewed. The kernel representations of the propagation operators are shown to have compact support in the time variable. This property implies that transmission and reflection data can be extended from one round trip to arbitrary time intervals. The compact support of the propagator kernels also restricts the admissible set of transmission kernels consistent with the model employed in this paper. Special cases of scattering and propagation kernels that can be expressed in closed form are presented.}},
author = {{Kristensson, Gerhard and Krueger, Robert J}},
issn = {{0022-2488}},
language = {{eng}},
number = {{6}},
pages = {{1667--1682}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Journal of Mathematical Physics}},
title = {{Direct and inverse scattering in the time domain for a dissipative wave equation. Part 1: Scattering operators}},
url = {{http://dx.doi.org/10.1063/1.527083}},
doi = {{10.1063/1.527083}},
volume = {{27}},
year = {{1986}},
}