A backscattering model based on corrector theory of homogenization for the random Helmholtz equation
This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above the sea ice layer, the main objective of this work is to deri...
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ftdatacite:10.48550/arxiv.1805.02822 2023-05-15T18:17:26+02:00 A backscattering model based on corrector theory of homogenization for the random Helmholtz equation Jing, Wenjia Pinaud, Olivier 2018 https://dx.doi.org/10.48550/arxiv.1805.02822 https://arxiv.org/abs/1805.02822 unknown arXiv arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ Analysis of PDEs math.AP FOS Mathematics 35J05, 35R30, 86A22, 60F99 Preprint Article article CreativeWork 2018 ftdatacite https://doi.org/10.48550/arxiv.1805.02822 2022-04-01T09:24:59Z This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above the sea ice layer, the main objective of this work is to derive a model for the backscattered signal measured at the source/detector location. The problem is difficult in that, in the practical configuration we consider, the wave impinges on the layer with a non-normal incidence. Since the sea ice is seen by the pulse as an effective (homogenized) medium, the energy is specularly reflected and the backscattered signal vanishes in a first order approximation. What is measured at the detector consists therefore of corrections to leading order terms, and we focus in this work on the homogenization corrector. We describe the propagation by a random Helmholtz equation, and derive an expression of the corrector in this layered framework. We moreover obtain a transport model for quadratic quantities in the random wavefield in a high frequency limit. : 30 pages Report Sea ice DataCite Metadata Store (German National Library of Science and Technology) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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language |
unknown |
topic |
Analysis of PDEs math.AP FOS Mathematics 35J05, 35R30, 86A22, 60F99 |
spellingShingle |
Analysis of PDEs math.AP FOS Mathematics 35J05, 35R30, 86A22, 60F99 Jing, Wenjia Pinaud, Olivier A backscattering model based on corrector theory of homogenization for the random Helmholtz equation |
topic_facet |
Analysis of PDEs math.AP FOS Mathematics 35J05, 35R30, 86A22, 60F99 |
description |
This work concerns the analysis of wave propagation in random media. Our medium of interest is sea ice, which is a composite of a pure ice background and randomly located inclusions of brine and air. From a pulse emitted by a source above the sea ice layer, the main objective of this work is to derive a model for the backscattered signal measured at the source/detector location. The problem is difficult in that, in the practical configuration we consider, the wave impinges on the layer with a non-normal incidence. Since the sea ice is seen by the pulse as an effective (homogenized) medium, the energy is specularly reflected and the backscattered signal vanishes in a first order approximation. What is measured at the detector consists therefore of corrections to leading order terms, and we focus in this work on the homogenization corrector. We describe the propagation by a random Helmholtz equation, and derive an expression of the corrector in this layered framework. We moreover obtain a transport model for quadratic quantities in the random wavefield in a high frequency limit. : 30 pages |
format |
Report |
author |
Jing, Wenjia Pinaud, Olivier |
author_facet |
Jing, Wenjia Pinaud, Olivier |
author_sort |
Jing, Wenjia |
title |
A backscattering model based on corrector theory of homogenization for the random Helmholtz equation |
title_short |
A backscattering model based on corrector theory of homogenization for the random Helmholtz equation |
title_full |
A backscattering model based on corrector theory of homogenization for the random Helmholtz equation |
title_fullStr |
A backscattering model based on corrector theory of homogenization for the random Helmholtz equation |
title_full_unstemmed |
A backscattering model based on corrector theory of homogenization for the random Helmholtz equation |
title_sort |
backscattering model based on corrector theory of homogenization for the random helmholtz equation |
publisher |
arXiv |
publishDate |
2018 |
url |
https://dx.doi.org/10.48550/arxiv.1805.02822 https://arxiv.org/abs/1805.02822 |
genre |
Sea ice |
genre_facet |
Sea ice |
op_rights |
arXiv.org perpetual, non-exclusive license http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
op_doi |
https://doi.org/10.48550/arxiv.1805.02822 |
_version_ |
1766191659632033792 |