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Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal

Jonsson, B. Lars G.; Gustafsson, Mats LU ; Weston, Vaughan H. and de Hoop, Maarten V. (2004) In SIAM Journal on Applied Mathematics 64(6). p.1954-1986
Abstract
In the present paper an iterative time-reversal algorithm that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The time-reversal retrofocusing is analyzed from a boundary-control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the... (More)
In the present paper an iterative time-reversal algorithm that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The time-reversal retrofocusing is analyzed from a boundary-control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
SIAM Journal on Applied Mathematics
volume
64
issue
6
pages
1954 - 1986
publisher
SIAM Publications
external identifiers
  • wos:000224122400006
  • scopus:11044226943
ISSN
0036-1399
DOI
10.1137/S0036139903426964
language
English
LU publication?
yes
id
212c62d2-3f86-43cb-a275-babbedb5773b (old id 144364)
alternative location
http://www.jstor.org/stable/4096105
date added to LUP
2007-07-05 13:35:49
date last changed
2017-01-01 07:05:12
@article{212c62d2-3f86-43cb-a275-babbedb5773b,
  abstract     = {In the present paper an iterative time-reversal algorithm that retrofocuses an acoustic wave field to its controllable part is established. For a fixed temporal support, i.e., transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the iterative time-reversal algorithm reduces the temporal support of the excitation from the requirement of negligible remaining energy to the requirement of controllability. The time-reversal retrofocusing is analyzed from a boundary-control perspective where time reversal is used to steer the acoustic wave field towards a desired state. The wave field is controlled by transducers located at subsets of the boundary, i.e., the controllable part of the boundary. The time-reversal cavity and time-reversal mirror cases are analyzed. In the cavity case, the transducers generate a locally plane wave in the fundamental mode through a set of ducts. Numerical examples are given to illustrate the convergence of the iterative time-reversal algorithm. In the mirror case, a homogeneous half space is considered. For this case the analytic expression for the retrofocused wave field is given for finite temporal support. It is shown that the mirror case does not have the same degree of steering as the cavity case. It is also shown that the pressure can be perfectly retrofocused for infinite temporal support. Two examples are given that indicate that the influence of the evanescent part of the wave field is small.},
  author       = {Jonsson, B. Lars G. and Gustafsson, Mats and Weston, Vaughan H. and de Hoop, Maarten V.},
  issn         = {0036-1399},
  language     = {eng},
  number       = {6},
  pages        = {1954--1986},
  publisher    = {SIAM Publications},
  series       = {SIAM Journal on Applied Mathematics},
  title        = {Retrofocusing of Acoustic Wave Fields by Iterated Time Reversal},
  url          = {http://dx.doi.org/10.1137/S0036139903426964},
  volume       = {64},
  year         = {2004},
}