Multi-scale discrete approximation of Fourier integral operators
(2012) In Multiscale Modeling & Simulation 10(1). p.111-135- Abstract
- Abstract in Undetermined
We develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost symmetric wave... (More) - Abstract in Undetermined
We develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost symmetric wave packet transform. Numerical wave propagation and imaging examples illustrate our computational procedures. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/2224387
- author
- Andersson, Fredrik LU ; de Hoop, Maarten V and Wendt, Herwig
- organization
- publishing date
- 2012
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- compression, reflection seismology, operator, separated representation, dyadic parabolic decomposition, wave packets, Fourier integral operators, multiscale computations
- in
- Multiscale Modeling & Simulation
- volume
- 10
- issue
- 1
- pages
- 111 - 135
- publisher
- Society for Industrial and Applied Mathematics
- external identifiers
-
- wos:000302183800006
- scopus:84861516818
- ISSN
- 1540-3459
- DOI
- 10.1137/100808174
- language
- English
- LU publication?
- yes
- id
- 93771e00-1307-4dca-bf7f-80031ed855e9 (old id 2224387)
- date added to LUP
- 2016-04-01 10:43:48
- date last changed
- 2022-01-26 01:58:26
@article{93771e00-1307-4dca-bf7f-80031ed855e9,
abstract = {{Abstract in Undetermined<br/>We develop a discretization and computational procedures for approximation of the action of Fourier integral operators the canonical relations of which are graphs. Such operators appear, for instance, in the formulation of imaging and inverse scattering of seismic reflection data. Our discretization and algorithms are based on a multiscale low-rank expansion of the action of Fourier integral operators using the dyadic parabolic decomposition of phase space and on explicit constructions of low-rank separated representations using prolate spheroidal wave functions, which directly reflect the geometry of such operators. The discretization and computational procedures connect to the discrete almost symmetric wave packet transform. Numerical wave propagation and imaging examples illustrate our computational procedures.}},
author = {{Andersson, Fredrik and de Hoop, Maarten V and Wendt, Herwig}},
issn = {{1540-3459}},
keywords = {{compression; reflection seismology; operator; separated representation; dyadic parabolic decomposition; wave packets; Fourier integral operators; multiscale computations}},
language = {{eng}},
number = {{1}},
pages = {{111--135}},
publisher = {{Society for Industrial and Applied Mathematics}},
series = {{Multiscale Modeling & Simulation}},
title = {{Multi-scale discrete approximation of Fourier integral operators}},
url = {{http://dx.doi.org/10.1137/100808174}},
doi = {{10.1137/100808174}},
volume = {{10}},
year = {{2012}},
}