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Multi-scale discrete approximation of Fourier integral operators

På svenska

Author

  • Fredrik Andersson
  • Maarten V de Hoop
  • Herwig Wendt

Summary, in English

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.

Publishing year

2012

Language

English

Pages

111-135

Publication/Series

Multiscale Modeling & Simulation

Volume

10

Issue

1

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Mathematics

Keywords

  • compression
  • reflection seismology
  • operator
  • separated representation
  • dyadic parabolic decomposition
  • wave packets
  • Fourier integral operators
  • multiscale computations

Status

Published

Research group

  • Harmonic Analysis and Applications

ISBN/ISSN/Other

  • ISSN: 1540-3459