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Multi-scale discrete approximation of Fourier integral operators

In English

Författare

  • 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.

Publiceringsår

2012

Språk

Engelska

Sidor

111-135

Publikation/Tidskrift/Serie

Multiscale Modeling & Simulation

Volym

10

Issue

1

Dokumenttyp

Artikel i tidskrift

Förlag

Society for Industrial and Applied Mathematics

Ämne

  • Mathematics

Nyckelord

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

Status

Published

Forskningsgrupp

  • Harmonic Analysis and Applications

ISBN/ISSN/Övrigt

  • ISSN: 1540-3459