Forward scattering series and Padé approximants for acoustic wavefield propagation in a vertically varying medium

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6 Citations (Scopus)

Abstract

We present the application of the theory of Padé approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component. We show that the sequence of Padé approximants to the partial sums in the forward scattering series for the 3D wave equation is convergent for any contrast and any incidence angle. This allows the construction of any reflected waves including phase-shifted post-critical plane waves and, for a point-source problem, refracted events or headwaves, and it also provides interesting interpretations of these solutions in the scattering theory formalism.

Original languageEnglish
Pages (from-to)180-202
Number of pages23
JournalCommunications in Computational Physics
Volume3
Issue number1
StatePublished - 1 Jan 2008

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acoustic propagation
forward scattering
wave equations
plane waves
incidence
reflected waves
point sources
formalism
acoustics
scattering

Keywords

  • Acoustic wave modeling
  • Forward scattering series
  • Padé approximants

Cite this

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abstract = "We present the application of the theory of Pad{\'e} approximants to extending the perturbative solutions of acoustic wave equation for a three dimensional vertically varying medium with one interface. These type of solutions have limited convergence properties depending on either the degree of contrast between the actual and the reference medium or the angle of incidence of a plane wave component. We show that the sequence of Pad{\'e} approximants to the partial sums in the forward scattering series for the 3D wave equation is convergent for any contrast and any incidence angle. This allows the construction of any reflected waves including phase-shifted post-critical plane waves and, for a point-source problem, refracted events or headwaves, and it also provides interesting interpretations of these solutions in the scattering theory formalism.",
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Forward scattering series and Padé approximants for acoustic wavefield propagation in a vertically varying medium. / Nita, Bogdan.

In: Communications in Computational Physics, Vol. 3, No. 1, 01.01.2008, p. 180-202.

Research output: Contribution to journalArticleResearchpeer-review

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