Some remarks on the Gaussian beam summation method

B. S. White*, A. Norris, A. Bayliss, R. Burridge

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

Summary. Recently, a method using superposition of Gaussian beams has been proposed for the solution of high‐frequency wave problems. The method is a potentially useful approach when the more usual techniques of ray theory fail: it gives answers which are finite at caustics, computes a nonzero field in shadow zones, and exhibits critical angle phenomena, including head waves. Subsequent tests by several authors have been encouraging, although some reported solutions show an unexplained dependence on the ‘free’ complex parameter ε which specifies the initial widths and phases of the Gaussian beams. We use methods of uniform asymptotic expansions to explain the behaviour of the Gaussian beam method. We show how it computes correctly the entire caustic boundary layer of a caustic of arbitrary complexity, and computes correctly in a region of critical reflection. However, the beam solution for head waves and in edge‐diffracted shadow zones are shown to have the correct asymptotic form, but with governing parameters that are explicitly ε‐dependent. We also explain the mechanism by which the beam solution degrades when there are strong lateral inhomogeneities. We compare numerically our predictions for some representative, model problems, with exact solutions obtained by other means.

Original languageEnglish (US)
Pages (from-to)579-636
Number of pages58
JournalGeophysical Journal of the Royal Astronomical Society
Volume89
Issue number2
DOIs
StatePublished - May 1987

Keywords

  • caustics
  • diffraction
  • head waves
  • ray theory

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics
  • Earth and Planetary Sciences(all)
  • Environmental Science(all)

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