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Small and Wide Angle X-Ray Scattering Studies of Biological Macromolecules in Solution
12:53

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Published on: January 8, 2013

On the width of a ray.

Irina I Rypina1, Michael G Brown

  • 1RSMAS/AMP, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149, USA. irypina@rsmas.miami.edu

The Journal of the Acoustical Society of America
|October 12, 2007
PubMed
Summary

This study derives a general expression for Fresnel zone width in inhomogeneous environments, crucial for understanding acoustic wave propagation and ray stability in stratified media with perturbations.

Area of Science:

  • Acoustic wave propagation
  • Geophysical signal analysis
  • Wave phenomena in random media

Background:

  • Previous work by Kravtsov and Orlov established foundational understanding.
  • Smooth inhomogeneous environments present unique challenges for wave propagation analysis.

Purpose of the Study:

  • To derive a general expression for Fresnel zone width in smooth inhomogeneous environments.
  • To analyze the impact of perturbations on ray propagation and introduce scattering effects.
  • To validate theoretical predictions against travel-time sensitivity kernel calculations.

Main Methods:

  • Derivation of a general expression for diffractive Fresnel zone width.
  • Analysis of ray behavior in stratified environments with and without perturbations.

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  • Introduction and quantification of scattering-induced contributions to ray width.

    • Main Results:

    • A general expression for Fresnel zone width (deltar(F)) was derived.
    • In stratified media, ray width is proportional to [equation].
    • Scattering-induced width (deltar(s)) is proportional to /alpha/r(R-r), leading to total effective width deltar(tot).

    Conclusions:

    • The derived expressions accurately model ray width in complex acoustic environments.
    • Perturbations significantly alter ray propagation, leading to micromultipathing.
    • Theoretical predictions align well with computational results from travel-time sensitivity kernels.