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Wave propagation in an inhomogeneous medium


Blum, Joseph William (1968) Wave propagation in an inhomogeneous medium. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/CQ38-0N14.


This paper is in two parts. In the first part we give a qualitative study of wave propagation in an inhomogeneous medium principally by geometrical optics and ray theory. The inhomogeneity is represented by a sound-speed profile which is dependent upon one coordinate, namely the depth; and we discuss the general characteristics of wave propagation which result from a source placed on the sound channel axis. We show that our mathematical model of the sound- speed in the ocean actually predicts some of the behavior of the observed physical phenomena in the underwater sound channel. Using ray theoretic techniques we investigate the implications of our profile on the following characteristics of SOFAR propagation: (i) the sound energy traveling further away from the axis takes less time to travel from source to receiver than sound energy traveling closer to the axis, (ii) the focusing of sound energy in the sound channel at certain ranges, (iii) the overall ray picture in the sound channel.

In the second part a more penetrating quantitative study is done by means of analytical techniques on the governing equations. We study the transient problem for the Epstein profile by employing a double transform to formally derive an integral representation for the acoustic pressure amplitude, and from this representation we obtain several alternative representations. We study the case where both source and receiver are on the channel axis and greatly separated. In particular we verify some of the earlier results derived by ray theory and obtain asymptotic results for the acoustic pressure in the far-field.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Cohen, Donald S.
Thesis Committee:
  • Unknown, Unknown
Defense Date:14 October 1968
Record Number:CaltechTHESIS:04082013-143307592
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7587
Deposited By: Dan Anguka
Deposited On:08 Apr 2013 22:00
Last Modified:09 Nov 2022 19:20

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