Theoretical and numerical studies of wave propagation and scattering in inhomogeneous media
Li, Yuan-Liang
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https://hdl.handle.net/2142/19962
Description
Title
Theoretical and numerical studies of wave propagation and scattering in inhomogeneous media
Author(s)
Li, Yuan-Liang
Issue Date
1991
Doctoral Committee Chair(s)
Liu, C.H.
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
Using the path-integral technique, an analytical expression of the three-dimensional Green's function for the background inhomogeneous medium with the linear refractive index profile is obtained. The technique is extended to treat the three-dimensional and range-dependent media with or without turning points. Two analytical expressions of the Green's functions are also obtained for such media. For a line source in the medium with the linear sound speed profile, the analytical expression of the Green's function is simply obtained using a mathematical identity.
For a general background medium with the refractive index varying in only one direction, one can replace the refractive index profile with many fine layers. In this case, the Green's functions can be expressed as the Sommerfeld-type integral and evaluated by numerical techniques. However, all of the conventional techniques determine the minimum number of integration points required to evaluate the integral on the trial-and-error basis and do not allow the user to choose the precise location of the desired observation points. To improve this, a new algorithm based on the chirp z-transform, called the CFFP, has been introduced. The new algorithm is called the CFFP. With this modification, the user can select the precise locations of the range of detectors. Furthermore, the new algorithm can adaptively increase the number of integration points for evaluation of the Sommerfeld-type integral. These features make the CFFP particularly useful for studying the problems of wave propagation and scattering in layered background media.
Using the analytical expression of the Green's function due to a point source embedded in a background medium with the linear refractive index profile and the Born approximation, the scattered fields from random irregularities are represented as a multiple integral. A new algorithm for efficiently computing the multiple integral has been derived. Numerical results shows that the total field level in the shadow zone can be drastically affected by the scattered fields from random irregularities.
To study the problem of scattering of acoustic waves from a rough ground, the analytical expression of the Green's function due to a line source embedded in a background medium with the linear sound-speed probe has also been successfully incorporated into the Helmholtz-Kirchhoff integral equation. The integral equation has been solved by the moment method. Numerical results show that the penetration of the shadow zone by the scattered fields usually is from the diffraction and back scattering of acoustic waves from a rough surface. The effects of scattering are also dependent on the inhomogeneities of the background medium.
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