The Scattering of Acoustic Waves by a Spherically Stratified Medium and an Obstacle

1978 ◽  
Vol 9 (5) ◽  
pp. 935-942 ◽  
Author(s):  
David Colton
Keyword(s):  
Acoustic Waves ◽  
Stratified Medium ◽  
Scattering Of Acoustic Waves

scholarly journals An inverse scattering problem for acoustic waves in a spherically stratified medium

1977 ◽  
Vol 20 (3) ◽  
pp. 257-263 ◽  
Author(s):  
David Colton
Keyword(s):  
Acoustic Waves ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattered Wave ◽  
Stratified Medium ◽  
Field Pattern ◽  
Soft Sphere ◽  
Far Field Pattern ◽  
Scattering Of Acoustic Waves ◽  
Local Speed

The inverse problem we will consider in this paper has its origins in the following problem connected with the scattering of acoustic waves in a nonhomogeneous medium. Let an incoming plane acoustic wave of frequency ω moving in the direction of the z axis be scattered off a “soft” sphere Ω of radius one which is surrounded by a pocket of rarefied or condensed air in which the local speed of sound is given by c(r) where r = |x| for x ∈ R3. Let us(x)eiωt be the velocity potential of the scattered wave and let r, θ, φ be spherical coordinates in R3. Then from a knowledge of the far field pattern f(θ, φ, λ) for λ = ω/c0 contained in some finite interval 0 < λ0 ≤ λ ≤ λ1,, we would like to determine the unknown function c(r).

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