An acoustic inverse scattering problem for spheres with radially inhomogeneous compressibility

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An inverse acoustic scattering problem the main aim of which is to reconstruct the one-dimensional variation of the acoustical parameters of a spherical object is investigated. The problem is first formulated conventionally through a coupled system of integral equations, and then this system is reduced to one-dimensional form by using the orthogonality properties of spherical harmonics. The inverse problem is solved in an iterative fashion via classical Newton algorithm. Some numerical simulations are carried out to test the feasibility of the method as well as to see the effects of some parameters on the solution. It is shown that the method is very effective for the profiles having smooth variations provided that an appropriate initial guess is chosen. However, some of the classical disadvantages of the Newton type algorithms are also observed in numerical experiments which may limit the applicability of the method to a certain extent.