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For the weakly inhomogeneous acoustic medium in Ω={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jan 1, 2002
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