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...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.展开更多
基金Supported by the Science Foundation of Southeast University (No.9207011148)
文摘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.
