Linearization Ill-Posedness for 2.5-D Ware Equation Inversion Model

Abstract For the weakly inhomogeneous acoustic medium in Ω={(x,y,z):z>0},we consider the inverse problemof determining the density function ρ(x,y).The inversion input for our inverse problem is the wave field givenon a line.We get an integral equation for the 2-D density perturbation from the linearization.By virtue of theintegral transform,we prove the uniqueness and the instability of the solution to the integral equation.Thedegree of ill-posedness for this problem is also given.