The inverse problem for a weakly inhomogeneous two-dimensional acoustic medium

Consider an acoustic half space /(x, y, z):z greater than 0/ characterized by density rho (x, z) and sound speed c(x, z), where rho and c are both close to constant. The problem of recovering rho and c using as data a line source impulse response function or a plane source impulse response function measured at the surface /z = 0/ is studied. The spectral structure of the linear operators arising in this problem is studied in some detail both analytically and numerically. A specific numerical solution method is proposed and illustrated in an example with synthetic data.