In the acoustic approximation, the Earth is described using only density and bulk modulus. Assuming smooth density variations, reflections can be described using a single function--the velocity of compressional waves. If a reference model which is close enough to the actual Earth is known, the problem of estimating the medium velocity from the observed data can be linearized. Using a least-squares formulation and working in the omega -k domain, the linearized inverse problem for a homogeneous reference medium can be solved by a noniterative algorithm which is economically competitive with prestack migration. Numerical tests with synthetic and real data demonstrate the feasibility and the numerical stability of the method. The numerical results compare well with those obtained by migration of unstacked data, although superior results will only be obtained when the physics of the problem (including elastic versus acoustic effects, three-dimensional propagation, and accurate source estimation) will realistically be taken into account.