We propose a method for the non-linear inversion of the velocity field from reflection profiles. The inverse problem is separated into a linear and a nonlinear domain. Linearized inversion is applied to the retrieval of the short wavelength features of the velocity or impedance field. This problem has a huge number of degrees of freedom but it can be solved by an efficient asymptotic migration-inversion method. The low frequency part of the velocity field-the background-is inverted using a non-linear genetic algorithm applied to an objective functional defined in migrated data space. Computer time is significantly reduced using this objective function instead of straighforward waveform fitting. We apply out method to the inversion of a 1-D background velocity model from a reflexion profile of the North Sea. For this problem, we found that the genetic algorithm is more reliable and efficient than other velocity analysis methods. ¿ American Geophysical Union 1993