Migration velocity analysis (MVA) is a technique defined in the image domain to determine the background velocity model controlling the kinematics of wave propagation. In the presence of discontinuous interfaces, the velocity gradient used to iteratively update the velocity model exhibits spurious oscillations. For more stable results, we replace the migration part by an inversion scheme. By definition, migration is the adjoint of the Born modeling operator, whereas inversion is its asymptotic inverse. We have developed new expressions in 1D and 2D cases based on two-way wave-equation operators. The objective function measures the quality of the images obtained by inversion in the extended domain depending on the subsurface offset. In terms of implementation, the new approach is very similar to classic MVA. A 1D analysis found that oscillatory terms around the interface positions can be removed by multiplying the inversion result with the velocity at a specific power before evaluating the objective function. Several 2D synthetic data sets are discussed through the computation of the gradient needed to update the model parameters. Even for discontinuous reflectivity models, the new approach provides results without artificial oscillations. The model update corresponds to a gradient of an existing objective function, which was not the case for the horizontal contraction approach proposed as an alternative to deal with gradient artifacts. It also correctly handles low-velocity anomalies, contrary to the horizontal contraction approach. Inversion velocity analysis offers new perspectives for the applicability of image-domain velocity analysis.