Full Waveform Inversion of elastic dataset is challenging due to the complexity introduced by free-surface effects or P-S wave conversions among others. In this context, large offsets are preferred for inversion because they favor transmission modes which are more linearly related to P-wave velocity. In this paper, we present an original approach which allows to dynamically select the near offset at each frequency. We illustrate this approach with the inversion of a dataset without density. In order to deal with a more realistic scenario, we next present the inversion with density effects included into the modeling. As inverting density is known to be a hard task, we choose to not invert it. This approach leads to the use of a phase misfit function, which is more connected to the kinematics of the problem than the classic L2 norm.