We present a new technique for inverting 4D seismic data constrained by dynamics and geology. The inversion is first performed at well positions where all the constraints are set and afterwards extended to the full 3D dataset. The geological and dynamical constraints are set in the model definition i.e. a layered description of the geology (with permeable and non permeable layers) which may be different at each well. This information is then propagated concurrently from each well to the whole dataset. The way the inversion is posed prevents from side lobes effect and enables to discriminate density and velocity effects (P in the case of post-stack data and P&S in the case of prestack). The more reliable information is the P velocity since it affects both reflectivity and travel time.