Full-waveform inversion (FWI) often attempts to resolve an ill-posed non-linear optimization problem in order to retrieve the unknown subsurface model from the seismic data. With model regularization, we alleviate the ill-posedness of FWI associated with salt bodies affected datasets by decoupling the minimization problem into two parts. We minimize the data misfit along with the total variation in the model, seeking an inverted model with sharp interfaces. In the second optimization, we penalize sharp velocity drops in the model, which is equivalent to computationally flooding of velocity field. Besides the minimal human intervention, our technique requires no information whatsoever of the top of the salt, which is required for conventional industrial salt flooding. Those features are demonstrated on a dataset corresponding to the BP 2004 model with frequencies less than 3 Hz muted to make the data more practical. The model is well retrieved if the same constant density acoustic code is used for preparing the observed data, which is still one of the most common FWI tests. However, our approach still allows us to reconstruct a reasonable depiction of the salt structure from data synthesized independently with a variable density model.