We developed a new model-based 4D inversion algorithm that propagated through a 4D data set from a well location, minimizing the traveltime and amplitude differences of the data. The model consisted of a finite number of layers in which the thickness and change in elastic parameters were solved in each layer. The inversion used a local optimization strategy at each trace, in which the solution of a previously inverted neighboring trace was used as the initial guess; it started from a 4D layer-based inversion solution found at a well location. Information from the well was, therefore, propagated into the data set whereas it remained consistent with the data. When several wells were used simultaneously, they propagated in a concurrent manner to determine each well’s area of influence. By using the time-shift and amplitude differences, it became possible to decouple density and P-wave velocity changes; however, even with this additional information, solutions were seldom consistent enough to provide coherent quantitative interpretation. We therefore introduced a new constraint based on production information and rock physics to guide the solution to realistic combinations of elastic parameters. We determined that this constraint was fairly independent of the geology. Examples of the prestack propagation inversion algorithm were shown on synthetic and real data examples. Comparisons were also made to standard 4D inversion highlighting the improvement in the coherency of the new results. We concluded that this type of model-based inversion was not designed to be used as a reconnaissance tool for 4D interpretation (this remains the job of data-driven inversion schemes) but was a powerful tool for either extracting as much information as possible from 4D seismic data or to test various hypothesis of different 4D scenarios.