Stratigraphic models are used in oil exploration in order to determine the geometry of sedimentary layers and to characterize the geological properties of the sediments. They simulate the infill of a sedimentary basin at large scales of space and time, governed by the interaction of accommodation change, sediment supply and sediment transport. One of the main difficulties in the use of such models is that all their input parameters have to be identified to fit well-log and seismic data. A basic issue is to compute the rate of accommodation change in order to fit the sediment thicknesses measured between each successive seismic marker. This leads to the solution to an inverse problem for which existence is proved in the single lithology case. Numerical algorithms are proposed and studied based on the construction of a reduced model and Newton–Krylov methods.