Quantitative modelling of the filling of sedimentary basins was begun in earnest in the 1960s. Dozens of themes and variations have been proposed since then, and have yielded an abundance of idealized stratigraphic patterns as functions of both imposed changes and basin properties. Post-plate-tectonic modelling began with ‘rigid-lid' models, which show the stratigraphic signature of subsidence variation. This work introduced the connection between stratigraphy and the rheology of the lithosphere. Rigid-lid models are the simplest type of geometric model, in which the sediment surface is assigned prescribed geometries, usually corresponding to different depositional environments. These can reproduce many aspects of overall stratal geometry but are formally restricted to relatively long timescales, for which quasi-steady surface topography can be assumed. So-called dynamic models attempt to represent the morphodynamics of the sediment surface by abstracting and averaging short-term transport processes. Most of the dynamic models proposed to date can be seen as special cases of a single general morpho-dynamic equation.
The most important result of the first wave of quantitative basin-filling models is that even relatively simple models can produce reasonable stratal patterns. We now have a wide array of tools for exploring scenarios, searching for general behaviours and effects, and making initial quantitative predictions. We have also learned that basin response to external forcing as recorded in stratigraphy can be as sensitive to the characteristics of the basin as to the forcing.
The main brake on the development of basin modelling is not computing power but lack of methods and data for testing the models we have already developed. Physical experiments, which are only just beginning, are one means of doing this. Experimental stratigraphy is a bridge to quantitative field tests, which will require collaboration among academic researchers from a wide range of areas, and between academia and industry, on projects of greater scale and degree of integration than we have seen so far. The advancement of quantitative sedimentary geology will also require significant changes in the way the subject is taught, at all levels.