A three-dimensional (3-D) forward stratigraphic model has been built to simulate geometries and lithologies of coastal environments (e.g., coastal plain, shoreface, and upper offshore) on time and spatial macroscopic scales (hundreds of thousands to tens of millions of years, and tens to hundreds of kilometers). The model is based on fluid-flow mechanic laws. A generalized diffusion equation, taking into account water discharge, simulates fluvial- and gravity-dominated sediment transport. Sediment load carried by water is proportional to the basin slope (moving force), water discharge (water transport capacity), lithology fraction (sediment availability), and diffusivity coefficient (transport efficiency).

A 3-D theoretical fluvial-dominated delta was simulated to test the geological consistency of the model. Although the model is based only on sediment transport laws, the parameters of which are assumed constant in this theoretical example, it reproduced correctly sequence stratigraphy concepts such as formation of genetic units, volumetric partitioning, and facies differentiation due to sea level variation.

Simulation of the Lower Cretaceous formation of the Paris basin (France) was done at a basin scale (basin size: 200 × 240 km²; formation duration: 10 m.y.) to fit the simulation outputs on well data. An inversion loop was used to quantify model parameters such as accommodation map, water and sediment supplies, carbonate growth law, and diffusivity coefficient. Sediment thickness was quantified with an error of less than 1 m at the 12 wells used during the inversion loop, and less than 10 m at 25 km from these wells.

These applications validate the geological consistency of the general physical principles used in the model. This 3-D improved diffusive model helps to determine an average geometry of sedimentary units and to characterize the facies content (depositional water depth, sand:shale:carbonate ratio) inside each of them. The model provides a quantitative tool for better understanding the 3-D stratigraphy of sedimentary basins.0