Computer models of stratigraphic development at continental margins often include elements in which sediment topography evolves according to a diffusion equation, representing effects of down-slope sediment transport. However, there has been little effort to verify the model, for example by showing whether deposit geometries are as expected from it or by considering whether transport is consistent with the model's assumptions. The issue is important for understanding transport, erosion and deposition in continental slopes more generally and the extent to which such processes are recorded in seabed morphology. Examples of slope topography illustrating diffusive-like characteristics are examined here. In the uppermost slope of the USA central Atlantic margin, sandy areas between canyon heads are smoothly convex-upwards and almost parabolic, a morphology similar to subaerial soil-mantled hillslopes known to evolve according to a diffusion equation. Other data of interfluves in muddy sediment from both Atlantic and Pacific USA margins also show this smooth convex-upwards form.
In subaerial hill crests, the upwards-convex parabolic shape arises where steady erosion by streams along channels provide constant flux boundary conditions (i.e., the parabola is the steady state solution to the diffusion equation). Although submarine processes will likely be different, the similar morphology of submarine interfluves prompts the question as to whether erosion along channels and movements of sediment between channels can also sometimes occur to cause a diffusive-like evolution of topography. The discussion therefore focuses on submarine processes affecting erosion and deposition, in particular to address whether the morphology results from true diffusion (which requires that sediment moves down-slope with a transport flux proportional to local bed gradient) or is fortuitous (sediment transport is instead unrelated to local bed gradient and the morphology arises from other effects on accumulation rates).
Mitchell, NC, and Huthnance, JM, "Comparing the smooth, parabolic shapes of interfluves in continental slopes to predictions of diffusion transport models," Marine Geology, 236, 189-208.