On the form and stability of seafloor stratigraphy and shelf profiles: A mathematical model and solution method

Numerical results often exhibit “equilibrium profile” solutions for a wide variety of different model scenarios. These profiles may be viewed as travelling waves, such that the rate of progradation gives the speed of this wave as it advances into the receiving basin. When realistic initial and boundary conditions are used, profiles are often seen to evolve toward forms that are independent of the initial bathymetry. Although episodic perturbations such as turbidities disrupt these forms, they still serve as attractors for the system dynamics. An application of the solution method presented in this paper also allows the shape of equilibrium profiles and the progradation rate to be determined from a specification of the initial bathymetry and the sediment deposition function. Several illustrative examples are given in closed form. Results are also presented that make it possible to compute the amount of time required for an equilibrium profile to be re-established after a perturbation.