On the Choice of Boundary Conditions in Continuum Models of Continental Deformation

Recent studies of continental deformation have treated the lithosphere as a viscous media and investigated the time evolution of the deformation caused by tectonic and buoyancy forces. We examine the differences between continuum models that keep velocity boundary conditions (b.c.) constant with time and models that keep stress b.c. constant with time and demonstrate these differences by using a simple example of a continental lithosphere that is subjected to horizontal compression. Our results show that in the case of constant stress b.c., the indentation velocity decreases with time, while in the case of constant velocity b.c., the indentation velocity remains constant with time. Observations from the Tibetan plateau and from the Andes indicate that the rate of indentation decreases with time. This suggests that when buoyancy forces are comparable in magnitude to tectonic forces, constant stress b.c. are more appropriate for time evolutionaxy models of continentel lithosphere. We propose a simple procedure that translates velocity b.c., which are easy to estimate, into stress b.c. at the initial stage, and keep the stress b.c. constant along the time progression of the calculations.