Analytical modelling of viscous diapirism through a strongly non-Newtonian overburden subject to horizontal forces

We study the early stages of diapirism and analyse the gravitational and buckling instabilities of a buoyant viscous layer overlain by a layer of strongly non-Newtonian power-law rheology (when a power-law exponent tends to infinity). This situation models rocksalt under a layer of a perfectly plastic overburden. The growth rate of small perturbations on the interface between the two layers and the wavelength of the most unstable perturbations are found and compared with those of structures consisting of two Newtonian or two strongly nonNewtonian viscous layers. Effects due to the effective viscosity and thickness ratios between the two layers are assessed. Considering the effective viscosity of the overburden to be much greater than the viscosity of the buoyant salt layer, we obtain the following results. In the case of simple gravitational instability and no-slip boundary conditions, the instability pattern is similar to that in a strongly non-Newtonian power-law material. An increase in the thickness of the overburden decreases the dominant wavelength of the most unstable mode, while the dominant wavelength is lengthened in the case of Newtonian viscous layers. When the system of layers is subjected to either horizontal extension or shortening, and the upper boundary of the system is stress-free, the buckling instability overwhelms the gravitational instability, and the dynamic growth rate of the instability depends linearly on the effective viscosity ratio. We conclude that the introduction of strongly non-Newtonian power-law rheology into diapir overburdens greatly affects instability parameters such as growth rate and dominant wavelength of perturbations and hence, alters interdiapir spacings.