o1993; @hirth2003]. When the viscosity at the surface is $\sim 10^3 - 10^4$ times that of the interior, the top thermal boundary layer is so viscous that it can no longer sink under its own weight and form subduction zones, and stagnant lid convection ensues. [e.g. @Richter1983; @christensen1984c; @ogawa1991; @Davaille1993; @Moresi1995; @slava1995]. Laboratory experiments indicate that the viscosity ratio between the surface and mantle interior for typical terrestrial planets, including Earth, is $\sim 10^{10}-10^{20}$, far larger than the threshold for stagnant lid convection. Stagnant lid convection is thus the “natural" state for rocky planets, and additional processes are necessary for plate tectonics to operate on Earth.

In order to generate plate-tectonic style mantle convection, rheological complexities capable of forming weak, localized shear zones in the high viscosity lithosphere are necessary. These weak shear zones (essentially plate boundaries) remove the strong viscous resistance to surface motion that temperature-dependent viscosity causes and thus allow subduction and plate motions to occur. We discuss plate boundary formation in terms of viscous weakening in the lithosphere because the majority of the lithosphere, including the region of peak strength in the mid-lithosphere, deforms via ductile or semibrittle/semiductile behavior; the lithosphere only “breaks" in a brittle fashion at shallow depths of $< 10-20$ km [@Berco2015_treatise]. Many mechanisms have been proposed for producing the lithospheric weakening and shear localization necessary for plate-tectonic style mantle convection [see reviews by @Tackley2000; @Berco2003; @bk2003b; @Regenauer2003; @Berco2015_treatise]; while we won’t detail each of these mechanisms, they do all share some general principles. Namely, shear-thinning non-Newtonian rheologies, have been found to be successful at generating plate-like mantle convection.

In a shear-thinning fluid, the strain-rate, $\dot{\varepsilon}$, is a non-linear function of the stress