Does the mantle control the maximum thickness of cratons?

Geochemical observations suggest that cratonic xenoliths originate from depths no greater than 250 km, which implies a maximum craton thickness. What determines this thickness? In general, the stability and longevity of cratons depend on their ability to resist deforming forces exerted from below by the flowing, evolving mantle. We employ an analytical approach to relate the lithospheric viscosity structure of a craton to shear tractions exerted by asthenospheric shear flow. As the net thickness of the chemical and thermal components of a craton increases, these tractions increase dramatically for non-Newtonian rheology and begin to deform the cratonic base. Thus, overly thick lithosphere is subjected to large basal stresses that weaken the thermal boundary layer and diminish its ability to buffer the craton from destructive mantle flow. This feedback prevents cratonic lithosphere from growing thicker than a maximum value. However, we show that this maximum thickness increases slightly with increasing vigor of mantle convection but decreases rapidly as convective vigor decreases. Thus, we predict relative stability of cratonic thickness during most of Earth's history but instability in the future.