Edge-modulated stagnant-lid convection and volcanic passive margins

The initial oceanic crust along volcanic passive margins is a factor of similar to 3 greater than that of typical oceanic crust ( 20 versus 6 - 7 km). Convection driven by the edge of the continental lithosphere may cause mantle material to circulate through the shallow zone of significant melting beneath the nascent ocean basin and cause the volume of melted mantle to exceed that required to replace the diverging lithospheric plates. This hypothesis is a well-known alternative to mantle plumes. I obtain dimensional scaling relations and develop numerical models which indicate that the melted volume is unlikely to be enhanced by a factor of similar to 3. This conclusion agrees with the results of numerical calculations by Nielsen and Hopper ( 2002, 2004). Dimensional scaling provides the relationship which shows that the vigor of convection in terms of laterally averaged heat flow ( or flow velocity) depends on the square of local thickness of the rheological boundary layer ( for linear viscosity). The derivation does not involve undulations in lithospheric thickness and thus provides the inference that the vigor of stagnant-lid convection depends only weakly on those features. Numerical models support this inference. Lithospheric edges do nucleate instabilities, but these instabilities are similar in magnitude to those in models started with a tiny perturbation from laterally homogeneous temperature. Subsequent convection is also similar for models started with tiny perturbations and with large lateral variations in lithospheric thickness. In terms of the scaling relationship, the asthenosphere beneath the thin lithosphere within rifts is an unfavorable site for circulation and extensive melting. The rheological boundary layer is in general thin below thin lithosphere, which causes stagnant-lid convection there to be weak. Care needs to be taken in numerical modeling of convection beneath passive margins. Starting conditions that drive large instabilities of features that could not have persisted in the Earth need to be avoided. Models should start rifting only after mature stagnant-lid convection is established.