Preferred aspect ratios of convection in a strongly temperature and pressure dependent viscous fluid

If it is assumed that mantle convection is shallow, i.e. limited to an upper layer of ～700 km, then the extent of surface plates must be such that aspect ratios are noticeably large, in contrast to many laboratory and numerical experiments. A rheology which depends strongly on temperature and pressure is provided as an explanation of why this may occur. The aspect ratio, it is suggested, is preferentially large because of the unwillingness of the stiff plates to subduct, which raises the problem of how subduction occurs. A hypothesis is proposed that this is caused by viscous heating in the asthenosphere, and the preferred aspect ratio is large enough such that partial melting takes place underneath the sinking slab, causing it to sink by releasing the sub-lithospheric pressure so that a transverse buckling may occur.