Analytic models for the dynamics of diffuse oceanic plate boundaries

Some plates deform across zones that are many hundreds to thousands of kilometres wide, much broader than traditional boundaries such as mid-ocean ridges, deep-sea trenches and oceanic transform faults, across which most deformation is concentrated in a zone just a few kilometres wide. These wide zones of deformation, commonly referred to as diffuse plate boundaries, occur in both continental and oceanic lithosphere. Composite plates are composed of two or more rigid, or nearly rigid, component plates separated by one or more diffuse plate boundaries (Royer & Gordon 1997); such 'complete' diffuse boundaries are terminated at both ends by triple junctions (although there are other diffuse boundaries that transform into narrow boundaries). Here we consider the dynamics of complete diffuse oceanic plate boundaries by constructing simple analytical models on a flat earth and on a spherical earth assuming that the viscous force resisting deformation is described by either a linear Newtonian law or a high-exponent power law. We investigate the observed tendency for the pole of relative motion between component plates separated by a diffuse plate boundary to lie within the diffuse boundary itself. We show that this tendency is due to geometrical effects that make it unlikely that the total torque acting between plates at a diffuse boundary could be oriented such that relative rotation occurs between the plates about a pole lying outside the boundary. This is demonstrated for both flat and spherical earth cases, assuming that resistance to strain along the diffuse boundary increases linearly with stress (Newtonian rheology). We further show that the pole of rotation is even more likely to lie in the diffuse plate boundary if the viscous force resisting deformation is described by a high-exponent power law rather than a Newtonian law.