Dynamics of diffuse oceanic plate boundaries: insensitivity to rheology

SUMMARY Diffuse plate boundaries, which are zones of deformation hundreds to thousands of kilometres wide, occur in both continental and oceanic lithosphere. Here, we build on our prior work in which we described analytic approximations to simple dynamical models that assume that the vertically averaged viscous force resisting deformation in diffuse oceanic plate boundaries (DOPBs) is described by either a linear Newtonian viscous rheology or a yield-stress (high-exponent power-law) rheology. An important observation is that the poles of relative rotation of adjacent component plates tend to lie in the diffuse plate boundary that separates them. A key cause of this tendency is that a faster spin is needed to balance a component of torque through the middle of a diffuse plate boundary than to balance an equal component of torque lying 90° from the middle of the diffuse boundary. The strength of that tendency depends on rheology, however, with the tendency being stronger for a yield-stress rheology than for a Newtonian viscous rheology. For the special case of the pole of rotation lying outside of and along the strike of the boundary, these large differences can be simply explained in terms of the distribution of boundary-perpendicular normal forces acting across the boundary. In the Newtonian case, the distribution of forces has an along-strike gradient that can balance a component of torque about the middle of the boundary, while in the yield-stress case, the distribution of forces has zero along-strike gradient and cannot balance a component of torque about the middle of the diffuse plate boundary. To expand our analysis to intermediate power laws of geophysical interest (i.e. power-law exponents of 3 to 30), as well as to investigate more thoroughly the behaviour for a high-exponent power law, we numerically integrate the force distribution to obtain the torques. Results for intermediate power laws resemble the yield-stress rheology much more than they resemble the Newtonian rheology and depend only weakly on the width of the deforming zone. To quantify the probability that a pole of rotation lies in a diffuse plate boundary, we numerically integrate the expectation assuming that all orientations of torque are equally probable. For a power-law exponent of n= 10: 49 per cent of possible torque orientations produce angular velocities outside the diffuse plate boundary if the boundary is 55° long (similar in length to the boundary between the Nubian and Somalian component plates); 21 per cent of possible torque orientations produce angular velocities outside the diffuse plate boundary if the boundary is 30° long (similar in length to the boundary between the Indian and Capricorn component plates and to that between the Capricorn and Australian component plates); and 6 per cent of possible torque orientations produce angular velocities outside the diffuse plate boundary if the boundary is 15° long (similar in length to the boundary between the North American and South American component plates and to that between the Macquarie and Australian component plates). These results reinforce the prior conclusion that the pole is more strongly locked into the boundary if a DOPB is short than if it is long. For all boundary lengths, but even more so for short boundaries, the relationship between angular velocity and torque depends only weakly on the power-law exponent of the rheology as long as n≥ 3. From this, we conclude that orientation of the relative torque across a DOPB can be inferred from the location of the pole of rotation without precise knowledge of the appropriate power-law exponent.