Kinematics to dynamics in the New Zealand plate-boundary zone

New Zealand straddles the boundary between the Australian and Pacific plate, with a transition from subduction of Pacific oceanic lithosphere beneath North Island, to oblique continental collision in South Island. Cenozoic relative plate motion has resulted in a complex pattern of faulting and block rotation in a zone up to 250 km wide, with displacements on individual faults up to 100s of kilometres. Active deformation must be driven by a combination of plate-boundary forces and internal buoyancy forces. I use a compilation of seismic reflection/refraction studies and high quality receiver function analyses, together with simple Airy isostasy, to determine regional crustal and mantle structure. Integration of the vertical normal stress to the base of the deforming layer yields the buoyancy stress. Horizontal gradients of this can be compared with horizontal gradients of strain rate, using the method of England & Molnar (1997), in the context of a simple thin sheet model of deformation. Thus, if deformation is that of a Newtonian fluid, then appropriate combinations of the horizontal gradients of vorticity and dilatation are related to gradients of buoyancy stress by the fluid viscosity. However, the short term geodetic deformation is strongly biased by elastic strain accumulation related to locking on the plate interface, and cannot be used to determine the plate-boundary velocity field averaged over many seismic cycles (see Lamb & Smith 2013). Therefore, I derive here a velocity field for the plate-boundary zone, which is representative of deformation over tens of thousands of years. This is based on an inversion of fault slip, strain rate azimuth and paleomagnetic data, in the context of the short term relative plate motions, solved in a network of triangles spanning the plate-boundary, using the method of Lamb (2000). A comparison of gradients of buoyancy stress with the appropriate combinations of gradients of vorticity and dilatation shows that deformation in the plate-boundary zone does have features that are fluid-like, characterized by a variable viscosity in the range 1 - 10 x 10^21 Pa s. Given the strain rates in the plate-boundary zone, viscosities imply plate-boundary deviatoric stresses < 20 MPa, and are consistent with previous low estimates of shear stresses in subduction zones based on a simple force balance (Lamb 2006). References: England, P.C., and P. Molnar, (1997), Science, 278, 647-649. Lamb, S. (2000), J. Geophys. Res., 105, 25,627-25,653. Lamb, S., (2006), J. Geophys. Res., 111, B07401, doi:10.1029/2005JB003916. Lamb, S., and E. Smith (2013), J. Geophys. Res. Solid Earth, 118, doi:10.1002/jgrb.50221.