We investigate anisotropy surrounding a continental back arc spreading region, the Central Volcanic Region (CVR), in the North Island of New Zealand and present a simple method for spatial averaging to examine heterogeneous anisotropy. S phases from local earthquakes yield consistent trench-parallel fast directions ($phi$) in the southern, compressional region but varied directions in the northern, extensional region. In the forearc east of the CVR, $phi$ is nearly trench-parallel, suggesting shear in the mantle or trench-parallel flow. In the western CVR, local phases from 50 to 80 km depth give $phi$ parallel to extension (120¿), and phases from 150 to 220 km depth yield similar $phi$ (150¿). These results suggest asthenospheric flow with olivine a axes oriented in the extension direction down to 100--150 km depth. In the eastern CVR, local phases show mixed $phi$, suggesting that it is a transition between the western CVR and the forearc. Trench-parallel $phi$ for shallow local events within the CVR may be caused by fluid-filled cracks. Trench-parallel $phi$ for deeper local events and for SKS phases can be explained by standard olivine fabrics developed by lithospheric shearing, by trench-parallel flow, and by fossil anisotropy in the subducting oceanic lithosphere. Alternatively, in the CVR they could be caused in part by hydrous minerals at the slab-mantle upper interface, which could cause olivine a axes to orient parallel to the trench due to a maximum shear stress oriented perpendicular to the trench along the slab. We suggest that trench-perpendicular flow in the extensional region helps to drive fluids away from the slab, while in the compressional region, trench-parallel flow fails to distribute the fluids, explaining the location of changes in geophysical properties.