GAUSSIAN CURVATURE AND THE RELATIONSHIP BETWEEN THE SHAPE AND THE DEFORMATION OF THE TONGA SLAB

We investigate a particular potential cause of deformation within the subducting Tonga slab: that associated with material that moves over a template while remaining in contact with it. In such a situation both the location and the style of deformation within the material depend, in a predictable way, on the shape of the template, and in particular on its Gaussian curvature. We look for such an association in the Ton ga slab, using earthquake locations to define the slab shape and their focal mechanisms to indicate the style of deformation. Only in one pl ace, at 25 degrees S and 500-600 km depth, does the style of the fault ing in the earthquakes demonstrably correspond with that required by t he Gaussian curvature if the slab were moving over a template. Althoug h the Gaussian curvature in other parts of the slab, particularly near the 'hook' at its northern end, would also require deformation if the slab were moving over a template, the pattern of earthquake mechanism s were in those places is not clear enough to confirm the association. Although we are limited by our ability to resolve only the coarsest f eatures (greater than or similar to 300 km) of the slab shape, we reac h the important conclusion that deformation in response to motion over a template is not the main cause of the intermediate and deep seismic ity in the Tonga slab. Most of the earthquakes, and all the biggest on es, occur where, even if the slab were moving over a template, it woul d not need to deform to do so. Some other explanation is required for these earthquakes.