Tensor-guided interpolation of subducting slab depths

Earthquakes and seismic surveys provide estimates of depths of subducting slabs, but only at scattered locations. To construct a useful three dimensional model of slab geometry we must interpolate slab depths at uniformly sampled locations on the earth’s surface, and the interpolation method should account for the curvature of that surface. In addition to estimates of depths from earthquake locations, focal mechanisms of subduction zone earthquakes also provide estimates of the strikes and dips of the subducting slab on which they occur. We use estimated strikes to construct a metric tensor field that guides a blended neighbor interpolation of estimated depths. Our interpolation serves as an example of using one set of scattered data to infer the spatial correlation of another, while accounting for the acquisition of those data on a non-planar surface.