Natural-Neighbor Isoseismals

Natural-neighbor (n-n) isoseismals are proposed as a new tool thatsolves the centennial problem of drawing objective and reproducible isoseismalsfrom earthquake damage sparsely observed in a region (felt reports). The algorithmuses the n-n coordinates for weighting, interpolating, and contouring the felt reports.In our computer implementation, at each step, the surface of irregularly distributedobservations is partitioned into a unique set of Voronoi polygons computed on a fineregular grid. The interpolation is local, because the weight of an experimental sitebrought to a new neighbour point is proportional to the area of the intersection oftheir Voronoi polygons. In the n-n approach, the interpolant (a) fits the data exactlyat the observation sites; (b) is isoparametric and bounded by the data values; and(c) is continuously differentiable at all points, except the data sites. Moreover, then-n isoseismals do not increase the complexity of the quantitative geophysical inter-pretation because they do not introduce new (contouring) parameters; and, finally,they may be intersected automatically with geological and topographical information.The new natural-neighbor isoseismals appear as a happy compromise between thecrude objectivity of the Voronoi tessellation and the intuitive appeal of the somewhatsubjective classical isoseismals.