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Natural-Neighbor Isoseismals

National Institute for Oceanography and for Experimental
Geophysics (OGS)
Borgo Grotta Gigante, 42c
34010 Sgonico, Trieste
Italy
(L.S., F.C., M.B.)
National Group for Defence Against Earthquakes (GNDT)
National Institute for Geophysics and Vulcanology (INGV), at OGS
Borgo Grotta Gigante, 42c
34010 Sgonico, Trieste
Italy
(F.P.)

Manuscript received 9 May 2001.

Natural-neighbor (n-n) isoseismals are proposed as a new tool that solves the centennial problem of drawing objective and reproducible isoseismals from earthquake damage sparsely observed in a region (felt reports). The algorithm uses the n-n coordinates for weighting, interpolating, and contouring the felt reports. In our computer implementation, at each step, the surface of irregularly distributed observations is partitioned into a unique set of Voronoi polygons computed on a fine regular grid. The interpolation is local, because the weight of an experimental site brought to a new neighbour point is proportional to the area of the intersection of their Voronoi polygons. In the n-n approach, the interpolant (a) fits the data exactly at 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, the n-n isoseismals do not increase the complexity of the quantitative geophysical interpretation 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 the crude objectivity of the Voronoi tessellation and the intuitive appeal of the somewhat subjective classical isoseismals.

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