Objective treatment and synthesis of macroseismic intensity data sets using tessellation

We propose to overcome the widespread practice of drawing isoseismal maps b y tessellating the spatial distribution of observed intensity data with Vor onoi polygons. It is shown that tracing isoseismals by hand or automaticall y, starting from irregularly spaced point observations, is an ill-posed pro blem, because (1) the regional intensity data set of an earthquake is the r esult of summing continuous components (such as radiation and attenuation) with discontinuous components (such as the effects of crustal and site geol ogy); (2) the Nyquist principle also holds when tracing isoseismals, thus d etails (spatial high frequencies) can be observed only in areas with many o bservation points; (3) the combined process of sampling plus contouring in automatic procedures constitutes a two-dimensional filter. Thus, the idea t hat isoseismals somehow generate a total picture of earthquake effects in a region, which overcomes the paucity of available point observations, is mi sleading. The objective and quantitative treatment of the Voronoi intensity polygons renders automatic inversion of observed intensity data sets feasi ble. In the case of the Northridge, 17 January 1994, and Sierra Madre, 28 J une 1991, earthquakes, our inversion of intensity is able to retrieve kinem atic information on the sources that is in reasonable agreement with seismo graphic measurements. In Figure 3, however, it appears doubtful that our ki nematic algorithm might be useful for improving regional seismic hazard cal culations. However, our method seems promising for treating earthquakes of the preinstrumental era.