We propose to overcome the widespread practice of drawing isoseismal maps by tessellating the spatial distribution of observed intensity data with Voronoi polygons. It is shown that tracing isoseismals by hand or automatically, starting from irregularly spaced point observations, is an ill-posed problem, because (1) the regional intensity data set of an earthquake is the result of summing continuous components (such as radiation and attenuation) with discontinuous components (such as the effects of crustal and site geology); (2) the Nyquist principle also holds when tracing isoseismals, thus details (spatial high frequencies) can be observed only in areas with many observation points; (3) the combined process of sampling plus contouring in automatic procedures constitutes a two-dimensional filter. Thus, the idea that isoseismals somehow generate a total picture of earthquake effects in a region, which overcomes the paucity of available point observations, is misleading. The objective and quantitative treatment of the Voronoi intensity polygons renders automatic inversion of observed intensity data sets feasible. In the case of the Northridge, 17 January 1994, and Sierra Madre, 28 June 1991, earthquakes, our inversion of intensity is able to retrieve kinematic information on the sources that is in reasonable agreement with seismographic measurements. In Figure 3, however, it appears doubtful that our kinematic algorithm might be useful for improving regional seismic hazard calculations. However, our method seems promising for treating earthquakes of the preinstrumental era.