{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,21]],"date-time":"2025-08-21T18:42:58Z","timestamp":1755801778434,"version":"3.44.0"},"reference-count":55,"publisher":"Seismological Society of America (SSA)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The mapping of seismic activity is often achieved by means of smoothing or interpolation methods. Depending on the tectonic context and on the objectives of a study, end users can select among several alternative methods to produce a reliable representation of seismicity rate spatial distribution. Over the long term, nonparametric kernel estimation methods have become popular to estimate the seismicity rate intensity (density) directly from the catalog data. Their use is, however, not completely devoid of arbitrary decisions, especially concerning the selection of kernel type and the parameterization of kernel bandwidth. This inconvenience thus calls for an objective optimization of kernel shapes or for a sound justification of choices made by end users. Such a quest for objectivity is particularly expected in (probabilistic) seismic hazard analysis (PSHA) and in earthquake forecasting experiments. We propose an alternative approach where the spatial distribution of the seismicity rates is based on a Voronoi diagram of epicentral locations. In doing so, we avoid the use of any artificial smoothing operator that would be associated with a given kernel shape. Instead, we introduce an uncertainty-driven smoothing process, in which the degree of smoothing is controlled by the range of location and magnitude uncertainties in the catalog data. We propagate these uncertainties using Monte Carlo random sampling, in which multiple realizations of the original catalog data are used, each with randomly perturbed earthquake locations and magnitudes. The method relies on simple geometrical concepts. We demonstrate its potential by considering two representative use cases: a smooth seismicity model to be used for PSHA in continental France and a past earthquake forecasting experiment in California. Both applications produce maps of seismicity rates matching closely those obtained with adaptive smoothing kernels. This algorithm thus results in a reliable, unbiased, and more transparent smoothing process based on catalog uncertainties. Compared with other approaches, we rely on a smaller number of operator-driven decisions to control the degree of smoothing, or to optimize the parameterization of the smoothing kernel. This data-driven smoothing approach thus constitutes a valuable alternative to nonparametric kernel estimation methods for the future development of seismicity models.<\/jats:p>","DOI":"10.1785\/0220240428","type":"journal-article","created":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T08:07:38Z","timestamp":1747814858000},"page":"3050-3062","source":"Crossref","is-referenced-by-count":0,"title":["Data-Driven Seismicity Models Based on Voronoi Diagrams"],"prefix":"10.1785","volume":"96","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1018-411X","authenticated-orcid":false,"given":"Guillaume","family":"Daniel","sequence":"first","affiliation":[{"name":"1EDF - Direction Technique, Aix-en-Provence, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4142-227X","authenticated-orcid":false,"given":"Pierre","family":"Arroucau","sequence":"additional","affiliation":[{"name":"1EDF - Direction Technique, Aix-en-Provence, France"}]}],"member":"790","published-online":{"date-parts":[[2025,5,21]]},"reference":[{"issue":"4","key":"2025082013064992600_rf1","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1093\/biomet\/asq047","article-title":"On the Voronoi estimator for the intensity of an inhomogeneous planar Poisson process","author":"Barr","year":"2010","journal-title":"Biometrika"},{"issue":"6","key":"2025082013064992600_rf2","doi-asserted-by":"crossref","first-page":"2285","DOI":"10.1007\/s10518-018-0344-6","article-title":"Intensity predictive attenuation models calibrated in Mw for metropolitan France","author":"Baumont","year":"2018","journal-title":"Bull. 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