{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:57:45Z","timestamp":1774357065829,"version":"3.50.1"},"reference-count":60,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T00:00:00Z","timestamp":1550016000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>An increase of seismic activity is often observed before large earthquakes. Events responsible for this increase are usually named foreshock and their occurrence probably represents the most reliable precursory pattern. Many foreshocks statistical features can be interpreted in terms of the standard mainshock-to-aftershock triggering process and are recovered in the Epidemic Type Aftershock Sequence ETAS model. Here we present a statistical study of instrumental seismic catalogs from four different geographic regions. We focus on some common features of foreshocks in the four catalogs which cannot be reproduced by the ETAS model. In particular we find in instrumental catalogs a significantly larger number of foreshocks than the one predicted by the ETAS model. We show that this foreshock excess cannot be attributed to catalog incompleteness. We therefore propose a generalized formulation of the ETAS model, the ETAFS model, which explicitly includes foreshock occurrence. Statistical features of aftershocks and foreshocks in the ETAFS model are in very good agreement with instrumental results.<\/jats:p>","DOI":"10.3390\/e21020173","type":"journal-article","created":{"date-parts":[[2019,2,14]],"date-time":"2019-02-14T03:21:46Z","timestamp":1550114506000},"page":"173","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["The Relevance of Foreshocks in Earthquake Triggering: A Statistical Study"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1444-1889","authenticated-orcid":false,"given":"Eugenio","family":"Lippiello","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, Viale Lincoln 5, 81100 Caserta, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cataldo","family":"Godano","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Physics, University of Campania \u201cL. Vanvitelli\u201d, Viale Lincoln 5, 81100 Caserta, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9247-6783","authenticated-orcid":false,"given":"Lucilla","family":"de Arcangelis","sequence":"additional","affiliation":[{"name":"Department of Engineering, University of Campania \u201cL. Vanvitelli\u2019, Via Roma 29, 81031 Aversa (CE), Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1080\/01621459.1988.10478560","article-title":"Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes","volume":"83","author":"Ogata","year":"1988","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1023\/A:1003403601725","article-title":"Space-time Point-process Models for Earthquake Occurrences","volume":"50","author":"Ogata","year":"1988","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/BF01406511","article-title":"A Monte Carlo method for high dimensional integration","volume":"55","author":"Ogata","year":"1989","journal-title":"Numer. 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Discuss."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/173\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:31:44Z","timestamp":1760185904000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/2\/173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,13]]},"references-count":60,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,2]]}},"alternative-id":["e21020173"],"URL":"https:\/\/doi.org\/10.3390\/e21020173","relation":{"has-preprint":[{"id-type":"doi","id":"10.20944\/preprints201810.0679.v1","asserted-by":"object"}]},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,2,13]]}}}