{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T04:24:13Z","timestamp":1791951853296,"version":"4.3.4"},"reference-count":62,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T00:00:00Z","timestamp":1434412800000},"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>We propose a wavelet-based approach to measure the Shannon entropy in the context of spatial point patterns. The method uses the fully anisotropic Morlet wavelet to estimate the energy distribution at different directions and scales. The spatial heterogeneity and complexity of spatial point patterns is then analyzed using the multiscale anisotropic wavelet entropy. The efficacy of the approach is shown through a simulation study. Finally, an application to the catalog of earthquake events in Chile is considered.<\/jats:p>","DOI":"10.3390\/e17064155","type":"journal-article","created":{"date-parts":[[2015,6,16]],"date-time":"2015-06-16T10:28:09Z","timestamp":1434450489000},"page":"4155-4172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["2D Anisotropic Wavelet Entropy with an Application to Earthquakes in Chile"],"prefix":"10.3390","volume":"17","author":[{"given":"Orietta","family":"Nicolis","sequence":"first","affiliation":[{"name":"Institute of Statistics, University of Valparaiso, Av. Gran Breta\u00f1a 1111 , Valparaiso, Chile"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jorge","family":"Mateu","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, University Jaume I of Castell\u00f3n, Campus Riu Sec, Castellon 12071, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,6,16]]},"reference":[{"key":"ref_1","first-page":"2010","article-title":"On the Motive Power of Heat, and on the Laws which may be Deduced from it for the Theory of Heat","volume":"20","author":"Clausius","year":"1850","journal-title":"Ann. Phys."},{"key":"ref_2","first-page":"679","article-title":"Einige Allgemeine Satze Iiber Warmegleichgewicht unter Gas-molekulen","volume":"63","author":"Boltzmann","year":"1871","journal-title":"Sitzungsber. Akad. Wiss. 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