{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:17:03Z","timestamp":1774527423270,"version":"3.50.1"},"reference-count":0,"publisher":"Society of Exploration Geophysicists","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1984,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The paper extends to three dimensions (3-D) the two-dimensional (2-D) Hilbert transform relations between potential field components. For the 3-D case, it is shown that the Hilbert transform is composed of two parts, with one part acting on the X component and one part on the Y component. As for the previously developed 2-D case, it is shown that in 3-D the vertical and horizontal derivatives are the Hilbert transforms of each other. The 2-D Cauchy-Riemann relations between a potential function and its Hilbert transform are generalized for the 3-D case.--Modified journal abstract.<\/jats:p>","DOI":"10.1190\/1.1441706","type":"journal-article","created":{"date-parts":[[2002,10,11]],"date-time":"2002-10-11T15:58:01Z","timestamp":1034351881000},"page":"780-786","source":"Crossref","is-referenced-by-count":453,"title":["Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transforms; fundamental relations"],"prefix":"10.1190","volume":"49","author":[{"given":"Misac N.","family":"Nabighian","sequence":"first","affiliation":[{"name":"Newmont Explor., Tucson, AZ, United States"}]}],"member":"186","published-online":{"date-parts":[[1984,6,1]]},"container-title":["Geophysics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.geoscienceworld.org\/seg\/geophysics\/article-pdf\/49\/6\/780\/3163143\/780.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.geoscienceworld.org\/seg\/geophysics\/article-pdf\/49\/6\/780\/3163143\/780.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T17:36:59Z","timestamp":1765388219000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.geoscienceworld.org\/geophysics\/article\/49\/6\/780\/71749\/Toward-a-three-dimensional-automatic"},"secondary":[{"URL":"http:\/\/geophysics.geoscienceworld.org\/cgi\/doi\/10.1190\/1.1441706","label":"geoscienceworld"}]},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,6,1]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1984,6,1]]}},"URL":"https:\/\/doi.org\/10.1190\/1.1441706","relation":{},"ISSN":["1942-2156","0016-8033"],"issn-type":[{"value":"1942-2156","type":"electronic"},{"value":"0016-8033","type":"print"}],"subject":[],"published-other":{"date-parts":[[1984,6,1]]},"published":{"date-parts":[[1984,6,1]]}}}