{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T13:03:00Z","timestamp":1775653380817,"version":"3.50.1"},"reference-count":0,"publisher":"Society of Exploration Geophysicists","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1986,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The second-order central difference is often used to approximate the derivatives of the wave equation. It is demonstrated that gains in computational efficiency can be made by using high-order approximations for these derivatives. A one-dimensional model is used to illustrate the relative accuracy of O(Delta t 2 , Delta x 2 ), O(Delta t 2 , Delta x 4 ), O(Delta t 4 , Delta x 4 ), and O(Delta t 4 , Delta x 10 ) central-difference schemes. For comparison, O(Delta t 2 ) and O(Delta t 4 ) pseudo-spectral schemes are used as an additional measure of performance. The results indicate that O(Delta t 4 , Delta x 10 ) differencing can achieve similar accuracy as the O(Delta t 4 ) spectral scheme. For practical illustration, a two-dimensional form of the O(Delta t 4 , Delta x 10 ) algorithm is used to compute the exploding reflector response of a salt-dome model and compared with a fine-grid O(Delta t 2 , Delta x 4 ) result. Transmissive sponge-like boundary conditions are also examined and shown to be effective.<\/jats:p>","DOI":"10.1190\/1.1442040","type":"journal-article","created":{"date-parts":[[2002,10,11]],"date-time":"2002-10-11T16:01:07Z","timestamp":1034352067000},"page":"54-66","source":"Crossref","is-referenced-by-count":632,"title":["The application of high-order differencing to the scalar wave equation"],"prefix":"10.1190","volume":"51","author":[{"given":"M. A.","family":"Dablain","sequence":"first","affiliation":[]}],"member":"186","published-online":{"date-parts":[[1986,1,1]]},"container-title":["Geophysics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.geoscienceworld.org\/seg\/geophysics\/article-pdf\/51\/1\/54\/3164403\/54.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.geoscienceworld.org\/seg\/geophysics\/article-pdf\/51\/1\/54\/3164403\/54.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T17:53:05Z","timestamp":1765389185000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.geoscienceworld.org\/geophysics\/article\/51\/1\/54\/72102\/The-application-of-high-order-differencing-to-the"},"secondary":[{"URL":"http:\/\/geophysics.geoscienceworld.org\/cgi\/doi\/10.1190\/1.1442040","label":"geoscienceworld"}]},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1986,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1986,1,1]]}},"URL":"https:\/\/doi.org\/10.1190\/1.1442040","relation":{},"ISSN":["1942-2156","0016-8033"],"issn-type":[{"value":"1942-2156","type":"electronic"},{"value":"0016-8033","type":"print"}],"subject":[],"published-other":{"date-parts":[[1986,1,1]]},"published":{"date-parts":[[1986,1,1]]}}}