{"id":42,"date":"2015-07-08T12:05:09","date_gmt":"2015-07-08T19:05:09","guid":{"rendered":"http:\/\/labs.wsu.edu\/tomsovic\/?page_id=42"},"modified":"2026-04-10T12:04:29","modified_gmt":"2026-04-10T19:04:29","slug":"long-range-underwater-sound","status":"publish","type":"page","link":"https:\/\/labs.wsu.edu\/tomsovic\/long-range-underwater-sound\/","title":{"rendered":"Long range underwater sound"},"content":{"rendered":"<div class=\"wsu-row wsu-row--single\" >\r\n    \n<div class=\"wsu-column\"  style=\"\">\r\n\t\n\n<h2 class=\"wp-block-heading\">Long range underwater sound and random matrix theory<\/h2>\n\n\n\n<p>Ocean acoustic propagation can be formulated as a wave guide with a weakly random medium generating multiple scattering. Twenty years ago, this was recognized as a quantum chaos problem, and yet random matrix theory, one pillar of quantum or wave chaos studies, has never been introduced into the subject. The modes of the wave guide provide a representation for the propagation, which in the parabolic approximation is unitary. Scattering induced by the ocean&#8217;s internal waves leads to a power-law random banded unitary matrix ensemble for long-range deep ocean acoustic propagation. The ensemble has similarities, but differs, from those introduced for studying the Anderson metal-insulator transition. The resulting long-range propagation ensemble statistics agree well with those of full wave propagation using the parabolic equation.<\/p>\n\n<\/div>\r\n\n<\/div>","protected":false},"excerpt":{"rendered":"","protected":false},"author":1067,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"categories":[],"tags":[],"wsuwp_university_location":[2],"wsuwp_university_org":[],"_links":{"self":[{"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/pages\/42"}],"collection":[{"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/users\/1067"}],"replies":[{"embeddable":true,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":2,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/pages\/42\/revisions"}],"predecessor-version":[{"id":312,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/pages\/42\/revisions\/312"}],"wp:attachment":[{"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/media?parent=42"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/categories?post=42"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/tags?post=42"},{"taxonomy":"wsuwp_university_location","embeddable":true,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/wsuwp_university_location?post=42"},{"taxonomy":"wsuwp_university_org","embeddable":true,"href":"https:\/\/labs.wsu.edu\/tomsovic\/wp-json\/wp\/v2\/wsuwp_university_org?post=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}