{"id":102025,"date":"2019-07-18T01:32:10","date_gmt":"2019-07-18T01:32:10","guid":{"rendered":"http:\/\/ahay.org\/blog\/?p=102025"},"modified":"2019-07-18T01:32:10","modified_gmt":"2019-07-18T01:32:10","slug":"low-rank-viscoacoustic-wave-extrapolation","status":"publish","type":"post","link":"https:\/\/ahay.org\/blog\/2019\/07\/18\/low-rank-viscoacoustic-wave-extrapolation\/","title":{"rendered":"Low-rank viscoacoustic wave extrapolation"},"content":{"rendered":"<p>A new paper is added to the <a href=\"\/wiki\/Reproducible_Documents\">collection of reproducible documents<\/a>: <a href=\"\/RSF\/book\/tccs\/fraclapl\/paper_html\/\">Viscoacoustic modeling and imaging using low-rank approximation<\/a><\/p>\n<p><img decoding=\"async\" src=\"\/RSF\/book\/tccs\/fraclapl\/marmq\/Fig\/visacu.png\" alt=\"\" title=\"\"> <img decoding=\"async\" src=\"\/RSF\/book\/tccs\/fraclapl\/marmq\/Fig\/comacu.png\" alt=\"\" title=\"\"><\/p>\n<blockquote><p>A constant-$Q$ wave equation involving fractional Laplacians was recently introduced for viscoacoustic modeling and imaging. This fractional wave equation has a convenient mixed-domain space-wavenumber formulation, which involves the fractional-Laplacian operators with a spatially varying power. We propose to apply low-rank approximation to the mixed-domain symbol, which enables a space-variable attenuation specified by the variable fractional power of the Laplacians. Using the proposed approximation scheme, we formulate the framework of the $Q$-compensated reverse-time migration ($Q$-RTM) for attenuation compensation. Numerical examples using synthetic data demonstrate the improved accuracy of using low-rank wave extrapolation with a constant-$Q$ fractional-Laplacian wave equation for seismic modeling and migration in attenuating media. Low-rank $Q$-RTM applied to viscoacoustic data is capable of producing images comparable in quality with those produced by conventional RTM from acoustic data.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>A new paper is added to the collection of reproducible documents: Viscoacoustic modeling and imaging using low-rank approximation A constant-$Q$ wave equation involving fractional Laplacians was recently introduced for viscoacoustic modeling and imaging. This fractional wave equation has a convenient mixed-domain space-wavenumber formulation, which involves the fractional-Laplacian operators with a spatially varying power. We propose [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","activitypub_content_warning":"","activitypub_content_visibility":"local","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"","footnotes":""},"categories":[5],"tags":[],"class_list":["post-102025","post","type-post","status-publish","format-standard","hentry","category-documentation"],"_links":{"self":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/102025","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/comments?post=102025"}],"version-history":[{"count":2,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/102025\/revisions"}],"predecessor-version":[{"id":102027,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/102025\/revisions\/102027"}],"wp:attachment":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/media?parent=102025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/categories?post=102025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/tags?post=102025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}