{"id":"https://openalex.org/W2962707560","doi":"https://doi.org/10.1137/12089586x","title":"A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion","display_name":"A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2962707560","doi":"https://doi.org/10.1137/12089586x","mag":"2962707560"},"language":"en","primary_location":{"id":"doi:10.1137/12089586x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12089586x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008274019","display_name":"Tan Bui\u2013Thanh","orcid":"https://orcid.org/0000-0003-3002-6474"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tan Bui-Thanh","raw_affiliation_strings":["Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049331711","display_name":"Omar Ghattas","orcid":"https://orcid.org/0000-0001-7742-2509"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Omar Ghattas","raw_affiliation_strings":["Institute for Computational Engineering & Sciences, Department of Mechanical Engineering, and Department of Geological Sciences, The University of Texas at Austin, Austin, TX 78712"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering & Sciences, Department of Mechanical Engineering, and Department of Geological Sciences, The University of Texas at Austin, Austin, TX 78712","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103831520","display_name":"James L. Martin","orcid":null},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Martin","raw_affiliation_strings":["Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012373865","display_name":"Georg Stadler","orcid":"https://orcid.org/0000-0001-7762-6544"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Georg Stadler","raw_affiliation_strings":["Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering & Sciences, The University of Texas at Austin, Austin, TX 78712","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5008274019"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":20.2572,"has_fulltext":false,"cited_by_count":368,"citation_normalized_percentile":{"value":0.99351036,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"35","issue":"6","first_page":"A2494","last_page":"A2523"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1908","display_name":"Geophysics"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.6951478719711304},{"id":"https://openalex.org/keywords/posterior-probability","display_name":"Posterior probability","score":0.6682890057563782},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.667424201965332},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6592476963996887},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6185520887374878},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5436238050460815},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5339760780334473},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.517282247543335},{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.4682057499885559},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.43001341819763184},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.42185139656066895},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3738974928855896},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.179212749004364},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08870649337768555}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6951478719711304},{"id":"https://openalex.org/C57830394","wikidata":"https://www.wikidata.org/wiki/Q278079","display_name":"Posterior probability","level":3,"score":0.6682890057563782},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.667424201965332},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6592476963996887},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6185520887374878},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5436238050460815},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5339760780334473},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.517282247543335},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.4682057499885559},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.43001341819763184},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.42185139656066895},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3738974928855896},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.179212749004364},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08870649337768555}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/12089586x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/12089586x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1535619635","display_name":null,"funder_award_id":"FA9550-09-1-0608","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2118871404","display_name":null,"funder_award_id":"DE-FG02-09ER25914","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2130435062","display_name":"CDI-Type II: Dynamics of Ice Sheets: Advanced Simulation Models, Large-Scale Data Inversion, and Quantification of Uncertainty in Sea Level Rise Projections","funder_award_id":"0941678","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2847796638","display_name":"CENTER FOR PREDICTIVE ENGINEERING AND COMPUTATIONAL SCIENCES","funder_award_id":"FC52-08NA28615","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3149632210","display_name":null,"funder_award_id":"DE-FC02-11ER26052","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3618738895","display_name":null,"funder_award_id":"DE-SC0009286","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3633521801","display_name":"LARGE SCALE OPTIMIZATION FOR BEYESIAN INFERENCE IN COMPLEX SYSTEMS","funder_award_id":"FG02-08ER25860","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G4629028822","display_name":"CDI Type II/Collaborative Research:  Ultra-high Resolution Dynamic Earth Models through Joint Inversion of Seismic and Geodynamic Data","funder_award_id":"1028889","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5105579375","display_name":null,"funder_award_id":"OPP-0941678","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G54015040","display_name":null,"funder_award_id":"CMS-1028889","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G577836541","display_name":"CMG Collaborative Research: Model Integration and Joint Inversion for Large-Scale Multi-Modal Geophysical Data","funder_award_id":"0724746","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7186324567","display_name":null,"funder_award_id":"DE-FG02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8458185417","display_name":null,"funder_award_id":"DE-FC52-08NA28615","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8543603247","display_name":null,"funder_award_id":"DE-SC0009286","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8684078510","display_name":null,"funder_award_id":"DE-FG02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1545319692","https://openalex.org/W1837874438","https://openalex.org/W1847067072","https://openalex.org/W1965802540","https://openalex.org/W1974372238","https://openalex.org/W1979313559","https://openalex.org/W2006251572","https://openalex.org/W2014367637","https://openalex.org/W2018349419","https://openalex.org/W2025669066","https://openalex.org/W2032117385","https://openalex.org/W2042545789","https://openalex.org/W2056984487","https://openalex.org/W2062221814","https://openalex.org/W2074836377","https://openalex.org/W2082261407","https://openalex.org/W2082959597","https://openalex.org/W2098065241","https://openalex.org/W2118065331","https://openalex.org/W2146961539","https://openalex.org/W2149498546","https://openalex.org/W2156192189","https://openalex.org/W2167943787","https://openalex.org/W2326774159","https://openalex.org/W2963777151","https://openalex.org/W3098170545","https://openalex.org/W3106128350","https://openalex.org/W4245445339"],"related_works":["https://openalex.org/W3006565005","https://openalex.org/W2964314781","https://openalex.org/W4287868071","https://openalex.org/W4389708677","https://openalex.org/W2611832276","https://openalex.org/W69468016","https://openalex.org/W2007093222","https://openalex.org/W3124172274","https://openalex.org/W2145178290","https://openalex.org/W2358572162"],"abstract_inverted_index":{"We":[0,19,201],"present":[1],"a":[2,39,145,152,171],"computational":[3,127,204],"framework":[4,128,162,195,205],"for":[5,166],"estimating":[6],"the":[7,10,21,31,46,50,55,70,78,90,97,105,112,116,131,156,168,176,180,186,193,207],"uncertainty":[8,44],"in":[9,45,64,214],"numerical":[11],"solution":[12,95,209],"of":[13,69,77,89,96,104,147,155,175,179,192,210,222,224],"linearized":[14],"infinite-dimensional":[15,71,91,132,158],"statistical":[16],"inverse":[17,72,99,159,212],"problems.":[18],"adopt":[20],"Bayesian":[22,208],"inference":[23],"formulation:":[24],"given":[25],"observational":[26],"data":[27],"and":[28,35,38,74,143,184],"their":[29],"uncertainty,":[30,37],"governing":[32],"forward":[33,117],"problem":[34,73,100,118,213],"its":[36],"prior":[40,59],"probability":[41,52],"distribution":[42,53],"describing":[43],"parameter":[47,56,199],"field,":[48],"find":[49],"posterior":[51,181,187],"over":[54],"field.":[57],"The":[58,161],"must":[60],"be":[61],"chosen":[62],"appropriately":[63],"order":[65],"to":[66,86,111,114,196],"guarantee":[67],"well-posedness":[68],"facilitate":[75],"computation":[76],"posterior.":[79],"Furthermore,":[80],"straightforward":[81],"discretizations":[82],"may":[83],"not":[84],"lead":[85],"convergent":[87,153],"approximations":[88],"problem.":[92,160],"And":[93],"finally,":[94],"discretized":[98],"via":[101],"explicit":[102],"construction":[103],"covariance":[106,182],"matrix":[107],"is":[108],"prohibitive":[109],"due":[110],"need":[113],"solve":[115],"as":[119,122],"many":[120],"times":[121],"there":[123],"are":[124],"parameters.":[125,225],"Our":[126],"builds":[129],"on":[130,206],"formulation":[133],"proposed":[134],"by":[135],"Stuart":[136],"[Acta":[137],"Numer.,":[138],"19":[139],"(2010),":[140],"pp.":[141],"451--559]":[142],"incorporates":[144,164],"number":[146],"components":[148],"aimed":[149],"at":[150],"ensuring":[151],"discretization":[154],"underlying":[157],"additionally":[163],"algorithms":[165],"manipulating":[167],"prior,":[169],"constructing":[170],"low":[172],"rank":[173],"approximation":[174],"data-informed":[177],"component":[178],"operator,":[183],"exploring":[185],"that":[188],"together":[189],"ensure":[190],"scalability":[191],"entire":[194],"very":[197],"high":[198],"dimensions.":[200],"demonstrate":[202],"this":[203],"an":[211],"three-dimensional":[215],"global":[216],"seismic":[217],"wave":[218],"propagation":[219],"with":[220],"hundreds":[221],"thousands":[223]},"counts_by_year":[{"year":2026,"cited_by_count":19},{"year":2025,"cited_by_count":29},{"year":2024,"cited_by_count":36},{"year":2023,"cited_by_count":48},{"year":2022,"cited_by_count":26},{"year":2021,"cited_by_count":49},{"year":2020,"cited_by_count":39},{"year":2019,"cited_by_count":26},{"year":2018,"cited_by_count":32},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":19},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}