{"id":"https://openalex.org/W4294770464","doi":"https://doi.org/10.1137/21m1430200","title":"Inverse Elastic Scattering for a Random Potential","display_name":"Inverse Elastic Scattering for a Random Potential","publication_year":2022,"publication_date":"2022-09-06","ids":{"openalex":"https://openalex.org/W4294770464","doi":"https://doi.org/10.1137/21m1430200"},"language":"en","primary_location":{"id":"doi:10.1137/21m1430200","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1430200","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5101579121","display_name":"Jianliang Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jianliang Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100742532","display_name":"Peijun Li","orcid":"https://orcid.org/0000-0001-5119-6435"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peijun Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100407783","display_name":"Xu Wang","orcid":"https://orcid.org/0000-0001-5114-4897"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu Wang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101579121"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0489,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.70818231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"54","issue":"5","first_page":"5126","last_page":"5159"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10662","display_name":"Ultrasonics and Acoustic Wave Propagation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11609","display_name":"Geophysical Methods and Applications","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7609845399856567},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6752787828445435},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.6069146394729614},{"id":"https://openalex.org/keywords/covariance-operator","display_name":"Covariance operator","score":0.5844038724899292},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5010466575622559},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4797326624393463},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.46264350414276123},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.44037312269210815},{"id":"https://openalex.org/keywords/gaussian-random-field","display_name":"Gaussian random field","score":0.43108826875686646},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.41957223415374756},{"id":"https://openalex.org/keywords/covariance-function","display_name":"Covariance function","score":0.4174797534942627},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3841398060321808},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.2311137616634369},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18112847208976746},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17255699634552002},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.10053446888923645}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7609845399856567},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6752787828445435},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.6069146394729614},{"id":"https://openalex.org/C103692563","wikidata":"https://www.wikidata.org/wiki/Q5178900","display_name":"Covariance operator","level":3,"score":0.5844038724899292},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5010466575622559},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4797326624393463},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.46264350414276123},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.44037312269210815},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.43108826875686646},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.41957223415374756},{"id":"https://openalex.org/C137250428","wikidata":"https://www.wikidata.org/wiki/Q5178897","display_name":"Covariance function","level":3,"score":0.4174797534942627},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3841398060321808},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2311137616634369},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18112847208976746},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17255699634552002},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.10053446888923645},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1430200","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1430200","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G309346365","display_name":null,"funder_award_id":"DMS-1912704","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5133581144","display_name":null,"funder_award_id":"12171057","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6455514343","display_name":null,"funder_award_id":"11871068","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6541878348","display_name":null,"funder_award_id":"11971470","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W603520154","https://openalex.org/W1532154335","https://openalex.org/W1569973690","https://openalex.org/W1602383637","https://openalex.org/W1802288072","https://openalex.org/W1974915238","https://openalex.org/W2017616467","https://openalex.org/W2048686704","https://openalex.org/W2067107552","https://openalex.org/W2067152211","https://openalex.org/W2076704034","https://openalex.org/W2117386296","https://openalex.org/W2133303397","https://openalex.org/W2136080835","https://openalex.org/W2476679168","https://openalex.org/W2477184272","https://openalex.org/W2542361426","https://openalex.org/W2768063502","https://openalex.org/W2798687076","https://openalex.org/W2883796673","https://openalex.org/W2885296385","https://openalex.org/W2948586430","https://openalex.org/W2962684351","https://openalex.org/W2962817357","https://openalex.org/W2984306690","https://openalex.org/W3033684160","https://openalex.org/W3137958891","https://openalex.org/W3140307638","https://openalex.org/W4298366280","https://openalex.org/W4380046008"],"related_works":["https://openalex.org/W3002473118","https://openalex.org/W2090206927","https://openalex.org/W1968962302","https://openalex.org/W1541863749","https://openalex.org/W782485990","https://openalex.org/W4299899709","https://openalex.org/W4321602985","https://openalex.org/W3176787524","https://openalex.org/W3103935687","https://openalex.org/W77814067"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,25,49,95,110],"concerned":[3],"with":[4,15,36,112],"an":[5,99],"inverse":[6,106],"scattering":[7,89,107],"problem":[8,90],"for":[9,161,169],"the":[10,23,37,52,56,60,74,77,84,87,92,105,116,120,128,131,136,144,150,158,162,170],"time-harmonic":[11],"elastic":[12,163],"wave":[13,62,164],"equation":[14],"a":[16,21,29,43,65,70,81,140],"random":[17,34,145],"potential.":[18,78,146],"Interpreted":[19],"as":[20],"distribution,":[22],"potential":[24],"assumed":[26],"to":[27,50],"be":[28,124],"microlocally":[30],"isotropic":[31],"generalized":[32],"Gaussian":[33],"field":[35],"covariance":[38,57,121],"operator":[39,58,122],"being":[40],"described":[41],"by":[42,97,127],"classical":[44],"pseudodifferential":[45],"operator.":[46],"The":[47,147],"goal":[48],"determine":[51],"principal":[53,117],"symbol":[54,118],"of":[55,76,86,119,130,143,157],"from":[59,73,139],"scattered":[61,132],"measured":[63],"in":[64,91,153],"bounded":[66],"domain":[67,75],"which":[68],"has":[69],"positive":[71],"distance":[72],"For":[79,104],"such":[80],"rough":[82],"potential,":[83],"well-posedness":[85],"direct":[88],"distribution":[93],"sense":[94],"established":[96],"studying":[98],"equivalent":[100],"Lippmann--Schwinger":[101],"integral":[102,172],"equation.":[103],"problem,":[108],"it":[109],"shown":[111],"probability":[113],"one":[114],"that":[115],"can":[123],"uniquely":[125],"determined":[126],"amplitude":[129],"waves":[133],"averaged":[134],"over":[135],"frequency":[137],"band":[138],"single":[141],"realization":[142],"analysis":[148,168],"employs":[149],"Born":[151],"approximation":[152],"high":[154],"frequency,":[155],"asymptotics":[156],"Green":[159],"tensor":[160],"equation,":[165],"and":[166],"microlocal":[167],"Fourier":[171],"operators.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
