{"id":"https://openalex.org/W2126684640","doi":"https://doi.org/10.1109/tit.1972.1054755","title":"A statistical theory of reverberation and similar first-order scattered fields--IV: Statistical models","display_name":"A statistical theory of reverberation and similar first-order scattered fields--IV: Statistical models","publication_year":1972,"publication_date":"1972-01-01","ids":{"openalex":"https://openalex.org/W2126684640","doi":"https://doi.org/10.1109/tit.1972.1054755","mag":"2126684640"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1972.1054755","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1972.1054755","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5109534960","display_name":"David Middleton","orcid":null},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Middleton","raw_affiliation_strings":["Department of Electrical Engineering, University of Rhode Island, Kingston, RI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Rhode Island, Kingston, RI, USA","institution_ids":["https://openalex.org/I17626003"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109534960"],"corresponding_institution_ids":["https://openalex.org/I17626003"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.25043937,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"18","issue":"1","first_page":"68","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11698","display_name":"Underwater Acoustics Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11698","display_name":"Underwater Acoustics Research","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"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/T11757","display_name":"Seismic Waves and Analysis","score":0.9929999709129333,"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/T11192","display_name":"Underwater Vehicles and Communication Systems","score":0.9886999726295471,"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/reverberation","display_name":"Reverberation","score":0.6963925957679749},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.5572025775909424},{"id":"https://openalex.org/keywords/specular-reflection","display_name":"Specular reflection","score":0.5095610618591309},{"id":"https://openalex.org/keywords/reflection","display_name":"Reflection (computer programming)","score":0.49374064803123474},{"id":"https://openalex.org/keywords/statistical-theory","display_name":"Statistical theory","score":0.48827362060546875},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4662320613861084},{"id":"https://openalex.org/keywords/scattering","display_name":"Scattering","score":0.4301048219203949},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.418011873960495},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3771655857563019},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3275456428527832},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3079615533351898},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2994289696216583},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.26280784606933594},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.2199714183807373}],"concepts":[{"id":"https://openalex.org/C95851461","wikidata":"https://www.wikidata.org/wiki/Q468809","display_name":"Reverberation","level":2,"score":0.6963925957679749},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.5572025775909424},{"id":"https://openalex.org/C118381688","wikidata":"https://www.wikidata.org/wiki/Q1079524","display_name":"Specular reflection","level":2,"score":0.5095610618591309},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.49374064803123474},{"id":"https://openalex.org/C48057537","wikidata":"https://www.wikidata.org/wiki/Q3551145","display_name":"Statistical theory","level":2,"score":0.48827362060546875},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4662320613861084},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.4301048219203949},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.418011873960495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3771655857563019},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3275456428527832},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3079615533351898},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2994289696216583},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.26280784606933594},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.2199714183807373},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1972.1054755","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1972.1054755","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","score":0.8799999952316284,"id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W209589608","https://openalex.org/W1591973018","https://openalex.org/W1972719781","https://openalex.org/W2055941340","https://openalex.org/W2126386863","https://openalex.org/W2141023504","https://openalex.org/W2147360511","https://openalex.org/W2321273107","https://openalex.org/W4231701757"],"related_works":["https://openalex.org/W2559833131","https://openalex.org/W2730225583","https://openalex.org/W2175900582","https://openalex.org/W1656519308","https://openalex.org/W4353109604","https://openalex.org/W2755051635","https://openalex.org/W2159617691","https://openalex.org/W2033029047","https://openalex.org/W2123949214","https://openalex.org/W2002881771"],"abstract_inverted_index":{"The":[0,40,134,173],"earlier":[1],"theory":[2,214],"(Parts":[3,179],"I":[4],"and":[5,26,33,49,60,62,64,79,115,128,147,158,165,171,198,201,207],"II)":[6],"is":[7,218],"extended":[8],"to":[9,162,215],"include":[10],"the":[11,18,22,28,31,55,71,76,80,90,97,113,120,186,189,211,222],"determination":[12],"of":[13,17,25,82,101,109,137,156,175,185,188,192,205,210],"various":[14,121],"important":[15],"statistics":[16],"reverberation":[19],"process":[20],"under":[21,96,153],"broadened":[23],"conditions":[24,42],"using":[27],"results":[29],"for":[30,126],"scattered":[32],"reflected":[34],"fields":[35],"developed":[36],"in":[37,142,151,195],"Part":[38],"III.":[39],"new":[41],"involve":[43],"nonzero":[44],"velocity":[45],"gradients,":[46],"absorbing":[47],"media,":[48],"multiple":[50],"reflections,":[51],"as":[52,54,106,225],"well":[53],"usual":[56],"Doppler,":[57],"general":[58,157,166],"signals":[59,140],"apertures,":[61],"mono-":[63],"bistatic":[65],"operation.":[66],"Of":[67],"principal":[68],"interest":[69],"are":[70,112,132,148],"mean":[72,77],"return":[73],"(specular":[74],"reflection),":[75],"intensity,":[78],"covariance":[81],"these":[83,127],"generally":[84],"nonstationary":[85],"processes,":[86],"following":[87],"reception":[88],"by":[89],"receiving":[91],"aperture.":[92],"These":[93],"we":[94],"determine":[95],"basic":[98],"Poisson":[99,190],"assumptions":[100],"primarily":[102],"independent":[103,193],"single":[104],"scattering,":[105],"before.":[107],"Also":[108],"major":[110],"importance":[111],"auto-":[114],"cointensity":[116],"spectra":[117],"associated":[118],"with":[119,182],"second-order":[122],"statistics.":[123],"General":[124],"relations":[125],"higher":[129],"order":[130],"moments":[131],"indicated.":[133],"quasi-stationary":[135],"cases":[136],"\"short\"":[138],"narrow-band":[139],"occur":[141],"many":[143],"practical":[144],"operational":[145],"situations":[146],"treated":[149],"here":[150],"detail,":[152],"a":[154,183,202],"variety":[155],"special":[159],"conditions,":[160],"appropriate":[161],"both":[163,196],"oceanographic":[164],"communication":[167],"applications":[168],"(e.g.,":[169],"detection":[170],"classification).":[172],"development":[174],"our":[176],"quasi-phenomenological":[177],"model":[178],"I-IV)":[180],"concludes":[181],"critique":[184],"role":[187],"assumption":[191],"scatterers":[194],"volume":[197],"surface":[199],"scatter":[200],"short":[203],"account":[204],"possible":[206],"needed":[208],"extensions":[209],"present":[212],"\"macroscopic\"":[213],"one":[216],"that":[217],"fully":[219],"physical":[220],"at":[221],"\"microscopic\"":[223],"level":[224],"well.":[226]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}