{"id":"https://openalex.org/W2995486284","doi":"https://doi.org/10.1111/1365-2478.12926","title":"Research Note: A unifying framework for the widely used stabilization of potential field inverse problems","display_name":"Research Note: A unifying framework for the widely used stabilization of potential field inverse problems","publication_year":2019,"publication_date":"2019-12-19","ids":{"openalex":"https://openalex.org/W2995486284","doi":"https://doi.org/10.1111/1365-2478.12926","mag":"2995486284"},"language":"en","primary_location":{"id":"doi:10.1111/1365-2478.12926","doi":"https://doi.org/10.1111/1365-2478.12926","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1365-2478.12926","pdf_url":null,"source":{"id":"https://openalex.org/S45030768","display_name":"Geophysical Prospecting","issn_l":"0016-8025","issn":["0016-8025","1365-2478"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geophysical Prospecting","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5081588924","display_name":"Saeed Vatankhah","orcid":"https://orcid.org/0000-0001-7403-6848","observed_orcids":["https://orcid.org/0000-0001-7403-6848"]},"institutions":[{"id":"https://openalex.org/I23946033","display_name":"University of Tehran","ror":"https://ror.org/05vf56z40","country_code":"IR","type":"education","lineage":["https://openalex.org/I23946033"]},{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN","IR"],"is_corresponding":false,"raw_author_name":"Saeed Vatankhah","raw_affiliation_strings":["Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China","Institute of Geophysics, University of Tehran, Iran"],"raw_orcid":"https://orcid.org/0000-0001-7403-6848","affiliations":[{"raw_affiliation_string":"Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]},{"raw_affiliation_string":"Institute of Geophysics, University of Tehran, Iran","institution_ids":["https://openalex.org/I23946033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033871686","display_name":"Rosemary Anne Renaut","orcid":"https://orcid.org/0000-0001-9296-0890","observed_orcids":["https://orcid.org/0000-0001-9296-0890"]},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rosemary Anne Renaut","raw_affiliation_strings":["School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100319074","display_name":"Shuang Liu","orcid":"https://orcid.org/0000-0001-9184-0782","observed_orcids":["https://orcid.org/0000-0001-9184-0782"]},"institutions":[{"id":"https://openalex.org/I3124059619","display_name":"China University of Geosciences","ror":"https://ror.org/04gcegc37","country_code":"CN","type":"education","lineage":["https://openalex.org/I3124059619"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Shuang Liu","raw_affiliation_strings":["Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, China","institution_ids":["https://openalex.org/I3124059619"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100319074"],"corresponding_institution_ids":["https://openalex.org/I3124059619"],"apc_list":{"value":2500,"currency":"USD","value_usd":2500},"apc_paid":null,"fwci":1.8666,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.82853165,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"68","issue":"4","first_page":"1416","last_page":"1421"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10572","display_name":"Geophysical and Geoelectrical Methods","score":0.9185000061988831,"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"}},"topics":[{"id":"https://openalex.org/T10572","display_name":"Geophysical and Geoelectrical Methods","score":0.9185000061988831,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.06499999761581421,"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/T10271","display_name":"Seismic Imaging and Inversion Techniques","score":0.005900000222027302,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/potential-field-inversion","display_name":"potential field inversion","score":0.9909999966621399},{"id":"https://openalex.org/keywords/regularization","display_name":"regularization","score":0.3790000081062317},{"id":"https://openalex.org/keywords/stabilizers","display_name":"stabilizers","score":0.9039999842643738},{"id":"https://openalex.org/keywords/l2-norm","display_name":"L2 norm","score":0.7459999918937683},{"id":"https://openalex.org/keywords/l1-norm","display_name":"L1 norm","score":0.9950000047683716},{"id":"https://openalex.org/keywords/l0-norm","display_name":"L0 norm","score":0.9919999837875366},{"id":"https://openalex.org/keywords/gradient-regularization","display_name":"gradient regularization","score":0.6930000185966492},{"id":"https://openalex.org/keywords/weight-functions","display_name":"weight functions","score":0.9440000057220459},{"id":"https://openalex.org/keywords/unified-framework","display_name":"unified framework","score":0.7689999938011169},{"id":"https://openalex.org/keywords/parameter-constraints","display_name":"parameter constraints","score":0.39800000190734863}],"concepts":[{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.7797540426254272},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.6725881695747375},{"id":"https://openalex.org/C2986897749","wikidata":"https://www.wikidata.org/wiki/Q231761","display_name":"Potential field","level":2,"score":0.6423007845878601},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5189842581748962},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4796450734138489},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.45827388763427734},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.44604507088661194},{"id":"https://openalex.org/C8058405","wikidata":"https://www.wikidata.org/wiki/Q46255","display_name":"Geophysics","level":1,"score":0.41117414832115173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37212902307510376},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32598933577537537},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1862621009349823},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14059174060821533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09269917011260986},{"id":"https://openalex.org/C114793014","wikidata":"https://www.wikidata.org/wiki/Q52109","display_name":"Geomorphology","level":1,"score":0.0867338478565216},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08202815055847168},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.05677071213722229},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1111/1365-2478.12926","doi":"https://doi.org/10.1111/1365-2478.12926","is_oa":false,"landing_page_url":"https://doi.org/10.1111/1365-2478.12926","pdf_url":null,"source":{"id":"https://openalex.org/S45030768","display_name":"Geophysical Prospecting","issn_l":"0016-8025","issn":["0016-8025","1365-2478"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Geophysical Prospecting","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1275636587","display_name":"Approximate Singular Value Expansions and Solutions of Ill-Posed Problems","funder_award_id":"1913136","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G431526375","display_name":null,"funder_award_id":"2016YFC0600109","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G5549641870","display_name":null,"funder_award_id":"41604087","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"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W145616578","https://openalex.org/W297101097","https://openalex.org/W1541876502","https://openalex.org/W1753053004","https://openalex.org/W1971563238","https://openalex.org/W1987875940","https://openalex.org/W1990381576","https://openalex.org/W1998762105","https://openalex.org/W2004544971","https://openalex.org/W2005013369","https://openalex.org/W2009803990","https://openalex.org/W2015670693","https://openalex.org/W2020219450","https://openalex.org/W2031604650","https://openalex.org/W2033242948","https://openalex.org/W2039157502","https://openalex.org/W2081728927","https://openalex.org/W2090890761","https://openalex.org/W2090988599","https://openalex.org/W2094518147","https://openalex.org/W2099679822","https://openalex.org/W2108064160","https://openalex.org/W2114424556","https://openalex.org/W2114569263","https://openalex.org/W2125294793","https://openalex.org/W2138163538","https://openalex.org/W2144049859","https://openalex.org/W2149082020","https://openalex.org/W2150904297","https://openalex.org/W2164289056","https://openalex.org/W2167794065","https://openalex.org/W2173567480","https://openalex.org/W2286852743","https://openalex.org/W2325461467","https://openalex.org/W2332990274","https://openalex.org/W2680951477","https://openalex.org/W2758766017","https://openalex.org/W2790359862","https://openalex.org/W2925265835","https://openalex.org/W4244894666"],"related_works":["https://openalex.org/W4386783841","https://openalex.org/W2136701804","https://openalex.org/W4309892170","https://openalex.org/W2547733082","https://openalex.org/W1655376508","https://openalex.org/W2968463234","https://openalex.org/W2923303166","https://openalex.org/W3012687401","https://openalex.org/W3112917159","https://openalex.org/W2923677349"],"abstract_inverted_index":{"ABSTRACT":[0],"We":[1],"present":[2],"a":[3,48],"brief":[4],"review":[5],"of":[6,16,30,37,69],"the":[7,14,31,35,38,67],"widely":[8],"used":[9],"and":[10,27,34],"well\u2010known":[11],"stabilizers":[12,22,42],"in":[13,47],"inversion":[15],"potential":[17,77],"field":[18,78],"data.":[19],"These":[20,41],"include":[21],"that":[23,62],"use":[24,68],"L2,":[25],"L1":[26],"L0":[28],"norms":[29],"model":[32,39],"parameters":[33],"gradients":[36],"parameters.":[40],"may":[43],"all":[44],"be":[45],"realized":[46],"common":[49,75],"setting":[50],"using":[51],"two":[52],"general":[53],"forms":[54],"with":[55],"different":[56],"weighting":[57],"functions.":[58],"Moreover,":[59],"we":[60],"show":[61],"this":[63],"unifying":[64],"framework":[65],"encompasses":[66],"additional":[70],"stabilizations":[71],"which":[72],"are":[73],"not":[74],"for":[76],"inversion.":[79]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-12-26T00:00:00"}
