Publication Information

{'id': 'https://openalex.org/W1940015878', 'doi': 'https://doi.org/10.1111/j.1365-246x.2012.05590.x', 'title': 'Orthogonality of harmonic potentials and fields in spheroidal and ellipsoidal coordinates: application to geomagnetism and geodesy', 'display_name': 'Orthogonality of harmonic potentials and fields in spheroidal and ellipsoidal coordinates: application to geomagnetism and geodesy', 'publication_year': 2012, 'publication_date': '2012-08-30', 'ids': {'openalex': 'https://openalex.org/W1940015878', 'doi': 'https://doi.org/10.1111/j.1365-246x.2012.05590.x', 'mag': '1940015878'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1111/j.1365-246x.2012.05590.x', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S108821158', 'display_name': 'Geophysical Journal International', 'issn_l': '0956-540X', 'issn': ['0956-540X', '1365-246X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311648', 'host_organization_name': 'Oxford University Press', 'host_organization_lineage': ['https://openalex.org/P4310311647', 'https://openalex.org/P4310311648'], 'host_organization_lineage_names': ['University of Oxford', 'Oxford University Press'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': False, 'oa_status': 'closed', 'oa_url': None, 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5055175879', 'display_name': 'F. J. Lowes', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I84884186', 'display_name': 'Newcastle University', 'ror': 'https://ror.org/01kj2bm70', 'country_code': 'GB', 'type': 'education', 'lineage': ['https://openalex.org/I84884186']}], 'countries': ['GB'], 'is_corresponding': False, 'raw_author_name': 'F. J. Lowes', 'raw_affiliation_strings': ['1School of Chemistry, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK. E-mail: [email protected]'], 'affiliations': [{'raw_affiliation_string': '1School of Chemistry, Newcastle University, Newcastle Upon Tyne, NE1 7RU, UK. E-mail: [email protected]', 'institution_ids': ['https://openalex.org/I84884186']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5041486531', 'display_name': 'D. E. Winch', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I129604602', 'display_name': 'University of Sydney', 'ror': 'https://ror.org/0384j8v12', 'country_code': 'AU', 'type': 'education', 'lineage': ['https://openalex.org/I129604602']}], 'countries': ['AU'], 'is_corresponding': False, 'raw_author_name': 'D. E. Winch', 'raw_affiliation_strings': ['School of Mathematics and Statistics, University of Sydney F07, Sydney, NSW 2006, Australia.'], 'affiliations': [{'raw_affiliation_string': 'School of Mathematics and Statistics, University of Sydney F07, Sydney, NSW 2006, Australia.', 'institution_ids': ['https://openalex.org/I129604602']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2590, 'currency': 'GBP', 'value_usd': 3176, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.765, 'has_fulltext': False, 'cited_by_count': 20, 'citation_normalized_percentile': {'value': 0.773992, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 89, 'max': 90}, 'biblio': {'volume': '191', 'issue': '2', 'first_page': '491', 'last_page': '507'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11786', 'display_name': 'Geomagnetism and Paleomagnetism Studies', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/1312', 'display_name': 'Molecular Biology'}, 'field': {'id': 'https://openalex.org/fields/13', 'display_name': 'Biochemistry, Genetics and Molecular Biology'}, 'domain': {'id': 'https://openalex.org/domains/1', 'display_name': 'Life Sciences'}}, 'topics': [{'id': 'https://openalex.org/T11786', 'display_name': 'Geomagnetism and Paleomagnetism Studies', 'score': 0.9994, 'subfield': {'id': 'https://openalex.org/subfields/1312', 'display_name': 'Molecular Biology'}, 'field': {'id': 'https://openalex.org/fields/13', 'display_name': 'Biochemistry, Genetics and Molecular Biology'}, 'domain': {'id': 'https://openalex.org/domains/1', 'display_name': 'Life Sciences'}}, {'id': 'https://openalex.org/T11405', 'display_name': 'Geophysics and Gravity Measurements', 'score': 0.9994, '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/T10572', 'display_name': 'Geophysical and Geoelectrical Methods', 'score': 0.9992, '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/satellite-geodesy', 'display_name': 'Satellite geodesy', 'score': 0.6172031}, {'id': 'https://openalex.org/keywords/prolate-spheroidal-coordinates', 'display_name': 'Prolate spheroidal coordinates', 'score': 0.5828521}, {'id': 'https://openalex.org/keywords/orthogonality', 'display_name': 'Orthogonality', 'score': 0.5762861}, {'id': 'https://openalex.org/keywords/ellipsoid', 'display_name': 'Ellipsoid', 'score': 0.44939217}, {'id': 'https://openalex.org/keywords/harmonic', 'display_name': 'Harmonic', 'score': 0.4367201}], 'concepts': [{'id': 'https://openalex.org/C13280743', 'wikidata': 'https://www.wikidata.org/wiki/Q131089', 'display_name': 'Geodesy', 'level': 1, 'score': 0.7697864}, {'id': 'https://openalex.org/C154839486', 'wikidata': 'https://www.wikidata.org/wiki/Q1928951', 'display_name': 'Satellite geodesy', 'level': 3, 'score': 0.6172031}, {'id': 'https://openalex.org/C129094480', 'wikidata': 'https://www.wikidata.org/wiki/Q7249552', 'display_name': 'Prolate spheroidal coordinates', 'level': 3, 'score': 0.5828521}, {'id': 'https://openalex.org/C17137986', 'wikidata': 'https://www.wikidata.org/wiki/Q215067', 'display_name': 'Orthogonality', 'level': 2, 'score': 0.5762861}, {'id': 'https://openalex.org/C127313418', 'wikidata': 'https://www.wikidata.org/wiki/Q1069', 'display_name': 'Geology', 'level': 0, 'score': 0.5336695}, {'id': 'https://openalex.org/C122224866', 'wikidata': 'https://www.wikidata.org/wiki/Q437882', 'display_name': 'Figure of the Earth', 'level': 2, 'score': 0.5274955}, {'id': 'https://openalex.org/C8058405', 'wikidata': 'https://www.wikidata.org/wiki/Q46255', 'display_name': 'Geophysics', 'level': 1, 'score': 0.49355257}, {'id': 'https://openalex.org/C57489055', 'wikidata': 'https://www.wikidata.org/wiki/Q190046', 'display_name': 'Ellipsoid', 'level': 2, 'score': 0.44939217}, {'id': 'https://openalex.org/C127934551', 'wikidata': 'https://www.wikidata.org/wiki/Q1148098', 'display_name': 'Harmonic', 'level': 2, 'score': 0.4367201}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.33043915}, {'id': 'https://openalex.org/C27451561', 'wikidata': 'https://www.wikidata.org/wiki/Q2588831', 'display_name': 'Orthogonal coordinates', 'level': 2, 'score': 0.30260116}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.28060946}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.22560501}, {'id': 'https://openalex.org/C58754882', 'wikidata': 'https://www.wikidata.org/wiki/Q1502887', 'display_name': 'Geodetic datum', 'level': 2, 'score': 0.15948892}, {'id': 'https://openalex.org/C24890656', 'wikidata': 'https://www.wikidata.org/wiki/Q82811', 'display_name': 'Acoustics', 'level': 1, 'score': 0.07789475}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1111/j.1365-246x.2012.05590.x', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S108821158', 'display_name': 'Geophysical Journal International', 'issn_l': '0956-540X', 'issn': ['0956-540X', '1365-246X'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310311648', 'host_organization_name': 'Oxford University Press', 'host_organization_lineage': ['https://openalex.org/P4310311647', 'https://openalex.org/P4310311648'], 'host_organization_lineage_names': ['University of Oxford', 'Oxford University Press'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}], 'best_oa_location': None, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 37, 'referenced_works': ['https://openalex.org/W1535035979', 'https://openalex.org/W1540317310', 'https://openalex.org/W1550128655', 'https://openalex.org/W1591932919', 'https://openalex.org/W1594874399', 'https://openalex.org/W169818938', 'https://openalex.org/W1965491113', 'https://openalex.org/W1970258005', 'https://openalex.org/W1970761541', 'https://openalex.org/W1980905373', 'https://openalex.org/W1982742974', 'https://openalex.org/W2009200323', 'https://openalex.org/W2018240881', 'https://openalex.org/W2021591635', 'https://openalex.org/W2023762643', 'https://openalex.org/W2027596592', 'https://openalex.org/W2044561234', 'https://openalex.org/W2044965325', 'https://openalex.org/W2057890600', 'https://openalex.org/W2058890877', 'https://openalex.org/W2059449392', 'https://openalex.org/W2060733274', 'https://openalex.org/W2060861684', 'https://openalex.org/W2088455220', 'https://openalex.org/W2121277987', 'https://openalex.org/W2126655359', 'https://openalex.org/W2133984646', 'https://openalex.org/W2152341430', 'https://openalex.org/W3000796701', 'https://openalex.org/W3022344118', 'https://openalex.org/W3023675899', 'https://openalex.org/W3038515387', 'https://openalex.org/W4246936399', 'https://openalex.org/W4285719527', 'https://openalex.org/W4403524715', 'https://openalex.org/W4403524722', 'https://openalex.org/W601144847'], 'related_works': ['https://openalex.org/W4232937008', 'https://openalex.org/W3011957717', 'https://openalex.org/W2942117009', 'https://openalex.org/W2604442233', 'https://openalex.org/W2314501390', 'https://openalex.org/W2082895625', 'https://openalex.org/W2072827492', 'https://openalex.org/W2055616319', 'https://openalex.org/W1940015878', 'https://openalex.org/W1548106770'], 'abstract_inverted_index': {'SUMMARY': [0], 'We': [1, 186, 210], 'investigate': [2], 'the': [3, 6, 11, 27, 30, 37, 40, 46, 49, 66, 75, 84, 93, 97, 109, 140, 153, 178, 182, 190, 197, 205, 222, 225, 233, 260, 264], 'orthogonality': [4, 28, 63, 102, 151], 'of': [5, 14, 29, 39, 48, 86, 96, 150, 189, 196, 204, 224, 235], 'potential': [7], 'distributions': [8], 'that': [9, 125, 156, 230, 245, 248], 'are': [10, 112, 232], 'basis': [12, 227, 265], 'solutions': [13], 'Laplace’s': [15, 251], 'equation': [16], 'appropriate': [17], 'to': [18, 74, 82, 139, 145, 177, 220], '3-D': [19], 'ellipsoidal': [20, 146, 184], '(including': [21], 'spheroidal)': [22], 'coordinate': [23, 241], 'systems,': [24], 'and': [25, 42, 167, 216, 242, 247], 'also': [26], 'corresponding': [31, 141], 'vector': [32, 67, 142, 214], 'gradient': [33], 'fields,': [34], 'both': [35], 'over': [36, 45, 152, 181], 'surface': [38, 154], 'ellipsoid,': [41], 'for': [43, 59, 65, 133, 200, 239], 'integration': [44], 'volume': [47], 'annular': [50], 'shell': [51], 'between': [52], 'two': [53], 'confocal': [54], 'ellipsoids.': [55], 'The': [56, 148], 'only': [57, 132, 212, 229, 244], 'situation': [58], 'which': [60], 'there': [61, 99], 'is': [62, 64, 78, 100, 120], 'gradients': [68], 'when': [69, 161], 'integratedovertheannularshell.Intheotherthreecases(potentialoversurfaceorannulus,and': [70], 'fieldoversurface)orthogonalitycanberestoredbyusinganappropriategeometricalweighting': [71], 'factor': [72], 'applied': [73], 'integrand;': [76], 'it': [77, 135], 'therefore': [79], 'still': [80], 'possible': [81], 'perform': [83], 'equivalent': [85], 'a': [87, 123, 128, 201], 'classical': [88], 'spherical': [89], 'harmonic': [90, 118], 'analysis.': [91], 'In': [92, 115], 'special': [94], 'case': [95], 'sphere,': [98], 'real': [101], 'in': [103, 107, 263], 'all': [104, 113], 'four': [105], 'cases;': [106], 'effect': [108], 'weighting': [110], 'factors': [111], 'unity.': [114], 'geodesy,': [116], 'spheroidal': [117, 202], 'analysis': [119, 203], 'done': [121], 'using': [122], 'method': [124], 'relies': [126], 'on': [127, 259], 'particular': [129], 'result': [130], 'valid': [131], 'potential;': [134], 'cannot': [136], 'be': [137, 159], 'extended': [138], 'field,': [143], 'or': [144], 'geometry.': [147], 'lack': [149], 'means': [155], 'care': [157], 'must': [158], 'taken': [160], 'interpreting': [162], 'conventional': [163], 'geomagnetic': [164], '‘power': [165], 'spectra’,': [166], 'geodetic': [168], '‘degree': [169], 'variance’,': [170], 'as': [171], 'these': [172], 'no': [173], 'longer': [174], 'correspond': [175], 'exactly': [176], 'mean-square': [179], 'values': [180], 'actual': [183, 226], 'surface.': [185], 'illustrate': [187], 'some': [188], 'problems': [191], 'by': [192], 'comparing': [193], 'different': [194], 'versions': [195], 'power': [198], 'spectrum': [199], 'global': [206], 'lithospheric': [207], 'magnetic': [208], 'field.': [209], 'use': [211], 'simple': [213], 'algebra,': [215], 'do': [217, 256], 'not': [218, 257], 'need': [219], 'know': [221], 'details': [223], 'solutions,': [228], 'they': [231, 249], 'product': [234], 'three': [236], 'functions,': [237], 'one': [238], 'each': [240], 'involving': [243], 'coordinate,': [246], 'satisfy': [250], 'equation.': [252], 'Similarly,': [253], 'our': [254], 'results': [255], 'depend': [258], 'normalization': [261], 'used': [262], 'functions.': [266]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1940015878', 'counts_by_year': [{'year': 2024, 'cited_by_count': 4}, {'year': 2023, 'cited_by_count': 1}, {'year': 2022, 'cited_by_count': 1}, {'year': 2019, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 4}, {'year': 2016, 'cited_by_count': 1}, {'year': 2015, 'cited_by_count': 4}, {'year': 2014, 'cited_by_count': 1}, {'year': 2013, 'cited_by_count': 1}], 'updated_date': '2025-01-07T10:18:49.890524', 'created_date': '2016-06-24'}