{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1363670321040435840.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1098/rsta.1950.0012"}},{"identifier":{"@type":"URI","@value":"https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1950.0012"}},{"identifier":{"@type":"URI","@value":"https://royalsocietypublishing.org/rsta/article-pdf/243/857/1/265879/rsta.1950.0012.pdf"}}],"dc:title":[{"@value":"A theory of the origin of microseisms"}],"description":[{"type":"abstract","notation":[{"@value":"<jats:title>Abstract</jats:title>\n                  <jats:p>In the past it has been considered unlikely that ocean waves are capable of generating microseismic oscillations of the sea bed over areas of deep water, since the decrease of the pressure variations with depth is exponential, according to the first-order theory generally used. However, it was recently shown by Miche that in the second approximation to the standing wave there is a second-order pressure variation which is not attenuated with depth and which must therefore ultimately predominate over the first-order pressure variations. In §§ 2 and 3 of the present paper the general conditions under which second-order pressure variations of this latter type will occur are considered. It is shown that in an infinite wave train there is in general a second-order pressure variation at infinite depth which is applied equally over the whole fluid and is associated with no particle motion. In the case of two progressive waves of the same wave-length travelling in opposite directions this pressure variation is proportional to the product of the (first-order) amplitudes of the two waves and is of twice their frequency. The pressure variation at infinite depth is found to be closely related to changes in the potential energy of the wave train as a whole. By introducing the two-dimensional frequency spectrum of the motion it is shown that in the general case variations in the mean pressure over a wide area only occur when the spectrum contains wave groups of the same wave-length travelling in opposite directions. (These are called opposite wave groups.) In § 4 the effect of the compressibility of the water is considered by evaluating the motion of an opposite pair of waves in a heavy compressible fluid to the second order of approximation. In place of the pressure variation at infinite depth, waves of compression are set up, and there is resonance between the bottom and the free surface when the depth of water is about (1/2 n + 1/4) times the length of a compression wave (n being an integer). The motion in a surface layer whose thickness is of the order of the length of a Stokes wave is otherwise unaffected by the compressibility. Section 5 is devoted to the question whether the second-order pressure variations in surface waves are capable of generating microseisms of the observed order of magnitude. By considering the displacement of the sea bed due to a concentrated force at the upper surface of the water it is shown that the effect of resonance will be to increase the disturbance by a factor of the order of 5 over its value in shallow water. The results of §§ 3 and 4 are used to derive an expression for the vertical displacement of the ground in terms of the frequency characteristics of the waves. The displacement from a storm area of 1000 sq.km, is estimated to be of the order of 6.5μ at a distance of 2000 km. Ocean waves may therefore be the cause of microseisms, provided that there is interference between groups of waves of the same frequency travelling in opposite directions. Suitable conditions of wave interference may occur at the centre of a cyclonic depression or possibly if there is wave reflexion from a coast. In the latter case the microseisms are likely to be smaller, except perhaps locally. Confirmation of the present theory is provided by the observations of Bernard and Deacon, who discovered independently that the period of the microseisms is in many cases about half that of the ocean waves associated with them.</jats:p>"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1380306912562723200","@type":"Researcher","foaf:name":[{"@value":"Michael Selwyn Longuet-Higgins"}],"jpcoar:affiliationName":[{"@value":"nt of Geodesy and Geophysics, University of Cambridge"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"00804614"},{"@type":"EISSN","@value":"20540272"}],"prism:publicationName":[{"@value":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences"}],"dc:publisher":[{"@value":"The Royal Society"}],"prism:publicationDate":"1950-09-27","prism:volume":"243","prism:number":"857","prism:startingPage":"1","prism:endingPage":"35"},"reviewed":"false","dc:rights":["https://royalsociety.org/journals/ethics-policies/data-sharing-mining/"],"url":[{"@id":"https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.1950.0012"},{"@id":"https://royalsocietypublishing.org/rsta/article-pdf/243/857/1/265879/rsta.1950.0012.pdf"}],"createdAt":"2006-12-18","modifiedAt":"2025-12-31","relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1050584642173823104","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"The 20-Year Highest Tropical Cyclone-Generated Waves Associated With the Maximum Energy of Seismic Noises"},{"@value":"The 20‐Year Highest Tropical Cyclone‐Generated Waves Associated With the Maximum Energy of Seismic Noises"}]},{"@id":"https://cir.nii.ac.jp/crid/1360002218637362560","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Earth's Background Free Oscillations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360004232087659136","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Two-dimensional sensitivity kernels for cross-correlation functions of background surface waves"}]},{"@id":"https://cir.nii.ac.jp/crid/1360004232408966912","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Development and demonstration of a gravity gradiometer onboard an autonomous underwater vehicle for detecting massive subseafloor deposits"}]},{"@id":"https://cir.nii.ac.jp/crid/1360004233290430464","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Enigmatic very low frequency tremors beneath the Shonai Plain in northeastern Japan"}]},{"@id":"https://cir.nii.ac.jp/crid/1360004234590414336","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Ambient seismic noise wavefield in Japan characterized by polarization analysis of Hi-net records"}]},{"@id":"https://cir.nii.ac.jp/crid/1360013168829363328","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Temporal changes in anthropogenic seismic noise levels associated with economic and leisure activities during the COVID-19 pandemic"}]},{"@id":"https://cir.nii.ac.jp/crid/1360016866455528704","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Understanding surface wave modal content for high-resolution imaging of submarine sediments with distributed acoustic sensing"}]},{"@id":"https://cir.nii.ac.jp/crid/1360017282189496192","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Extraction of\n                    <i>P</i>\n                    Wave From Ambient Seafloor Noise Observed by Distributed Acoustic Sensing"}]},{"@id":"https://cir.nii.ac.jp/crid/1360283692533077376","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Single-station cross-correlation analysis of ambient seismic noise: application to stations in the surroundings of the 2008 Iwate-Miyagi Nairiku earthquake"}]},{"@id":"https://cir.nii.ac.jp/crid/1360285708408132096","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Ambient seafloor noise excited by earthquakes in the Nankai subduction zone"}]},{"@id":"https://cir.nii.ac.jp/crid/1360290617852724608","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Near-Field Body-Wave Extraction From Ambient Seafloor Noise in the Nankai Subduction Zone"}]},{"@id":"https://cir.nii.ac.jp/crid/1360290617861149056","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Seismic energy radiation and along-strike heterogeneities of shallow tectonic tremors at the Nankai Trough and Japan Trench"}]},{"@id":"https://cir.nii.ac.jp/crid/1360298339675763328","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"A Global Centroid Single Force Catalog of P‐Wave Microseisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360565168402920960","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Teleseismic\n            <i>S</i>\n            wave microseisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360576118782739968","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Temporal Variation and Frequency Dependence of Seismic Ambient Noise on Mars From Polarization Analysis"}]},{"@id":"https://cir.nii.ac.jp/crid/1360580229797981056","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Multimode dispersion measurement of surface waves extracted by multicomponent ambient noise cross-correlation functions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360865814741897600","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Extraction of Mantle Discontinuities From Teleseismic Body‐Wave Microseisms"}]},{"@id":"https://cir.nii.ac.jp/crid/1360865815502217088","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Ambient noise multimode surface wave tomography"}]},{"@id":"https://cir.nii.ac.jp/crid/1360869854362278272","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Coseismic crustal seismic velocity changes associated with the 2024 MW 7.5 Noto earthquake, Japan"}]},{"@id":"https://cir.nii.ac.jp/crid/1390001205308483456","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"A STUDY BY FIELD OBSERVATION ON THE SLIGHTLY-LONG-PERIOD MICROTREMORS OF GROUND"},{"@language":"ja","@value":"地盤の微動に現われるやや長周期成分についての実測による検討"}]},{"@id":"https://cir.nii.ac.jp/crid/1390001205319810432","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"海岸護岸周辺の常時微動特性と波浪諸元との関連性に関する研究"},{"@language":"en","@value":"CHARACTERISTICS OF MICROSEISMS MEASURED NEAR THE NIIGATA WEST COAST IN RELATION TO WAVE FREQUENCY SPECTRUM"},{"@language":"ja-Kana","@value":"カイガン ゴガン シュウヘン ノ ジョウジ ビドウ トクセイ ト ハロウ ショゲン ト ノ カンレンセイ ニ カンスル ケンキュウ"}]},{"@id":"https://cir.nii.ac.jp/crid/1390282679279705728","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Earth’s Background Free Oscillations"},{"@language":"ja","@value":"常時地球自由振動"},{"@language":"ja-Kana","@value":"ジョウジ チキュウ ジユウ シンドウ"},{"@value":"Earth^|^rsquo;s Background Free Oscillations"}]},{"@id":"https://cir.nii.ac.jp/crid/1390282680613516544","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"ja","@value":"堆積盆地基盤面形状推定のための長周期微動水平/上下スペクトルの逆解析 : 数値実験による検証"},{"@language":"en","@value":"INVERSION OF MICROSEISM HORIZONTAL-TO-VERTICAL SPECTRAL RATIO FOR DETERMINING THE BOUNDARY SHAPE OF A BASIN STRUCTURE : Verification by numerical experiment"},{"@language":"ja-Kana","@value":"タイセキ ボンチ キバン メン ケイジョウ スイテイ ノ タメ ノ チョウ シュウキ ビドウ スイヘイ ジョウゲ スペクトル ノ ギャクカイセキ スウチ ジッケン ニ ヨル ケンショウ"}]},{"@id":"https://cir.nii.ac.jp/crid/1390569700727823872","@type":"Article","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@language":"en","@value":"Microseisms Observed in the Eastern Part of Fukushima Prefecture, Japan during Passage of Typhoon Hagibis in 2019"},{"@language":"ja","@value":"令和元年東日本台風通過時に福島県東部で観測された脈動について"},{"@language":"ja-Kana","@value":"レイワ ガンネン ヒガシニホン タイフウ ツウカジ ニ フクシマケン トウブ デ カンソク サレタ ミャクドウ ニ ツイテ"}]},{"@id":"https://cir.nii.ac.jp/crid/2050870367120486400","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["isReferencedBy"],"jpcoar:relatedTitle":[{"@value":"Geographical distribution of shear wave anisotropy within marine sediments in the northwestern Pacific"}]}],"dataSourceIdentifier":[{"@type":"CROSSREF","@value":"10.1098/rsta.1950.0012"},{"@type":"CROSSREF","@value":"10.1029/2012jb009258_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1093/gji/ggy334_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.4294/zisin.61.115_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1038/s41598-021-00063-6_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1029/2022gl098162_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1093/gji/ggu115_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1038/ncomms7132_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1186/s40645-015-0057-2_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.2208/kaigan.72.i_121_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.3389/feart.2020.610993_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1016/j.tecto.2020.228714_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1029/2021jb023484_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1126/science.aaf7573_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.4294/zisin.2020-2_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.2208/jscej.1990.424_169_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1016/j.oceaneng.2015.06.008_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1029/2020gl087123_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1093/gji/ggac225_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1146/annurev-earth-050212-124020_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1093/gji/ggac420_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1029/2023gl105017_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1186/s40645-023-00605-8_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1186/s40623-025-02177-x_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1029/2024jc021929_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.3130/aijs.71.69_3_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"},{"@type":"CROSSREF","@value":"10.1016/j.crte.2011.02.004_references_DOI_3arTlrjuRKPT4Ly55fYibCxjdF7"}]}