{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T14:38:32Z","timestamp":1775659112585,"version":"3.50.1"},"reference-count":72,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T00:00:00Z","timestamp":1539302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N000140410417"],"award-info":[{"award-number":["N000140410417"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>It has been shown that hurricanes generate seismic noise, called microseisms, through the creation and non-linear interaction of ocean surface waves. Here we model microseisms generated by the spatially inhomogeneous waves of a hurricane using the non-linear wave equation where a second-order acoustic field is created by first-order ocean surface wave motion. We treat range-dependent waveguide environments to account for microseisms that propagate from the deep ocean to a receiver on land. We compare estimates based on the ocean surface wave field measured in hurricane Bonnie in 1998 with seismic measurements made roughly 1000 km away in Florida.<\/jats:p>","DOI":"10.3390\/rs10101624","type":"journal-article","created":{"date-parts":[[2018,10,12]],"date-time":"2018-10-12T10:54:03Z","timestamp":1539341643000},"page":"1624","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Modeling Microseism Generation by Inhomogeneous Ocean Surface Waves in Hurricane Bonnie Using the Non-Linear Wave Equation"],"prefix":"10.3390","volume":"10","author":[{"given":"Joshua D.","family":"Wilson","sequence":"first","affiliation":[{"name":"General Dynamics\u2014Applied Physical Sciences, Groton, CT 06340, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1007\/s11001-010-9105-x","article-title":"Seismic Monitoring of Western Pacific Typhoons","volume":"31","author":"Chi","year":"2010","journal-title":"Mar. Geophys. Res."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"8825","DOI":"10.1002\/2014GL062319","article-title":"Tracking Major Storms from Microseismic and Hydroacoustic Observations on the Seafloor","volume":"10","author":"Davy","year":"2014","journal-title":"Geophys. Res. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"L23306","DOI":"10.1029\/2008GL036111","article-title":"Global P, PP and PKP Wave Microseisms Observed from Distant Storms","volume":"35","author":"Gerstoft","year":"2008","journal-title":"Geophys. Res. Lett."},{"key":"ref_4","first-page":"89","article-title":"Microseisms and ocean storms","volume":"36","author":"Gilmore","year":"1946","journal-title":"Seismol. Soc. Bull."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Lin, J., Wang, Y., Wang, W., Li, X., Fang, S., Chen, C., and Zheng, H. (2018). Seismic Remote Sensing of Super Typhoon Lupit (2009) with Seismological Array Observations in NE China. Remote Sens., 10.","DOI":"10.3390\/rs10020235"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"9518","DOI":"10.1002\/2017JC013310","article-title":"Microseisms Generated by Super Typhoon Megi in the Western Pacific Ocean","volume":"10","author":"Lin","year":"2017","journal-title":"J. Geophys. Res. Oceans"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1785\/BSSA0300010035","article-title":"An experimental investigation of the nature and origin of microseisms at St. Louis, Missouri","volume":"30","author":"Ramirez","year":"1940","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"L15301","DOI":"10.1029\/2010GL044288","article-title":"Pelagic and Coastal Sources of P-Wave Microseisms","volume":"37","author":"Zhang","year":"2010","journal-title":"Geophys. Res. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1111\/j.1365-246X.1932.tb00402.x","article-title":"The effect of geologic structure upon microseismic disturbance","volume":"3","author":"Lee","year":"1932","journal-title":"R. Astron. Soc. Mon. Not. Geophys. Suppl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1029\/TR029i002p00163","article-title":"A Theory of Microseisms with Geologic Applications","volume":"29","author":"Press","year":"1948","journal-title":"Trans. Am. Geophys. Union"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1029\/97RG02287","article-title":"Broadband seismology and noise under the ocean","volume":"36","author":"Webb","year":"1998","journal-title":"Rev. Geophys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1680","DOI":"10.1175\/2410.1","article-title":"Numerical simulation of sea surface directional wave spectra under hurricane wind forcing","volume":"33","author":"Moon","year":"2003","journal-title":"J. Phys. Oceanogr."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2472","DOI":"10.1175\/1520-0485(2001)031<2472:HDWSSV>2.0.CO;2","article-title":"Hurricane directional wave spectrum spatial variation in the open ocean","volume":"31","author":"Wright","year":"2001","journal-title":"J. Phys. Oceanogr."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1098\/rsta.1950.0012","article-title":"A theory of the origin of microseisms","volume":"243","year":"1950","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"ref_15","first-page":"582","article-title":"Underwater sound waves generated by surface waves in the ocean","volume":"2","author":"Brekhovskikh","year":"1966","journal-title":"Izv. Atmos. Ocean. Phys."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3161","DOI":"10.1121\/1.4818782","article-title":"Wave-Wave Interactions and Deep Ocean Acoustics","volume":"134","author":"Guralnik","year":"2013","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1029\/RG001i002p00177","article-title":"A statistical analysis of the generation of microseisms","volume":"1","author":"Hasselmann","year":"1963","journal-title":"Rev. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1121\/1.381203","article-title":"Estimates of underwater sound (and infrasound) produced by nonlinearly interacting ocean waves","volume":"60","author":"Hughes","year":"1976","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1935","DOI":"10.1121\/1.397847","article-title":"The generation of infrasonic ambient noise in the ocean by nonlinear interactions of ocean surface waves","volume":"85","author":"Kibblewhite","year":"1989","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1121\/1.385458","article-title":"Underwater sound from surface waves according to the Lighthill-Ribner theory","volume":"69","author":"Lloyd","year":"1981","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2241","DOI":"10.1121\/1.400970","article-title":"The theoretical description of wave-wave interactions as a noise source in the ocean","volume":"89","author":"Kibblewhite","year":"1991","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"3358","DOI":"10.1121\/1.407215","article-title":"Acoustic source levels associated with the nonlinear interactions of ocean waves","volume":"94","author":"Kibblewhite","year":"1993","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.1121\/1.400527","article-title":"Sound generation in the vicinity of the sea surface: Source mechanisms and the coupling to the received sound field","volume":"89","author":"Cato","year":"1991","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1096","DOI":"10.1121\/1.400528","article-title":"Theoretical and measured underwater noise from surface wave orbital motion","volume":"89","author":"Cato","year":"1991","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1121\/1.1918525","article-title":"Parametric Acoustic Array","volume":"35","author":"Westervelt","year":"1963","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1098\/rsta.1930.0008","article-title":"Microseisms associated with disturbed weather in the Indian seas","volume":"229","author":"Banerji","year":"1930","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2562","DOI":"10.1121\/1.1567277","article-title":"Microseism and infrasound generation by cyclones","volume":"113","author":"Bowen","year":"2003","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1007\/BF03035627","article-title":"Theory of microseisms","volume":"1","author":"Banerji","year":"1935","journal-title":"Proc. Indian Acad. Sci."},{"key":"ref_29","unstructured":"Hill, M.N. (1966). Microseisms, in the Sea, Ideas and Observations on Progress in the Study of the Seas, Interscience."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Wilson, J.D. (2006). Classifying Hurricanes with Undersea Sound. [Ph.D. Thesis, Massachusetts Institute of Technology].","DOI":"10.1575\/1912\/1262"},{"key":"ref_31","first-page":"131","article-title":"Mouvements ondulatoires de la mer en profonder constante ou decroissante","volume":"114","author":"Miche","year":"1944","journal-title":"Ann. Ponts Chauss\u00e9es"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1667","DOI":"10.1175\/1520-0485(2002)032<1667:HDWSSV>2.0.CO;2","article-title":"Hurricane directional wave spectrum spatial variation at landfall","volume":"32","author":"Walsh","year":"2002","journal-title":"J. Phys. Oceanogr."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/BF01453989","article-title":"Short Review and Recent Results on Microseisms","volume":"5","author":"Bernard","year":"1983","journal-title":"Geophys. Surv."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1785\/BSSA0600041139","article-title":"Ocean Microseism Measurements with a Neutral Buoyancy Free-Floating Midwater Seismometer","volume":"60","author":"Bradner","year":"1970","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1121\/1.398438","article-title":"Directional Spectra Observations of Seafloor Microseisms from an Ocean-Bottom Seismometer Array","volume":"86","author":"Goodman","year":"1989","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1785\/BSSA0210010001","article-title":"Microseisms in North America","volume":"21","author":"Gutenberg","year":"1931","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1098\/rspa.1935.0056","article-title":"On the direction of Approach of Microseismic Waves","volume":"886","author":"Lee","year":"1935","journal-title":"Proc. R. Soc. Lond. Ser. A"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1415","DOI":"10.1029\/JZ070i006p01415","article-title":"Earth noise, 5 to 500 millicycles per second 1. Spectral stationarity, normality, and nonlinearity","volume":"70","author":"Haubrich","year":"1965","journal-title":"J. Geophys. Res."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1029\/JZ070i006p01429","article-title":"Earth noise, 5 to 500 millicycles per second 2. Reaction of the earth to oceans and atmosphere","volume":"70","author":"Haubrich","year":"1965","journal-title":"J. Geophys. Res."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1029\/RG007i003p00539","article-title":"Microseisms: coastal and pelagic sources","volume":"7","author":"Haubrich","year":"1969","journal-title":"Rev. Geophys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1121\/1.392931","article-title":"Wave-wave interactions, microseisms, and infrasonic ambient noise in the ocean","volume":"78","author":"Kibblewhite","year":"1985","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"974","DOI":"10.1121\/1.385622","article-title":"Infrasonic ambient ocean noise measurements: Eleuthera","volume":"69","author":"Nichols","year":"1981","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_43","first-page":"1","article-title":"Polarized Earth\u2019s ambient microseismic noise","volume":"12","author":"Schimmel","year":"2005","journal-title":"Geochem. Geophys. Geosyst."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2141","DOI":"10.1121\/1.405226","article-title":"The equilibrium oceanic microseism spectrum","volume":"92","author":"Webb","year":"1992","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_45","unstructured":"Holland, G.J. (1993). Global Guide to Tropical Cyclone Forecasting, World Meteorological Organization."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Komen, G.J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, S., and Janssen, P.A.E.M. (1994). Dynamics and Modeling of Ocean Waves, Cambridge University Press.","DOI":"10.1017\/CBO9780511628955"},{"key":"ref_47","unstructured":"Kinsman, B. (1965). Wind Waves, Their Generation and Propagation on the Sea Surface, Prentice-Hall."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Mandel, L., and Wolf, E. (1995). Optical Coherence and Quantum Optics, Cambridge University Press.","DOI":"10.1017\/CBO9781139644105"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"888","DOI":"10.1175\/1520-0485(1978)008<0888:TDSAKO>2.0.CO;2","article-title":"The directional spectra and kinematics of surface gravity waves in tropical storm Delia","volume":"8","author":"Forristall","year":"1978","journal-title":"J. Phys. Oceanogr."},{"key":"ref_50","unstructured":"Toleman, H.L. (1999). User Manual and System Documentation of WAVEWATCH-III, Version 1.18; Techreport Note. 166."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1121\/1.1918241","article-title":"Interactions between sound waves","volume":"34","author":"Dean","year":"1962","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1121\/1.1908830","article-title":"Scattering of sound by sound","volume":"29","author":"Westervelt","year":"1957","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_53","unstructured":"Morse, P.M., and Ingard, K.U. (1968). Theoretical Acoustics, Mc-Graw-Hill."},{"key":"ref_54","unstructured":"Beyer, R.T. (1997). Nonlinear Acoustics, Acoustical Society of America, Woodbury."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2002). Optimum Array Processing. Part IV of Detection, Estimation and Modulation Theory, Wiley-Interscience.","DOI":"10.1002\/0471221104"},{"key":"ref_56","unstructured":"Papoulis, A., and Pillai, S.U. (1965). Probability, Random Variables and Stochastic Processes, McGraw-Hill."},{"key":"ref_57","unstructured":"Tucker, M.J., and Pitt, E.G. (2001). Waves in Ocean Engineering, Elsevier."},{"key":"ref_58","unstructured":"Avila, L.A. (1998). Preliminary Report, Hurricane Bonnie 19\u201330 August 1998."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"3547","DOI":"10.1121\/1.412440","article-title":"Deterministic Reverberation from Ocean Ridges","volume":"97","author":"Makris","year":"1995","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_60","unstructured":"Lay, T., and Wallace, T.C. (1995). Modern Global Seismology, Academic Press."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1111\/j.1365-246X.1926.tb05382.x","article-title":"The Effect of the Ocean on Rayleigh Waves","volume":"1","author":"Stoneley","year":"1926","journal-title":"Geophys. Suppl. Mon. Not. R. Astron. Soc."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1190\/1.1437607","article-title":"Propagation of Explosive Sound in a Liquid Layer Overlying a Semi-Infinite Elastic Solid","volume":"15","author":"Press","year":"1950","journal-title":"Geophysics"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"2087","DOI":"10.1121\/1.392667","article-title":"A Simple Shallow Water Propagation Model Including Shear Wave Effects","volume":"78","author":"Ellis","year":"1985","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Ewing, W.M., Jardetzky, W.S., and Press, F. (1957). Elastic Waves in Layered Media, McGraw-Hill.","DOI":"10.1063\/1.3060203"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"2316","DOI":"10.1121\/1.400074","article-title":"Adiabatic Normal-Mode Theory of Sound Propagating Including Shear Waves in a Range-Dependent Ocean Floor","volume":"88","author":"Arvello","year":"1990","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"1868","DOI":"10.1785\/012003088","article-title":"Results from OSNPE; improved teleseismic earthquake detection at the seafloor","volume":"94","author":"Sutherland","year":"2001","journal-title":"Bull. Seism. Soc. Am."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"1339","DOI":"10.1007\/PL00001134","article-title":"Monitoring the Comprehensive Nuclear-Test-Ban Treaty; Preface","volume":"158","author":"Mitchell","year":"2001","journal-title":"Pure Appl. Geophys."},{"key":"ref_68","first-page":"1341","article-title":"Monitoring the Comprehensive Nuclear-Test-Ban Treaty; Introduction","volume":"158","author":"Ritzwoller","year":"2001","journal-title":"Pure Appl. Geophys."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1007\/PL00001225","article-title":"A fast and reliable method for surface wave tomography","volume":"158","author":"Barmin","year":"2001","journal-title":"Pure Appl. Geophys."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1016\/j.lithos.2004.09.012","article-title":"Rayleigh wave tomography in the North Atlantic: High resolution images of the Iceland, Azores and Eifel mantle plumes","volume":"79","author":"Pilidou","year":"2005","journal-title":"Lithos"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"502","DOI":"10.1785\/0120000296","article-title":"Rayleigh wave group-velocity studies beneath the Indian Ocean","volume":"95","author":"Singh","year":"2005","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1121\/1.1909303","article-title":"Extension of the Method of Normal Modes to Sound Propagation in an Almost-Stratified Medium","volume":"37","author":"Pierce","year":"1965","journal-title":"J. Acoust. Soc. 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