{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:13:12Z","timestamp":1760235192066,"version":"build-2065373602"},"reference-count":54,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,5]],"date-time":"2021-08-05T00:00:00Z","timestamp":1628121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["PHY1344265"],"award-info":[{"award-number":["PHY1344265"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>We develop a linear inversion technique for measuring the modal composition and directionality of ambient seismic noise. The technique draws from similar techniques used in astrophysics and gravitational-wave physics, and relies on measuring cross-correlations between different seismometer channels in a seismometer array. We characterize the sensitivity and the angular resolution of this technique using a series of simulations and real-world tests. We then apply the technique to data acquired by the three-dimensional seismometer array at the Homestake mine in Lead, SD, to estimate the composition and directionality of the seismic noise at microseism frequencies. We show that, at times of low-microseism amplitudes, noise is dominated by body waves (P and S), while at high-microseism times, the noise is dominated by surface Rayleigh waves.<\/jats:p>","DOI":"10.3390\/rs13163097","type":"journal-article","created":{"date-parts":[[2021,8,5]],"date-time":"2021-08-05T21:43:53Z","timestamp":1628199833000},"page":"3097","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Linear Inversion Approach to Measuring the Composition and Directionality of the Seismic Noise Field"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2689-0190","authenticated-orcid":false,"given":"Patrick M.","family":"Meyers","sequence":"first","affiliation":[{"name":"School of Physics, University of Melbourne, Parkville, VIC 3010, Australia"},{"name":"OzGrav, University of Melbourne, Parkville, VIC 3010, Australia"}]},{"given":"Tanner","family":"Prestegard","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA"}]},{"given":"Vuk","family":"Mandic","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1809-6672","authenticated-orcid":false,"given":"Victor C.","family":"Tsai","sequence":"additional","affiliation":[{"name":"Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3332-5146","authenticated-orcid":false,"given":"Daniel C.","family":"Bowden","sequence":"additional","affiliation":[{"name":"Institute of Geophysics, ETH, 8092 Z\u00fcrich, Switzerland"}]},{"given":"Andrew","family":"Matas","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Gravitational Physics (Albert Einstein Institute), D-14476 Potsdam-Golm, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2128-9897","authenticated-orcid":false,"given":"Gary","family":"Pavlis","sequence":"additional","affiliation":[{"name":"Department of Geological Sciences, Indiana University, Bloomington, IN 47405, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5666-7945","authenticated-orcid":false,"given":"Ross","family":"Caton","sequence":"additional","affiliation":[{"name":"Department of Geological Sciences, Indiana University, Bloomington, IN 47405, USA"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1029\/2007GL031091","article-title":"A year of microseisms in southern California","volume":"34","author":"Gerstoft","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_2","first-page":"777","article-title":"The origin of deep ocean microseisms in the North Atlantic Ocean","volume":"464","author":"Kedar","year":"2008","journal-title":"Proc. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1017\/jfm.2012.548","article-title":"Noise generation in the solid Earth, oceans and atmosphere, from nonlinear interacting surface gravity waves in finite depth","volume":"716","author":"Ardhuin","year":"2013","journal-title":"J. Fluid Mech."},{"key":"ref_4","first-page":"1","article-title":"Origin of deep ocean microseisms by using teleseismic body waves","volume":"115","author":"Hubans","year":"2010","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6741","DOI":"10.1002\/2016JB013017","article-title":"Where do ocean microseisms come from? A study of Love-to-Rayleigh wave ratios","volume":"121","author":"Juretzek","year":"2016","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"919","DOI":"10.1126\/science.aaf7573","article-title":"Teleseismic S Wave Microseisms","volume":"353","author":"Nishida","year":"2016","journal-title":"Science"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.epsl.2016.05.035","article-title":"Source locations of teleseismic P, SV, and SH waves observed in microseisms recorded by a large aperture seismic array in China","volume":"449","author":"Liu","year":"2016","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1002\/2017JB015015","article-title":"Improving Microseismic P Wave Source Location With Multiple Seismic Arrays","volume":"123","author":"Harmon","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3011","DOI":"10.1121\/1.1417528","article-title":"On the emergence of the Green\u2019s function in the correlations of a diffuse field","volume":"110","author":"Lobkis","year":"2001","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1615","DOI":"10.1126\/science.1108339","article-title":"High-resolution surface-wave tomography from ambient seismic noise","volume":"307","author":"Shapiro","year":"2005","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1555","DOI":"10.1111\/j.1365-246X.2009.04239.x","article-title":"On establishing the accuracy of noise tomography travel-time measurements in a realistic medium","volume":"178","author":"Tsai","year":"2009","journal-title":"Geophys. J. Int."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/53.665","article-title":"Beamforming: A Versatile Approach to Spatial Filtering","volume":"5","author":"Buckley","year":"1988","journal-title":"IEEE ASSP Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2-1","DOI":"10.1029\/2000RG000100","article-title":"Array seismology: Methods and applications","volume":"40","author":"Rost","year":"2002","journal-title":"Rev. Geophys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1093\/gji\/ggw373","article-title":"Ambient noise tomography with non-uniform noise sources and low aperture networks: Case study of deep geothermal reservoirs in northern Alsace, France","volume":"208","author":"Lehujeur","year":"2017","journal-title":"Geophys. J. Int."},{"key":"ref_15","first-page":"1725","article-title":"Three-component array processing","volume":"78","author":"Esmersoy","year":"1985","journal-title":"VELA Program Twenty-Five Year Rev. Basic Res."},{"key":"ref_16","first-page":"1725","article-title":"Polarization analysis of three-component array data","volume":"78","author":"Jurkevics","year":"1988","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1029\/96GL01599","article-title":"Resolving diversely polarized, superimposed signals in three-component seismic array data","volume":"23","author":"Wagner","year":"1996","journal-title":"Geophys. Res. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"5339","DOI":"10.1002\/jgrb.50375","article-title":"Time-lapse analysis of ambient surface wave anisotropy: A three-component array study above an underground gas storage","volume":"118","author":"Riahi","year":"2013","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1093\/gji\/ggy058","article-title":"Three-component ambient noise beamforming in the Parkfield area","volume":"213","author":"Riahi","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1111\/j.1365-246X.2011.05064.x","article-title":"A theory for microtremor H\/V spectral ratio: Application for a layered medium","volume":"186","author":"Campillo","year":"2011","journal-title":"Geophys. J. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1921","DOI":"10.1785\/BSSA0700051921","article-title":"The seismic response of sediment-filled valleys. Part 2. The case of incident P and SV waves","volume":"70","author":"Bard","year":"1980","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1263","DOI":"10.1785\/BSSA0700041263","article-title":"The seismic response of sediment-filled valleys. Part 1. The case of incident SH waves","volume":"70","author":"Bard","year":"1980","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1002\/2016GL071885","article-title":"Earthquake ground motion amplification for surface waves","volume":"43","author":"Bowden","year":"2017","journal-title":"Geophys. Res. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s41114-019-0022-2","article-title":"Terrestrial gravity fluctuations","volume":"22","author":"Harms","year":"2019","journal-title":"Living Rev. Relativ."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1121\/1.396151","article-title":"Matched field processing: Source localization in correlated noise as an optimum parameter estimation problem","volume":"83","author":"Baggeroer","year":"1988","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"KS33","DOI":"10.1190\/geo2011-0438.1","article-title":"Multiscale matched-field processing for noise-source localization in exploration geophysics","volume":"77","author":"Corciulo","year":"2012","journal-title":"Geophysics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"6871","DOI":"10.1029\/2018JB015526","article-title":"Matched Field Processing of Three-Component Seismic Array Data Applied to Rayleigh and Love Microseisms","volume":"123","author":"Gal","year":"2018","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1111\/j.1365-246X.2010.04721.x","article-title":"Noise cross-correlation sensitivity kernels","volume":"183","author":"Tromp","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1093\/gji\/ggx429","article-title":"Towards full waveform ambient noise inversion","volume":"212","author":"Sager","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2019JB018644","article-title":"Global-Scale Full-Waveform Ambient Noise Inversion","volume":"125","author":"Sager","year":"2020","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1093\/gji\/ggab210","article-title":"Rapid finite-frequency microseismic noise source inversion at regional to global scales","volume":"227","author":"Igel","year":"2021","journal-title":"Geophys. J. Int."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1761","DOI":"10.1093\/gji\/ggz261","article-title":"Rayleigh-wave multicomponent cross-correlation-based source strength distribution inversion. Part 1: Theory and numerical examples","volume":"218","author":"Xu","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_33","first-page":"415","article-title":"Space and time spectra of stationary stochastic waves, with special reference to microtremors","volume":"35","author":"Aki","year":"1957","journal-title":"Bull. Earthq. Res. Inst."},{"key":"ref_34","first-page":"1973","article-title":"Spatial correlation in arbitrary noise fields with application to ambient sea noise","volume":"54","author":"Cox","year":"2010","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1470","DOI":"10.1111\/j.1365-246X.2010.04802.x","article-title":"Distribution of noise sources for seismic interferometry","volume":"183","author":"Harmon","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1111\/j.1365-246X.2012.05597.x","article-title":"Extension of the spatial autocorrelation (SPAC) method to mixed-component correlations of surface waves","volume":"191","author":"Haney","year":"2012","journal-title":"Geophys. J. Int."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"S179","DOI":"10.1088\/0264-9381\/23\/8\/S23","article-title":"A radiometer for stochastic gravitational waves","volume":"23","author":"Ballmer","year":"2006","journal-title":"Class. Quantum Gravity"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"122002","DOI":"10.1103\/PhysRevD.80.122002","article-title":"Probing the anisotropies of a stochastic gravitational-wave background using a network of ground-based laser interferometers","volume":"80","author":"Thrane","year":"2009","journal-title":"Phys. Rev. D"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"042003","DOI":"10.1103\/PhysRevD.92.042003","article-title":"Phase-coherent mapping of gravitational-wave backgrounds using ground-based laser interferometers","volume":"92","author":"Romano","year":"2015","journal-title":"Phys. Rev. D"},{"key":"ref_40","unstructured":"Prestegard, T. (2016). Unmodeled Searches for Long-Lasting Gravitational-Wave Signals with LIGO and Studies of Underground Seismic Noise for Future Gravitational-Wave Detectors. [Ph.D. Thesis, University of Minnesota]."},{"key":"ref_41","unstructured":"Meyers, P. (2018). Cross-Correlation Searches for Persistent Gravitational Waves with Advanced LIGO and Noise Studies for Current and Future Ground-Based Gravitational-Wave Detectors. [Ph.D. Thesis, University of Minnesota]."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1559","DOI":"10.1093\/gji\/ggy072","article-title":"Near-surface compressional and shear wave speeds constrained by body-wave polarization analysis","volume":"213","author":"Park","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"14377","DOI":"10.1029\/2019GL084892","article-title":"Frequency-dependent P wave polarization and its subwavelength near-surface depth sensitivity","volume":"46","author":"Park","year":"2019","journal-title":"Geophys. Res. Lett."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"EN167","DOI":"10.1190\/geo2014-0612.1","article-title":"Nonperturbational surface-wave inversion: A Dix-type relation for surface waves","volume":"80","author":"Haney","year":"2015","journal-title":"Geophysics"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1785\/0120190026","article-title":"Direct Observations of Surface-Wave Eigenfunctions at the Homestake 3D Array","volume":"109","author":"Meyers","year":"2019","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1145\/355984.355989","article-title":"LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares","volume":"8","author":"Paige","year":"1982","journal-title":"ACM Trans. Math. Softw."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"409","DOI":"10.6028\/jres.049.044","article-title":"Methods of Conjugate Gradients for Solving Linear Systems","volume":"49","author":"Hestenes","year":"1952","journal-title":"J. Res. Natl. Bur. Stand."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"759","DOI":"10.1086\/427976","article-title":"HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere","volume":"622","author":"Gorski","year":"2005","journal-title":"Astrophys. J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2420","DOI":"10.1785\/0220170228","article-title":"A 3D Broadband Seismometer Array Experiment at the Homestake Mine","volume":"89","author":"Mandic","year":"2018","journal-title":"Seismol. Res. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"2941","DOI":"10.1029\/2018JB016608","article-title":"Coherence-Based Approaches for Estimating the Composition of the Seismic Wavefield","volume":"124","author":"Coughlin","year":"2019","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/2013EO010001","article-title":"What Is Climate?","volume":"94","author":"Lovejoy","year":"2013","journal-title":"Eos Trans. Am. Geophys. Union"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Stehly, L., Campillo, M., and Shapiro, N.M. (2006). A study of the seismic noise from its long-range correlation properties. J. Geophys. Res. Solid Earth, 111.","DOI":"10.1029\/2005JB004237"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"8241","DOI":"10.1002\/2017JB014808","article-title":"Lakes as a Source of Short-Period (0.5\u20132 s) Microseisms","volume":"122","author":"Xu","year":"2017","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Bensen, G.D., Ritzwoller, M.H., and Shapiro, N.M. (2008). Broadband ambient noise surface wave tomography across the United States. J. Geophys. Res. Solid Earth, 113.","DOI":"10.1029\/2007JB005248"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/16\/3097\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:41:21Z","timestamp":1760164881000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/16\/3097"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,5]]},"references-count":54,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["rs13163097"],"URL":"https:\/\/doi.org\/10.3390\/rs13163097","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,8,5]]}}}