{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:11:02Z","timestamp":1760235062918,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T00:00:00Z","timestamp":1625788800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009893","name":"Instituto Mexicano del Petr\u00f3leo","doi-asserted-by":"publisher","award":["PCTRES"],"award-info":[{"award-number":["PCTRES"]}],"id":[{"id":"10.13039\/501100009893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>It is a well-established principle that cross-correlating seismic observations at different receiver locations can yield estimates of band-limited inter-receiver Green\u2019s functions. This principle, known as Green\u2019s function retrieval or seismic interferometry, is a powerful technique that can transform noise into signals which enable remote interrogation and imaging of the Earth\u2019s subsurface. In practice it is often necessary and even desirable to rely on noise already present in the environment. Theory that underpins many applications of ambient noise interferometry assumes that the sources of noise are uncorrelated in time. However, many real-world noise sources such as trains, highway traffic and ocean waves are inherently correlated in space and time, in direct contradiction to the these theoretical foundations. Applying standard interferometric techniques to recordings from correlated energy sources makes the Green\u2019s function liable to estimation errors that so far have not been fully accounted for theoretically nor in practice. We show that these errors are significant for common noise sources, always perturbing or entirely obscuring the phase one wishes to retrieve. Our analysis explains why stacking may reduce the phase errors, but also shows that in commonly encountered circumstances stacking will not remediate the problem. This analytical insight allowed us to develop a novel workflow that significantly mitigates effects arising from the use of correlated noise sources. Our methodology can be used in conjunction with already existing approaches, and improves results from both correlated and uncorrelated ambient noise. Hence, we expect it to be widely applicable in ambient noise studies.<\/jats:p>","DOI":"10.3390\/rs13142703","type":"journal-article","created":{"date-parts":[[2021,7,9]],"date-time":"2021-07-09T10:50:38Z","timestamp":1625827838000},"page":"2703","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Seismic Interferometry from Correlated Noise Sources"],"prefix":"10.3390","volume":"13","author":[{"given":"Daniella","family":"Ayala-Garcia","sequence":"first","affiliation":[{"name":"School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FE, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1222-1583","authenticated-orcid":false,"given":"Andrew","family":"Curtis","sequence":"additional","affiliation":[{"name":"School of GeoSciences, The University of Edinburgh, Edinburgh EH9 3FD, UK"}]},{"given":"Michal","family":"Branicki","sequence":"additional","affiliation":[{"name":"School of Mathematics, The University of Edinburgh, Edinburgh EH9 3FE, UK"},{"name":"The Alan Turing Institute for Data Science, London NW1 2DB, UK"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1126\/science.1078551","article-title":"Long-range correlations in the diffuse seismic coda","volume":"299","author":"Campillo","year":"2003","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"SI33","DOI":"10.1190\/1.2213955","article-title":"Green\u2019s function representations for seismic interferometry","volume":"71","author":"Wapenaar","year":"2006","journal-title":"Geophysics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.1190\/1.2349814","article-title":"Seismic interferometry\u2014Turning noise into signal","volume":"25","author":"Curtis","year":"2006","journal-title":"Lead. Edge"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1190\/1.1439927","article-title":"Synthesis of a layered medium from its acoustic transmission response","volume":"33","author":"Claerbout","year":"1968","journal-title":"Geophysics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1190\/1.1438420","article-title":"Acoustic daylight imaging via spectral factorization: Helioseismology and reservoir monitoring","volume":"18","author":"Rickett","year":"1999","journal-title":"Lead. Edge"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"134301","DOI":"10.1103\/PhysRevLett.87.134301","article-title":"Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies","volume":"87","author":"Weaver","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3054","DOI":"10.1063\/1.1617373","article-title":"How to estimate the Green\u2019s function of a heterogeneous medium between two passive sensors? Application to acoustic waves","volume":"83","author":"Derode","year":"2003","journal-title":"Appl. Phys. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2006GL029097","article-title":"Electromagnetic Green\u2019s functions retrieval by cross-correlation and cross-convolution in media with losses","volume":"34","author":"Slob","year":"2007","journal-title":"Geophys. Res. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1111\/j.1365-2478.2008.00697.x","article-title":"Global-scale seismic interferometry: Theory and numerical examples","volume":"56","author":"Ruigrok","year":"2008","journal-title":"Geophys. Prospect."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1126\/science.1176389","article-title":"Global surface wave tomography using seismic hum","volume":"326","author":"Nishida","year":"2009","journal-title":"Science"},{"key":"ref_11","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_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2007JB005395","article-title":"Three-dimensional crustal S wave velocity structure in Japan using microseismic data recorded by Hi-net tiltmeters","volume":"113","author":"Nishida","year":"2008","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2009GL041974","article-title":"New insight into Cainozoic sedimentary basins and Palaeozoic suture zones in southeast Australia from ambient noise surface wave tomography","volume":"37","author":"Arroucau","year":"2010","journal-title":"Geophys. Res. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"SI139","DOI":"10.1190\/1.2216190","article-title":"The virtual source method: Theory and case study","volume":"71","author":"Bakulin","year":"2006","journal-title":"Geophysics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1190\/1.2748490","article-title":"Virtual source applications to imaging and reservoir monitoring","volume":"26","author":"Bakulin","year":"2007","journal-title":"Lead. Edge"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"SA95","DOI":"10.1190\/1.3486453","article-title":"An interferometric theory of source-receiver scattering and imaging","volume":"75","author":"Halliday","year":"2010","journal-title":"Geophysics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1016\/j.pepi.2005.12.005","article-title":"Tomographic investigation of the wear along the San Jacinto fault, southern California","volume":"155","author":"Hong","year":"2006","journal-title":"Phys. Earth Planet. Inter."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1038\/ngeo615","article-title":"Virtual seismometers in the subsurface of the Earth from seismic interferometry","volume":"2","author":"Curtis","year":"2009","journal-title":"Nat. Geosci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"254301","DOI":"10.1103\/PhysRevLett.93.254301","article-title":"Retrieving the elastodynamic Green\u2019s function of an arbitrary inhomogeneous medium by cross correlation","volume":"93","author":"Wapenaar","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"046601","DOI":"10.1103\/PhysRevE.81.046601","article-title":"Source-receiver wave field interferometry","volume":"81","author":"Curtis","year":"2010","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1016\/j.epsl.2012.06.008","article-title":"The benefit of hindsight in observational science: Retrospective seismological observations","volume":"345","author":"Curtis","year":"2012","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1002\/2014JB011607","article-title":"Constructing new seismograms from old earthquakes: Retrospective seismology at multiple length scales","volume":"120","author":"Entwistle","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Chen, Y., and Saygin, E. (2020). Empirical Green\u2019s Function Retrieval Using Ambient Noise Source-Receiver Interferometry. J. Geophys. Res. Solid Earth, 125.","DOI":"10.1029\/2019JB018261"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1111\/j.1365-246X.2011.05007.x","article-title":"Seismic interferometry by crosscorrelation and by multidimensional deconvolution: A systematic comparison","volume":"185","author":"Wapenaar","year":"2011","journal-title":"Geophys. J. Int."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.pgeola.2011.04.002","article-title":"Seismic interferometry and ambient noise tomography in the British Isles","volume":"123","author":"Nicolson","year":"2012","journal-title":"Proc. Geol. Assoc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"C006952","DOI":"10.1029\/2011JC006952","article-title":"Ocean wave sources of seismic noise","volume":"116","author":"Ardhuin","year":"2011","journal-title":"J. Geophys. Res. Ocean."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1121\/1.1835507","article-title":"Arrival-time structure of the time-averaged ambient noise cross-correlation function in an oceanic waveguide","volume":"117","author":"Sabra","year":"2005","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1190\/1.2840369","article-title":"Seismic surface waves in a suburban environment: Active and passive interferometric methods","volume":"27","author":"Halliday","year":"2008","journal-title":"Lead. Edge"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"SA97","DOI":"10.1190\/geo2010-0188.1","article-title":"Shear wave imaging from traffic noise using seismic interferometry by cross-coherence","volume":"76","author":"Nakata","year":"2011","journal-title":"Geophysics"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"628","DOI":"10.1190\/tle32060628.1","article-title":"Love waves from local traffic noise interferometry","volume":"32","author":"Behm","year":"2013","journal-title":"Lead. Edge"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1785\/0220200023","article-title":"Virtual Sources of Body Waves from Noise Correlations in a Mineral Exploration Context","volume":"91","author":"Dales","year":"2020","journal-title":"Seismol. Res. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"9529","DOI":"10.1029\/2019GL083438","article-title":"Train traffic as a powerful noise source for monitoring active faults with seismic interferometry","volume":"46","author":"Brenguier","year":"2019","journal-title":"Geophys. Res. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1093\/gji\/ggw033","article-title":"Seismic interferometry of railroad induced ground motions: Body and surface wave imaging","volume":"205","author":"Quiros","year":"2016","journal-title":"Geophys. Suppl. Mon. Not. R. Astron. Soc."},{"key":"ref_34","first-page":"623","article-title":"Humming Trains in Seismology: An Opportune Source for Probing the Shallow Crust","volume":"92","author":"Mordret","year":"2021","journal-title":"Seismol. Soc. Am."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Liu, Y., Yue, Y., Li, Y., and Luo, Y. (2021). On the Retrievability of Seismic Waves From High-Speed-Train-Induced Vibrations Using Seismic Interferometry. IEEE Geosci. Remote. Sens. Lett.","DOI":"10.1109\/LGRS.2021.3050205"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"SI23","DOI":"10.1190\/1.2210607","article-title":"Green\u2019s functions extraction and surface-wave tomography from microseisms in southern California","volume":"71","author":"Gerstoft","year":"2006","journal-title":"Geophysics"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"SA1","DOI":"10.1190\/1.3298736","article-title":"Directional balancing for seismic and general wavefield interferometry","volume":"75","author":"Curtis","year":"2010","journal-title":"Geophysics"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1093\/gji\/ggw420","article-title":"Generalised interferometry-I. Theory for inter-station correlations","volume":"208","author":"Fichtner","year":"2017","journal-title":"Geophys. J. Int."},{"key":"ref_39","unstructured":"Van der Neut, J.R. (2021, June 17). Interferometric Redatuming by Multidimensional Deconvolution. Available online: http:\/\/homepage.tudelft.nl\/t4n4v\/9_Theses_students\/Neut.pdf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1002\/2014JB011262","article-title":"Retrieving surface waves from ambient seismic noise using seismic interferometry by multidimensional deconvolution","volume":"120","author":"Mikesell","year":"2015","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3577","DOI":"10.1121\/1.3397612","article-title":"Influence of the noise sources motion on the estimated Green\u2019s functions from ambient noise cross-correlations","volume":"127","author":"Sabra","year":"2010","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Schuster, G. (2009). Seismic Interferometry, Cambridge University Press.","DOI":"10.1017\/CBO9780511581557"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1111\/j.1365-246X.2008.03918.x","article-title":"Seismic interferometry, surface waves and source distribution","volume":"175","author":"Halliday","year":"2008","journal-title":"Geophys. J. Int."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"V79","DOI":"10.1190\/1.2733020","article-title":"Improving the virtual source method by wavefield separation","volume":"72","author":"Mehta","year":"2007","journal-title":"Geophysics"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"046610","DOI":"10.1103\/PhysRevE.69.046610","article-title":"Extracting the Green\u2019s function from the correlation of coda waves: A derivation based on stationary phase","volume":"69","author":"Snieder","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Thorbecke, J., and Wapenaar, K. (2008). Analysis of spurious events in seismic interferometry. SEG Technical Program Expanded Abstracts 2008, Society of Exploration Geophysicists.","DOI":"10.1190\/1.3059181"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"SI47","DOI":"10.1190\/1.2213218","article-title":"Interferometric modeling of wave propagation in inhomogeneous elastic media using time reversal and reciprocity","volume":"71","author":"Curtis","year":"2006","journal-title":"Geophysics"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1093\/gji\/ggt389","article-title":"Surface wave retrieval in layered media using seismic interferometry by multidimensional deconvolution","volume":"196","author":"Wapenaar","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1111\/j.1365-2478.2012.01056.x","article-title":"On the relation between seismic interferometry and the simultaneous-source method","volume":"60","author":"Wapenaar","year":"2012","journal-title":"Geophys. Prospect."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"SA83","DOI":"10.1190\/geo2011-0008.1","article-title":"Velocity analysis using both reflections and refractions in seismic interferometry","volume":"76","author":"King","year":"2011","journal-title":"Geophysics"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1111\/j.1365-246X.2012.05593.x","article-title":"Seismic waves estimation and wavefield decomposition: Application to ambient vibrations","volume":"191","author":"Reller","year":"2012","journal-title":"Geophys. J. Int."},{"key":"ref_52","unstructured":"Rudin, W. (1976). Principles of Mathematical Analysis, McGraw-Hill."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/14\/2703\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:28:16Z","timestamp":1760164096000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/14\/2703"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,9]]},"references-count":52,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["rs13142703"],"URL":"https:\/\/doi.org\/10.3390\/rs13142703","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,7,9]]}}}