{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T12:05:14Z","timestamp":1777637114247,"version":"3.51.4"},"reference-count":76,"publisher":"Society of Exploration Geophysicists","issue":"4","license":[{"start":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T00:00:00Z","timestamp":1591056000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["library.seg.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2020,7,1]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>We have recast the forward pass of a multilayered convolutional neural network (CNN) as the solution to the problem of sparse least-squares migration (LSM). The CNN filters and feature maps are shown to be analogous, but not equivalent, to the migration Green\u2019s functions and the quasi-reflectivity distribution, respectively. This provides a physical interpretation of the filters and feature maps in deep CNN in terms of the operators for seismic imaging. Motivated by the connection between sparse LSM and CNN, we adopt the neural network version of sparse LSM. Unlike the standard LSM method that finds the optimal reflectivity image, neural network LSM (NNLSM) finds the optimal quasi-reflectivity image and the quasi-migration Green\u2019s functions. These quasi-migration Green\u2019s functions are also denoted as the convolutional filters in a CNN and are similar to migration Green\u2019s functions. The advantage of NNLSM over standard LSM is that its computational cost is significantly less and it can be used for denoising coherent and incoherent noise in migration images. Its disadvantage is that the NNLSM quasi-reflectivity image is only an approximation to the actual reflectivity distribution. However, the quasi-reflectivity image can be used as an attribute image for high-resolution delineation of geologic bodies.<\/jats:p>","DOI":"10.1190\/geo2019-0412.1","type":"journal-article","created":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T11:14:18Z","timestamp":1591096458000},"page":"WA241-WA253","update-policy":"https:\/\/doi.org\/10.1190\/crossmark-policy","source":"Crossref","is-referenced-by-count":25,"title":["Deep convolutional neural network and sparse least-squares migration"],"prefix":"10.1190","volume":"85","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1430-7914","authenticated-orcid":false,"given":"Zhaolun","family":"Liu","sequence":"first","affiliation":[{"name":"King Abdullah University of Science and Technology 1 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Department of Geosciences, Princeton, New Jersey 08544, . E-mail: zhaolunl@princeton.edu (corresponding author).","place":["USA"]},{"name":"Princeton University 1 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Department of Geosciences, Princeton, New Jersey 08544, . E-mail: zhaolunl@princeton.edu (corresponding author).","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2480-8974","authenticated-orcid":false,"given":"Yuqing","family":"Chen","sequence":"additional","affiliation":[{"name":"King Abdullah University of Science and Technology 2 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Deep Earth Imaging Future Science Platform, Kensington, . E-mail: Yu. Chen@csiro.au .","place":["Australia"]},{"name":"CSIRO 2 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Deep Earth Imaging Future Science Platform, Kensington, . E-mail: Yu. Chen@csiro.au .","place":["Australia"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4746-2512","authenticated-orcid":false,"given":"Gerard","family":"Schuster","sequence":"additional","affiliation":[{"name":"King Abdullah University of Science and Technology 3 , Department of Earth Science and Engineering, Thuwal 23955-6900, Saudi Arabia. E-mail: gerard.schuster@kaust.edu.sa ."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"186","published-online":{"date-parts":[[2020,6,13]]},"reference":[{"key":"2025121211260247500_r1","unstructured":"Aarre\n              V.\n            \n          , 2016, Understanding spectral decomposition by Victor Aarre: https:\/\/youtu.be\/1nDyMHs8zuw, accessed: 19April2019."},{"key":"2025121211260247500_r3","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1190\/tle37010058.1","article-title":"Deep-learning tomography","volume":"37","author":"Araya-Polo","year":"2018","journal-title":"The Leading Edge"},{"issue":"2","key":"2025121211260247500_r4","doi-asserted-by":"crossref","first-page":"T347","DOI":"10.1190\/INT-2018-0044.1","article-title":"Missing log data interpolation and semiautomatic seismic well ties using data matching techniques","volume":"7","author":"Bader","year":"2019","journal-title":"Interpretation"},{"key":"2025121211260247500_r5","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1137\/080716542","article-title":"A fast iterative shrinkage-thresholding algorithm for linear inverse problems","volume":"2","author":"Beck","year":"2009","journal-title":"SIAM Journal on Imaging Sciences"},{"key":"2025121211260247500_r6","doi-asserted-by":"crossref","unstructured":"Bharadwaj\n              P.\n            \n            \n              Demanet\n              L.\n            \n            \n              Fournier\n              A.\n            \n          , 2018, Focused blind deconvolution of interferometric Green\u2019s functions: 88th Annual International Meeting, SEG, Expanded Abstracts, 4085\u20134090, doi: http:\/\/dx.doi.org\/10.1190\/segam2018-2965039.1.","DOI":"10.1190\/segam2018-2965039.1"},{"key":"2025121211260247500_r7","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1190\/tle36030234.1","article-title":"Time-lapse reservoir property change estimation from seismic using machine learning","volume":"36","author":"Cao","year":"2017","journal-title":"The Leading Edge"},{"key":"2025121211260247500_r8","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1190\/1.1444557","article-title":"An optimal true-amplitude least-squares prestack depth-migration operator","volume":"64","author":"Chavent","year":"1999","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"issue":"6","key":"2025121211260247500_r9","doi-asserted-by":"crossref","first-page":"S425","DOI":"10.1190\/geo2016-0585.1","article-title":"Q-least-squares reverse time migration with viscoacoustic deblurring filters","volume":"82","author":"Chen","year":"2017","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"issue":"3","key":"2025121211260247500_r10","doi-asserted-by":"crossref","first-page":"S127","DOI":"10.1190\/geo2018-0256.1","article-title":"Migration of viscoacoustic data using acoustic reverse time migration with hybrid deblurring filters","volume":"84","author":"Chen","year":"2019","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r11","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1023\/A:1015210828153","article-title":"Sparse linear algebra and geophysical migration: A review of direct and iterative methods","volume":"29","author":"De Roeck","year":"2002","journal-title":"Numerical Algorithms","ISSN":"https:\/\/id.crossref.org\/issn\/1017-1398","issn-type":"print"},{"issue":"4","key":"2025121211260247500_r12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1190\/geo2019-0433.1","article-title":"Seismic stratigraphy interpretation by deep convolutional neural networks: A semi-supervised workflow","volume":"85","author":"Di","year":"2020","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r13","unstructured":"Donoho\n              D. L.\n            \n          , 2019, Deepnet spectra and the two cultures of data science: Presented at the Al-Kindi Distinguished Statistics Lectures, KAUST."},{"key":"2025121211260247500_r14","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1190\/1.1444812","article-title":"Kirchhoff modeling, inversion for reflectivity, and subsurface illumination","volume":"65","author":"Duquet","year":"2000","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r15","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.jappgeo.2016.10.027","article-title":"Sparse least-squares reverse time migration using seislets","volume":"136","author":"Dutta","year":"2017","journal-title":"Journal of Applied Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0926-9851","issn-type":"print"},{"issue":"2","key":"2025121211260247500_r16","doi-asserted-by":"crossref","first-page":"S143","DOI":"10.1190\/geo2016-0254.1","article-title":"Elastic least-squares reverse time migration","volume":"82","author":"Feng","year":"2017","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r17","doi-asserted-by":"crossref","unstructured":"Heide\n              F.\n            \n            \n              Heidrich\n              W.\n            \n            \n              Wetzstein\n              G.\n            \n          , 2015, Fast and flexible convolutional sparse coding: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 5135\u20135143.","DOI":"10.1109\/CVPR.2015.7299149"},{"issue":"4","key":"2025121211260247500_r18","doi-asserted-by":"crossref","first-page":"A41","DOI":"10.1190\/1.3124753","article-title":"Curvelet-based migration preconditioning and scaling","volume":"74","author":"Herrmann","year":"2009","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"issue":"6","key":"2025121211260247500_r19","doi-asserted-by":"crossref","first-page":"U45","DOI":"10.1190\/geo2018-0688.1","article-title":"First-arrival picking with a U-net convolutional network","volume":"84","author":"Hu","year":"2019","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r20","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1190\/tle36030249.1","article-title":"A scalable deep learning platform for identifying geologic features from seismic attributes","volume":"36","author":"Huang","year":"2017","journal-title":"The Leading Edge"},{"issue":"2","key":"2025121211260247500_r21","doi-asserted-by":"crossref","first-page":"V83","DOI":"10.1190\/geo2017-0294.1","article-title":"Intelligent interpolation by Monte Carlo machine learning","volume":"83","author":"Jia","year":"2018","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r22","doi-asserted-by":"crossref","first-page":"2093","DOI":"10.1190\/1.1444503","article-title":"Multichannel blind deconvolution of seismic signals","volume":"63","author":"Kaaresen","year":"1998","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r23","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.petrol.2010.07.003","article-title":"A new approach to improve neural networks\u2019 algorithm in permeability prediction of petroleum reservoirs using supervised committee machine neural network (SCMNN)","volume":"73","author":"Karimpouli","year":"2010","journal-title":"Journal of Petroleum Science and Engineering","ISSN":"https:\/\/id.crossref.org\/issn\/0920-4105","issn-type":"print"},{"issue":"4","key":"2025121211260247500_r24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1190\/geo2019-0315.1","article-title":"Improving resolution of migrated images by approximating the inverse hessian using deep learning","volume":"85","author":"Kaur","year":"2020","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r25","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1190\/1.1543212","article-title":"Least-squares wave-equation migration for AVP\/AVA 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1\u20135.","DOI":"10.3997\/2214-4609.201803061"},{"key":"2025121211260247500_r31","doi-asserted-by":"crossref","unstructured":"Liu\n              Z.\n            \n            \n              Schuster\n              G.\n            \n          , 2019, Multilayer sparse LSM = deep neural network: 89th Annual International Meeting, SEG, Expanded Abstracts, 2323\u20132327, doi: http:\/\/dx.doi.org\/10.1190\/segam2019-3215033.1.","DOI":"10.1190\/segam2019-3215033.1"},{"key":"2025121211260247500_r32","doi-asserted-by":"crossref","unstructured":"Lu\n              K.\n            \n            \n              Feng\n              S.\n            \n          , 2018, Auto-windowed super-virtual interferometry via machine learning: A strategy of first-arrival traveltime automatic picking for noisy seismic data: SEG Maximizing Asset Value Through Artificial Intelligence and Machine Learning Workshop, 10\u201314.","DOI":"10.1190\/AIML2018-03.1"},{"key":"2025121211260247500_r33","doi-asserted-by":"crossref","unstructured":"Mandelli\n              S.\n            \n            \n              Borra\n              F.\n            \n            \n              Lipari\n              V.\n            \n            \n              Bestagini\n              P.\n            \n            \n              Sarti\n              A.\n            \n            \n              Tubaro\n              S.\n            \n          , 2018, Seismic data interpolation through convolutional autoencoder: 88th Annual International Meeting, SEG, Expanded Abstracts, 4101\u20134105, doi: http:\/\/dx.doi.org\/10.1190\/segam2018-2995428.1.","DOI":"10.1190\/segam2018-2995428.1"},{"key":"2025121211260247500_r34","article-title":"Interpolation and denoising of seismic data using convolutional neural networks","author":"Mandelli","year":"2019"},{"key":"2025121211260247500_r35","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1190\/1.1444517","article-title":"Least-squares migration of incomplete reflection data","volume":"64","author":"Nemeth","year":"1999","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r36","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1038\/381607a0","article-title":"Emergence of simple-cell receptive field properties by learning a sparse code for natural images","volume":"381","author":"Olshausen","year":"1996","journal-title":"Nature","ISSN":"https:\/\/id.crossref.org\/issn\/0028-0836","issn-type":"print"},{"key":"2025121211260247500_r37","article-title":"Convolutional neural networks analyzed via convolutional sparse coding","author":"Papyan","year":"2016"},{"key":"2025121211260247500_r38","first-page":"2887","article-title":"Convolutional neural networks analyzed via convolutional sparse coding","volume":"18","author":"Papyan","year":"2017","journal-title":"The Journal of Machine Learning Research"},{"key":"2025121211260247500_r39","doi-asserted-by":"crossref","unstructured":"Papyan\n              V.\n            \n            \n              Romano\n              Y.\n            \n            \n              Sulam\n              J.\n            \n            \n              Elad\n              M.\n            \n          , 2017b, Convolutional dictionary learning via local processing: Proceedings of the IEEE International Conference on Computer Vision, 5296\u20135304.","DOI":"10.1109\/ICCV.2017.566"},{"key":"2025121211260247500_r40","doi-asserted-by":"crossref","unstructured":"Perez\n              D. O.\n            \n            \n              Velis\n              D. R.\n            \n            \n              Sacchi\n              M. D.\n            \n          , 2013, Estimating sparse-spike attributes from ava data using a fast iterative shrinkage-thresholding algorithm and least squares: 83rd Annual International Meeting, SEG, Expanded Abstracts, 3062\u20133067, doi: http:\/\/dx.doi.org\/10.1190\/segam2013-0381.1.","DOI":"10.1190\/segam2013-0381.1"},{"issue":"3","key":"2025121211260247500_r41","doi-asserted-by":"crossref","first-page":"SE201","DOI":"10.1190\/INT-2018-0225.1","article-title":"Multiresolution neural networks for tracking seismic horizons from few training images","volume":"7","author":"Peters","year":"2019","journal-title":"Interpretation"},{"key":"2025121211260247500_r42","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1190\/tle38070534.1","article-title":"Neural networks for geophysicists and their application to seismic data interpretation","volume":"38","author":"Peters","year":"2019","journal-title":"The Leading Edge"},{"issue":"4","key":"2025121211260247500_r43","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1190\/geo2019-0282.1","article-title":"Missing well log prediction using convolutional long short-term memory network","volume":"85","author":"Pham","year":"2020","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"issue":"5","key":"2025121211260247500_r44","doi-asserted-by":"crossref","first-page":"SM185","DOI":"10.1190\/1.2738849","article-title":"A Helmholtz iterative solver for 3D seismic-imaging problems","volume":"72","author":"Plessix","year":"2007","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"issue":"3","key":"2025121211260247500_r45","doi-asserted-by":"crossref","first-page":"A39","DOI":"10.1190\/geo2017-0524.1","article-title":"Unsupervised seismic facies analysis via deep convolutional autoencoders","volume":"83","author":"Qian","year":"2018","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r46","article-title":"Seismic full-waveform inversion using deep learning tools and techniques","author":"Richardson","year":"2018"},{"key":"2025121211260247500_r47","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.jngse.2009.08.003","article-title":"Using artificial neural networks to generate synthetic well logs","volume":"1","author":"Rolon","year":"2009","journal-title":"Journal of Natural Gas Science and Engineering"},{"key":"2025121211260247500_r48","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1190\/tle36040340.1","article-title":"A comparison of popular neural network facies-classification schemes","volume":"36","author":"Ross","year":"2017","journal-title":"The Leading Edge"},{"key":"2025121211260247500_r49","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1190\/1.1443845","article-title":"High-resolution velocity gathers and offset space reconstruction","volume":"60","author":"Sacchi","year":"1995","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"key":"2025121211260247500_r50","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1306\/03110301030","article-title":"Estimation of missing logs by regularized neural networks","volume":"87","author":"Saggaf","year":"2003","journal-title":"AAPG Bulletin","ISSN":"https:\/\/id.crossref.org\/issn\/0149-1423","issn-type":"print"},{"key":"2025121211260247500_r51","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1016\/j.ejpe.2016.11.002","article-title":"Estimation of the non records logs from existing logs using artificial neural networks","volume":"26","author":"Salehi","year":"2017","journal-title":"Egyptian Journal of Petroleum"},{"key":"2025121211260247500_r52","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1017\/S0016774600022812","article-title":"Expressions of shallow gas in the Netherlands North Sea","volume":"82","author":"Schroot","year":"2003","journal-title":"Netherlands Journal of Geosciences \u2014 Geologie en Mijnbouw"},{"key":"2025121211260247500_r53","doi-asserted-by":"crossref","unstructured":"Schuster\n              G.\n            \n            \n              Liu\n              Z.\n            \n          , 2019, Least squares migration: Current and future directions: 81st Annual International Conference and Exhibition, EAGE, Extended Abstracts, 1\u20135.","DOI":"10.3997\/2214-4609.201901270"},{"key":"2025121211260247500_r54","doi-asserted-by":"crossref","unstructured":"Schuster\n              G. 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D.\n            \n          , 2005, Sparse regularization for least-squares AVP migration: CSEG National Convention, Expanded Abstracts, 117\u2013120."},{"issue":"1","key":"2025121211260247500_r66","doi-asserted-by":"crossref","first-page":"S11","DOI":"10.1190\/1.2387139","article-title":"High-resolution wave-equation amplitude-variation-with-ray-parameter (AVP) imaging with sparseness constraints","volume":"72","author":"Wang","year":"2007","journal-title":"Geophysics","ISSN":"https:\/\/id.crossref.org\/issn\/0016-8033","issn-type":"print"},{"issue":"2","key":"2025121211260247500_r67","doi-asserted-by":"crossref","first-page":"V119","DOI":"10.1190\/geo2018-0699.1","article-title":"Seismic trace interpolation for irregularly spatial sampled data using convolutional 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