{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:29:31Z","timestamp":1772252971616,"version":"3.50.1"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T00:00:00Z","timestamp":1672876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42074154"],"award-info":[{"award-number":["42074154"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42130805"],"award-info":[{"award-number":["42130805"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The Marchenko method is a data-driven way that makes it possible to calculate Green\u2019s functions from virtual points in the subsurface using the reflection data at the surface and requiring only a macro velocity model. This method requires collocated sources and receivers. However, in practice, irregular sampling of sources or receivers will cause gaps and distortions in the obtained focusing functions and Green\u2019s functions. To solve this problem, this paper proposes to integrate a sparse inversion into the iterative Marchenko scheme. Specifically, we add sparsity constraints to the Marchenko equations and apply the sparse inversion during the iterative process. To reduce the strict requirements on acquisition geometries, our work deals with the situation in which the sources are subsampled where the integrations are carried out over the receivers, while the existing point spread function method solves the situation where the receivers are subsampled. We make a step to handle both situations at the same time by integrating this method with our work because of the same iterative framework. Our new method is applied to a two-dimensional numerical example with irregularly sampled data. The result shows that it can effectively fill gaps in the obtained focusing functions and Green\u2019s functions in the Marchenko method.<\/jats:p>","DOI":"10.3390\/rs15020322","type":"journal-article","created":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T04:51:31Z","timestamp":1672894291000},"page":"322","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Sparse Inversion for the Iterative Marchenko Scheme of Irregularly Sampled Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2575-0644","authenticated-orcid":false,"given":"Jingwen","family":"Zeng","sequence":"first","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Liguo","family":"Han","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"S63","DOI":"10.1190\/geo2013-0095.1","article-title":"Seismic reflector imaging using internal multiples with Marchenko-type equations","volume":"79","author":"Slob","year":"2014","journal-title":"Geophysics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"WA39","DOI":"10.1190\/geo2013-0302.1","article-title":"Marchenko imaging","volume":"79","author":"Wapenaar","year":"2014","journal-title":"Geophysics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"WC117","DOI":"10.1190\/geo2020-0854.1","article-title":"Marchenko redatuming, imaging, and multiple elimination and their mutual relations","volume":"86","author":"Wapenaar","year":"2021","journal-title":"Geophysics"},{"key":"ref_4","unstructured":"Lomas, A. 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