{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T21:02:21Z","timestamp":1775854941096,"version":"3.50.1"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T00:00:00Z","timestamp":1722988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CREWES industrial sponsors","award":["CRDPJ 543578-19"],"award-info":[{"award-number":["CRDPJ 543578-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We implement an inversion-based deblending method in the common midpoint gathers (CMP) as an alternative to the standard common receiver gather (CRG) domain methods. The primary advantage of deblending in the CMP domain is that reflections from dipping layers are centred around zero offsets. As a result, CMP gathers exhibit a simpler structure compared to common receiver gathers (CRGs), where these reflections are apex-shifted. Consequently, we can employ a zero-offset hyperbolic Radon operator to process CMP gathers. This operator is a computationally more efficient alternative to the apex-shifted hyperbolic Radon required for processing CRG gathers. Sparse transforms, such as the Radon transform, can stack reflections and produce sparse models capable of separating blended sources. We utilize the Radon operator to develop an inversion-based deblending framework that incorporates a sparse model constraint. The inclusion of a sparsity constraint in the inversion process enhances the focusing of the transform and improves data recovery. Inversion-based deblending enables us to account for all observed data by incorporating the blending operator into the cost function. Our synthetic and field data examples demonstrate that inversion-based deblending in the CMP domain can effectively separate blended sources.<\/jats:p>","DOI":"10.3390\/a17080344","type":"journal-article","created":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T11:33:52Z","timestamp":1723030432000},"page":"344","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Inversion-Based Deblending in Common Midpoint Domain Using Time Domain High-Resolution Radon"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-0191-2647","authenticated-orcid":false,"given":"Kai","family":"Zhuang","sequence":"first","affiliation":[{"name":"Department of Earth, Energy, and Environment, Faculty of Science, University of Calgary, Calgary, AB T2N 1N4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9726-789X","authenticated-orcid":false,"given":"Daniel","family":"Trad","sequence":"additional","affiliation":[{"name":"Department of Earth, Energy, and Environment, Faculty of Science, University of Calgary, Calgary, AB T2N 1N4, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2090-2100","authenticated-orcid":false,"given":"Amr","family":"Ibrahim","sequence":"additional","affiliation":[{"name":"Department of Physics, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Garottu, R. (1983). Simultaneous recording of several vibroseis seismic lines. SEG Technical Program Expanded Abstracts 1983, Society of Exploration Geophysicists.","DOI":"10.1190\/1.1893848"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Beasley, C.J., Chambers, R.E., and Jiang, Z. (1998). A new look at simultaneous sources. SEG Technical Program Expanded Abstracts 1998, Society of Exploration Geophysicists.","DOI":"10.1190\/1.1820149"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1190\/1.2954033","article-title":"A new look at marine simultaneous sources","volume":"27","author":"Beasley","year":"2008","journal-title":"Lead. Edge"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"Q9","DOI":"10.1190\/1.3556597","article-title":"Separation of blended data by iterative estimation and subtraction of blending interference noise","volume":"76","author":"Mahdad","year":"2011","journal-title":"Geophysics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"WD37","DOI":"10.1190\/geo2015-0078.1","article-title":"Independent simultaneous source acquisition and processing","volume":"80","author":"Abma","year":"2015","journal-title":"Geophysics"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1190\/1.2954035","article-title":"Changing the mindset in seismic data acquisition","volume":"27","author":"Berkhout","year":"2008","journal-title":"Lead. Edge"},{"key":"ref_7","unstructured":"Lin, T., and Herrmann, F. (2009, January 8\u201311). Designing Simultaneous Acquisitions with Compressive Sensing. Proceedings of the 71st EAGE Conference and Exhibition Incorporating SPE EUROPEC, Amsterdam, The Netherlands."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Ibrahim, A. (2015). Separating Simultaneous Seismic Sources Using Robust Inversion of Radon and Migration Operators. [Ph.D. Thesis, University of Alberta].","DOI":"10.1190\/geo2015-0044.1"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1560","DOI":"10.1190\/1.1836829","article-title":"Minimum weighted norm interpolation of seismic records","volume":"69","author":"Liu","year":"2004","journal-title":"Geophysics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1071\/EG14051","article-title":"Deblending using a space-varying median filter","volume":"46","author":"Chen","year":"2015","journal-title":"Explor. Geophys."},{"key":"ref_11","unstructured":"Mahmoudian, F., Curtis, J., De Meersman, K., Kennedy, R., and Staples, G. (2024, June 25). Deblending of Simultaneous Source Data. Available online: https:\/\/geoconvention.com\/wp-content\/uploads\/abstracts\/2023\/91390-deblending-of-simultaneous-source-.pdf."},{"key":"ref_12","unstructured":"Stanton, A., and Wilkinson, K. (2018). Robust deblending of simultaneous source seismic data. arXiv."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"A59","DOI":"10.1190\/1.3141895","article-title":"The concept of double blending: Combining incoherent shooting with incoherent sensing","volume":"74","author":"Berkhout","year":"2009","journal-title":"Geophysics"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Jiang, Z., and Abma, R. (2010). An analysis on the simultaneous imaging of simultaneous source data. SEG Technical Program Expanded Abstracts 2010, Society of Exploration Geophysicists.","DOI":"10.1190\/1.3513493"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2727","DOI":"10.1190\/1.1441893","article-title":"Velocity-stack and slant-stack stochastic inversion","volume":"50","author":"Thorson","year":"1985","journal-title":"Geophysics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1190\/1.1443253","article-title":"Suppression of multiple reflections using the Radon transform","volume":"57","author":"Foster","year":"1992","journal-title":"Geophysics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1190\/1.1543224","article-title":"Latest views of the sparse Radon transform","volume":"68","author":"Trad","year":"2003","journal-title":"Geophysics"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Trad, D., Hargreaves, N., verWest, B., and Wombell, R. (2004). Multiple Attenuation Using an Apex Shift Radon Transform. SEG Expanded Abstracts, Society of Exploration Geophysicists.","DOI":"10.4043\/16944-MS"},{"key":"ref_19","unstructured":"Claerbout, J.F. (1992). Earth Soundings Analysis: Processing versus Inversion, Blackwell Scientific Publications."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/0021-9991(88)90115-5","article-title":"Fast Ip solution of large, sparse, linear systems: Application to seismic travel time tomography","volume":"75","author":"Scales","year":"1988","journal-title":"J. Comput. Phys."},{"key":"ref_21","unstructured":"Brougois, A., Bourget, M., Lailly, P., Poulet, M., Ricarte, P., and Versteeg, R. (June, January 28). Marmousi, model and data. Proceedings of the EAEG workshop-practical aspects of seismic data inversion, Copenhagen, Denmark."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Naranjo, J.C., Ekstrand, E.J., Etgen, J., Hargrove, K.L., Brewton, J.G., Garcia, O., Astvatsaturov, G., Hite, D., Howieson, B., and Bai, B. (2011). Survey design and implementation of a multiple wide-azimuth towed streamer seismic acquisition strategy at the Tiber Discovery; deep water Gulf of Mexico, USA. SEG Technical Program Expanded Abstracts 2011, Society of Exploration Geophysicists.","DOI":"10.1190\/1.3627449"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/8\/344\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:31:27Z","timestamp":1760110287000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/17\/8\/344"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,7]]},"references-count":22,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["a17080344"],"URL":"https:\/\/doi.org\/10.3390\/a17080344","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,8,7]]}}}