{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T11:06:02Z","timestamp":1790075162940,"version":"4.0.1"},"reference-count":35,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2026,9,19]],"date-time":"2026-09-19T00:00:00Z","timestamp":1789776000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB3905004"],"award-info":[{"award-number":["2023YFB3905004"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Seismic exploration has progressively expanded into urban fringe regions and areas with intensive human activities, where anthropogenic interference has increased markedly, aggravating the background noise problem and substantially affecting the accuracy of subsequent seismic data processing. Conventional denoising methods struggle to cope with such complex noise patterns and typically rely on manually designed parameter settings, which limits their ability to suppress complex background noise in real seismic data. With the rapid development of deep learning, various neural-network-based methods have been introduced for seismic data denoising. However, existing deep learning approaches are constrained by the high resolution of seismic data and limited computational resources and therefore commonly perform denoising on cropped data patches rather than on the complete seismic section. This limitation weakens the network\u2019s capability to perceive global contextual information, degrading denoising performance and potentially introducing blocking artifacts. To address these issues, we propose a fluctuation-prior-regularized denoising framework that explicitly decomposes the complete seismic data denoising task into global and local denoising subtasks, enabling globally consistent denoising under complex conditions. To overcome the limitations of CNNs and Transformers, we adopt Retentive Networks Meet Vision Transformers (RMT) as the backbone for feature extraction in this work. And a fluctuation-prior-constrained local denoising mechanism is introduced, allowing local patches to indirectly capture global information. In addition, a grouped regularization strategy for global and local tasks is proposed, enabling both optimization tasks to better capture their respective task-specific characteristics. Experimental results on noisy shot gathers constructed from field records and on field-recorded background noise demonstrate that the proposed DFRSeisnet achieves superior denoising performance while effectively alleviating blocking artifacts.<\/jats:p>","DOI":"10.3390\/s26185938","type":"journal-article","created":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:21:48Z","timestamp":1790072508000},"page":"5938","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["DFRSeisNet: Fluctuation-Prior-Regularized Background Noise Attenuation for Seismic Signal Denoising"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2218-0853","authenticated-orcid":false,"given":"Fei","family":"Deng","sequence":"first","affiliation":[{"name":"College of Computer Science and Cyber Security, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3028-9079","authenticated-orcid":false,"given":"Liang","family":"Pang","sequence":"additional","affiliation":[{"name":"College of Computer Science and Cyber Security, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"validation","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-2367-5153","authenticated-orcid":false,"given":"Shuang","family":"Wang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Earth Exploration and Information Techniques of Ministry of Education, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"supervision","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"}]},{"given":"Wen","family":"Peng","sequence":"additional","affiliation":[{"name":"Research and Development Center, Bureau of Geophysical Prospecting, China National Petroleum Corporation, Zhuozhou 072751, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"data-curation","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1785\/0120030050","article-title":"Assessment of the urbanization effect on seismic response","volume":"94","author":"Boutin","year":"2004","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2280","DOI":"10.1785\/0220230408","article-title":"Imaging urban hidden faults with ambient noise recorded by dense seismic arrays","volume":"95","author":"Biondi","year":"2024","journal-title":"Seismol. Res. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"147215","DOI":"10.1109\/ACCESS.2019.2946443","article-title":"Mine fracturing monitoring analysis based on high-precision distributed wireless microseismic acquisition station","volume":"7","author":"Qiao","year":"2019","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1029\/2018JB016661","article-title":"Reliable real-time seismic signal\/noise discrimination with machine learning","volume":"124","author":"Meier","year":"2019","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1785\/0120100182","article-title":"A comparison of seismic instrument noise coherence analysis techniques","volume":"101","author":"Ringler","year":"2011","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_6","first-page":"3000312","article-title":"Investigation and practical applications of seismo-electromagnetic joint exploration","volume":"74","author":"Qiao","year":"2024","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"4668","DOI":"10.1109\/TGRS.2017.2697444","article-title":"Seismic exploration random noise on land: Modeling and application to noise suppression","volume":"55","author":"Li","year":"2017","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3568671","article-title":"A survey on seismic sensor based target detection, localization, identification, and activity recognition","volume":"55","author":"Choudhary","year":"2023","journal-title":"ACM Comput. Surv."},{"key":"ref_9","first-page":"655","article-title":"Statistical features of the random noise in land seismic prospecting","volume":"60","author":"Zhong","year":"2017","journal-title":"Chin. J. Geophys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1266","DOI":"10.1109\/PROC.1984.13016","article-title":"Seismic data gathering","volume":"72","author":"Cooper","year":"1984","journal-title":"Proc. IEEE"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"V437","DOI":"10.1190\/geo2023-0762.1","article-title":"Robust seismic data denoising via self-supervised deep learning","volume":"89","author":"Li","year":"2024","journal-title":"Geophysics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5913016","DOI":"10.1109\/TGRS.2022.3158389","article-title":"Unsupervised erratic seismic noise attenuation with robust deep convolutional autoencoders","volume":"60","author":"Qian","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1584","DOI":"10.1190\/1.1443547","article-title":"Single-channel digital filter design for seismic applications","volume":"59","author":"Linville","year":"1994","journal-title":"Geophysics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1016\/j.jappgeo.2016.03.007","article-title":"Ground-roll noise extraction and suppression using high-resolution linear Radon transform","volume":"128","author":"Hu","year":"2016","journal-title":"J. Appl. Geophys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"V71","DOI":"10.1190\/geo2011-0172.1","article-title":"Seismic data interpolation and denoising in the frequency\u2013wavenumber domain","volume":"77","author":"Naghizadeh","year":"2012","journal-title":"Geophysics"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"6609","DOI":"10.1007\/s10586-018-2355-0","article-title":"Seismic data processing method based on wavelet transform for de-noising","volume":"22","author":"Lu","year":"2019","journal-title":"Clust. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1007\/s11770-005-0034-4","article-title":"The second-generation wavelet transform and its application in denoising of seismic data","volume":"2","author":"Cao","year":"2005","journal-title":"Appl. Geophys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/TNNLS.2022.3205421","article-title":"DeepSeg: Deep segmental denoising neural network for seismic data","volume":"34","author":"Iqbal","year":"2023","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_19","first-page":"7502805","article-title":"Self-supervised learning for seismic data reconstruction and denoising","volume":"19","author":"Meng","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_20","first-page":"5902813","article-title":"A deep learning method for denoising based on a fast and flexible convolutional neural network","volume":"60","author":"Li","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_21","first-page":"7503405","article-title":"A convolutional autoencoder method for simultaneous seismic data reconstruction and denoising","volume":"19","author":"Jiang","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_22","first-page":"8022205","article-title":"Unsupervised CNN based on self-similarity for seismic data denoising","volume":"19","author":"Fang","year":"2021","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_23","first-page":"5900809","article-title":"Desert seismic low-frequency noise attenuation using low-rank decomposition-based denoising convolutional neural network","volume":"60","author":"Ma","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"5915817","DOI":"10.1109\/TGRS.2022.3178212","article-title":"Multiscale spatial attention network for seismic data denoising","volume":"60","author":"Dong","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_25","first-page":"5907525","article-title":"Self-supervised pretraining transformer for seismic data denoising","volume":"62","author":"Wang","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_26","first-page":"5919715","article-title":"STUGAN: An integrated Swin transformer-based generative adversarial networks for seismic data reconstruction and denoising","volume":"62","author":"Zhang","year":"2024","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","first-page":"7501905","article-title":"Swin transformer for seismic denoising","volume":"21","author":"Li","year":"2024","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3142","DOI":"10.1109\/TIP.2017.2662206","article-title":"Beyond a Gaussian denoiser: Residual learning of deep CNN for image denoising","volume":"26","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Image Process."},{"key":"ref_29","first-page":"380","article-title":"Digital image reconstruction and resampling for geometric manipulation","volume":"SMC-5","author":"Simon","year":"1975","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_30","unstructured":"Kendall, A., Gal, Y., and Cipolla, R. (2018). Multi-task learning using uncertainty to weigh losses for scene geometry and semantics. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Fan, Q., Huang, H., Chen, M., Liu, H., and He, R. (2024). RMT: Retentive networks meet vision transformers. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, IEEE.","DOI":"10.1109\/CVPR52733.2024.00539"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015). U-Net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Shi, W., Caballero, J., Husz\u00e1r, F., Totz, J., Aitken, A.P., Bishop, R., Rueckert, D., and Wang, Z. (2016). Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE.","DOI":"10.1109\/CVPR.2016.207"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (2016). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE.","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1150","DOI":"10.1190\/1.1444415","article-title":"3-D seismic attributes using a semblance-based coherency algorithm","volume":"63","author":"Marfurt","year":"1998","journal-title":"Geophysics"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5938\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T10:27:36Z","timestamp":1790072856000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/18\/5938"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,19]]},"references-count":35,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["s26185938"],"URL":"https:\/\/doi.org\/10.3390\/s26185938","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,19]]}}}