{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:52:54Z","timestamp":1760230374979,"version":"build-2065373602"},"reference-count":58,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,7,24]],"date-time":"2022-07-24T00:00:00Z","timestamp":1658620800000},"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":["41930431","42104113","41904103","BK20210526"],"award-info":[{"award-number":["41930431","42104113","41904103","BK20210526"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Jiangsu Province of China","award":["41930431","42104113","41904103","BK20210526"],"award-info":[{"award-number":["41930431","42104113","41904103","BK20210526"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>High-precision elastic reverse-time migration (ERTM) imaging has always been one of the trends in the development of geophysics. However, current wavefield simulations using time-domain finite-difference (FD) approaches in ERTM have second-order temporal accuracy, resulting in travel time changes and waveform distortion in wavefield propagation with large time steps, i.e., temporal dispersion. Errors caused by the temporal dispersion can lead to erroneous imaging locations and out-of-focus diffraction events. A new ERTM and its workflow are established here using temporal and spatial high-order FD accuracy wavefields and the vector-based imaging condition. Our method computes elastic vector-based wavefields by solving a P- and S-wave decomposition form of a quasi-stress\u2013velocity equation. An advanced finite-difference scheme is employed in the wavefield solution to achieve simulation with temporal fourth-order accuracy and spatial arbitrary even-order accuracy. The normalized dot-product imaging condition of the source and receiver P\/S wavefields is then applied to generate high-quality images. The elastic wavefield simulation and ERTM numerical examples presented here reveal that the anti-dispersion workflow can improve modeling and imaging accuracy. In addition, the field data application shows that our method can achieve reasonable and reliable ERTM images. This method can integrate the most advanced imaging techniques into this computational framework to improve imaging accuracy.<\/jats:p>","DOI":"10.3390\/rs14153542","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T01:42:13Z","timestamp":1658713333000},"page":"3542","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A High-Precision Elastic Reverse-Time Migration for Complex Geologic Structure Imaging in Applied Geophysics"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1664-0024","authenticated-orcid":false,"given":"Jinwei","family":"Fang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Deep Geomechanics & Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China"}]},{"given":"Ying","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Earth Science, Northeast Petroleum University, Daqing 163318, China"}]},{"given":"Hui","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Geophysics, China University of Petroleum, Changping, Beijing 102249, China"}]},{"given":"Hanming","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geophysics, China University of Petroleum, Changping, Beijing 102249, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1160-9922","authenticated-orcid":false,"given":"Qingchen","family":"Zhang","sequence":"additional","affiliation":[{"name":"Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430077, China"}]},{"given":"Ning","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Earth Science, Northeast Petroleum University, Daqing 163318, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,24]]},"reference":[{"key":"ref_1","unstructured":"Claerbout, J. (1985). Imaging the Earth\u2019s Interior, Blackwell."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1074","DOI":"10.1190\/tle32091074.1","article-title":"Tomographic full-waveform inversion (TFWI) by combining FWI and wave-equation migration velocity analysis","volume":"32","author":"Biondi","year":"2013","journal-title":"Lead Edge"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"R55","DOI":"10.1190\/geo2013-0291.1","article-title":"From tomography to FWI with a single objective function","volume":"79","author":"Alkhalifah","year":"2014","journal-title":"Geophysics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"R597","DOI":"10.1190\/geo2017-0775.1","article-title":"Full model wavenumber inversion (FMWI): Identifying sources of information for the illusive middle model wavenumbers","volume":"83","author":"Alkhalifah","year":"2018","journal-title":"Geophysics"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1109\/MSP.2017.2779165","article-title":"Retrieving low wavenumber information in FWI: An overview of the cycle-skipping phenomenon and solutions","volume":"35","author":"Hu","year":"2018","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"334","DOI":"10.1007\/s12182-020-00431-3","article-title":"A review on reflection-waveform inversion","volume":"17","author":"Yao","year":"2020","journal-title":"Pet. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3MJ","DOI":"10.1190\/1.1926579","article-title":"A brief history of seismic migration","volume":"70","author":"Bednar","year":"2005","journal-title":"Geophysics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1190\/1.1442363","article-title":"On the imaging of reflectors in the earth","volume":"52","author":"Bleistein","year":"1987","journal-title":"Geophysics"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1190\/1.1441751","article-title":"Kirchhoff elastic wave migration for the case of noncoincident source and receiver","volume":"49","author":"Kuo","year":"1984","journal-title":"Geophysics"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1007\/s12182-019-00388-y","article-title":"Target-oriented Gaussian beam migration using a modified ray tracing scheme","volume":"16","author":"Zhang","year":"2019","journal-title":"Pet. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1190\/1.1444783","article-title":"Multicomponent Kirchhoff migration","volume":"65","author":"Hokstad","year":"2000","journal-title":"Geophysics"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1190\/1.1440298","article-title":"Downward continuation of moveout-corrected seismograms","volume":"37","author":"Claerbout","year":"1972","journal-title":"Geophysics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1190\/1.1440899","article-title":"Wave equation migration with the phase-shift method","volume":"43","author":"Gazdag","year":"1978","journal-title":"Geophysics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1190\/1.1440826","article-title":"Migration by Fourier transform","volume":"43","author":"Stolt","year":"1978","journal-title":"Geophysics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1029\/93JB02518","article-title":"Wide-angle elastic wave one-way propagation in heterogeneous media and an elastic wave complex-screen method","volume":"99","author":"Wu","year":"1994","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"S207","DOI":"10.1190\/1.2969776","article-title":"Beamlet migration using local cosine basis","volume":"73","author":"Wu","year":"2008","journal-title":"Geophysics"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Whitmore, N.D. (1983). Iterative depth migration by backward time propagation. SEG Technical Program Expanded Abstracts, Society of Exploration Geophysicists.","DOI":"10.1190\/1.1893867"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1111\/j.1365-2478.1983.tb01060.x","article-title":"Migration by extrapolation of time-dependent boundary values","volume":"31","author":"McMechan","year":"1983","journal-title":"Geophys. Prospect."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"WA3","DOI":"10.1190\/1.3554411","article-title":"A stable TTI reverse time migration and its implementation","volume":"76","author":"Zhang","year":"2011","journal-title":"Geophysics"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"T121","DOI":"10.1190\/geo2018-0538.1","article-title":"Efficient modeling of wave propagation in a vertical transversely isotropic attenuative medium based on fractional Laplacian","volume":"84","author":"Zhu","year":"2019","journal-title":"Geophysics"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"T469","DOI":"10.1190\/geo2021-0084.1","article-title":"Pseudoelastic pure P-mode wave equation","volume":"86","author":"Sun","year":"2021","journal-title":"Geophysics"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"e2021JB023280","DOI":"10.1029\/2021JB023280","article-title":"Propagating seismic waves in VTI attenuating media using fractional viscoelastic wave equation","volume":"27","author":"Wang","year":"2022","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1190\/1.1442041","article-title":"Reverse-time migration of offset vertical seismic profiling data using the excitation-time imaging condition","volume":"51","author":"Chang","year":"1986","journal-title":"Geophysics"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1109\/PROC.1986.13486","article-title":"Pre-stack reverse-time migration for elastic waves with application to synthetic offset vertical seismic profiles","volume":"74","author":"Sun","year":"1986","journal-title":"Proc. IEEE"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"S1","DOI":"10.1190\/geo2014-0014.1","article-title":"Five ways to avoid storing source wavefield snapshots in 2D elastic prestack reverse time migration","volume":"80","author":"Nguyen","year":"2015","journal-title":"Geophysics"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"S111","DOI":"10.1190\/geo2016-0146.1","article-title":"Vector-based elastic reverse time migration based on scalar imaging condition","volume":"82","author":"Du","year":"2017","journal-title":"Geophysics"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"889","DOI":"10.1190\/1.1442147","article-title":"P-SV wave propagation in heterogeneous media: Velocity-stress finite-difference method","volume":"51","author":"Virieux","year":"1986","journal-title":"Geophysics"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Etgen, J.T., and Brandsberg-Dahl, S. (2009). The pseudo-analytical method: Application of pseudo-Laplacians to acoustic and acoustic anisotropic wave propagation. SEG Technical Program Expanded Abstracts, Society of Exploration Geophysicists.","DOI":"10.1190\/1.3255375"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1027","DOI":"10.1093\/gji\/ggt040","article-title":"Residual extrapolation operators for efficient wavefield construction","volume":"193","author":"Alkhalifah","year":"2013","journal-title":"Geophys. J. Int."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"T51","DOI":"10.1190\/geo2013-0174.1","article-title":"The optimized expansion based low-rank method for wavefield extrapolation","volume":"79","author":"Wu","year":"2014","journal-title":"Geophysics"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1093\/gji\/ggx543","article-title":"Efficient anisotropic quasi-P wavefield extrapolation using an isotropic low-rank approximation","volume":"213","author":"Zhang","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1111\/j.1365-2478.2012.01064.x","article-title":"Seismic wave extrapolation using lowrank symbol approximation","volume":"61","author":"Fomel","year":"2013","journal-title":"Geophys. Prospect."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"T157","DOI":"10.1190\/geo2013-0290.1","article-title":"Lowrank seismic-wave extrapolation on a staggered grid","volume":"79","author":"Fang","year":"2014","journal-title":"Geophysics"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1250","DOI":"10.1093\/gji\/ggu077","article-title":"An efficient finite-difference method with high-order accuracy in both time and space domains for modeling scalar-wave propagation","volume":"197","author":"Tan","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.jappgeo.2016.07.021","article-title":"General rectangular grid-based time-space domain high-order finite-difference methods for modeling scalar wave propagation","volume":"133","author":"Chen","year":"2016","journal-title":"J. Appl. Geophys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2160","DOI":"10.1785\/0120170068","article-title":"Modeling of the acoustic wave equation by staggered-grid finite-difference schemes with high-order temporal and spatial accuracy","volume":"107","author":"Ren","year":"2017","journal-title":"Bull. Seism. Soc. Am."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"844","DOI":"10.1093\/gji\/ggz059","article-title":"High-order temporal and implicit spatial staggered-grid finite-difference operators for modeling seismic wave propagation","volume":"217","author":"Ren","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"T259","DOI":"10.1190\/geo2018-0551.1","article-title":"Time-space-domain temporal high-order staggered-grid finite-difference schemes by combining orthogonality and pyramid stencils for 3D elastic-wave propagation","volume":"84","author":"Xu","year":"2019","journal-title":"Geophysics"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s10712-020-09607-3","article-title":"Viscoelastic Wave Simulation with High Temporal Accuracy Using Frequency-Dependent Complex Velocity","volume":"42","author":"Zhang","year":"2021","journal-title":"Surv. Geophys."},{"key":"ref_40","first-page":"1","article-title":"Elastic wave modeling with high-order temporal and spatial accuracies by a selectively modified and linearly optimized staggered-grid finite-difference scheme","volume":"60","author":"Zhou","year":"2022","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"S229","DOI":"10.1190\/1.2981241","article-title":"Isotropic angle-domain elastic reverse-time migration","volume":"73","author":"Yan","year":"2008","journal-title":"Geophysics"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"S489","DOI":"10.1190\/geo2018-0023.1","article-title":"Isotropic elastic reverse time migration using the phase-and amplitude-corrected vector P-and S-wavefields","volume":"83","author":"Yang","year":"2018","journal-title":"Geophysics"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"D13","DOI":"10.1190\/1.3431045","article-title":"2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media","volume":"75","author":"Zhang","year":"2010","journal-title":"Geophysics"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"T63","DOI":"10.1190\/geo2015-0184.1","article-title":"Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media","volume":"81","author":"Cheng","year":"2016","journal-title":"Geophysics"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"S173","DOI":"10.1190\/geo2016-0419.1","article-title":"Elastic wavefield separation based on the Helmholtz decomposition","volume":"82","author":"Zhu","year":"2017","journal-title":"Geophysics"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"C13","DOI":"10.1190\/geo2017-0138.1","article-title":"P-and S-decomposition in anisotropic media with localized low-rank approximations","volume":"83","author":"Wang","year":"2018","journal-title":"Geophysics"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"S383","DOI":"10.1190\/geo2015-0704.1","article-title":"Scalar and vector imaging based on wave mode decoupling for elastic reverse time migration in isotropic and transversely isotropic media","volume":"81","author":"Wang","year":"2016","journal-title":"Geophysics"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"104381","DOI":"10.1016\/j.cageo.2019.104381","article-title":"Elastic full-waveform inversion based on GPU accelerated temporal fourth-order finite-difference approximation","volume":"135","author":"Fang","year":"2020","journal-title":"Comput. Geosci."},{"key":"ref_49","first-page":"1","article-title":"Three-dimensional elastic full-waveform inversion using temporal fourth-order finite-difference approximation","volume":"19","author":"Fang","year":"2021","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"T361","DOI":"10.1190\/geo2020-0934.1","article-title":"Time-dispersion correction for arbitrary even-order Lax-Wendroff methods and the application on full-waveform inversion","volume":"86","author":"Ren","year":"2021","journal-title":"Geophysics"},{"key":"ref_51","first-page":"4166","article-title":"Time and space dispersion in finite difference and its influence on reverse time migration and full-waveform inversion","volume":"64","author":"Ren","year":"2021","journal-title":"Chin. J. Geophys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"801","DOI":"10.1109\/TGRS.2016.2615330","article-title":"Modeling elastic wave propagation using K-space operator-based temporal high-order staggered-grid finite-difference method","volume":"55","author":"Chen","year":"2016","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1190\/1.1442422","article-title":"Fourth-order finite-difference P-SV seismograms","volume":"53","author":"Levander","year":"1988","journal-title":"Geophysics"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"A37","DOI":"10.1190\/geo2020-0159.1","article-title":"Data-driven low-frequency signal recovery using deep-learning predictions in full-waveform inversion","volume":"85","author":"Fang","year":"2020","journal-title":"Geophysics"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"S315","DOI":"10.1190\/geo2016-0564.1","article-title":"Elastic least-squares reverse time migration","volume":"82","author":"Duan","year":"2017","journal-title":"Geophysics"},{"key":"ref_56","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"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"R129","DOI":"10.1190\/geo2017-0236.1","article-title":"3D elastic full-waveform inversion using P-wave excitation amplitude: Application to ocean bottom cable field data","volume":"83","author":"Oh","year":"2018","journal-title":"Geophysics"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"871","DOI":"10.1109\/TGRS.2020.2994959","article-title":"Elastic full waveform inversion with angle decomposition and wavefield decoupling","volume":"59","author":"Luo","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3542\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:55:37Z","timestamp":1760140537000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3542"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,24]]},"references-count":58,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14153542"],"URL":"https:\/\/doi.org\/10.3390\/rs14153542","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,7,24]]}}}