{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:17:12Z","timestamp":1760149032135,"version":"build-2065373602"},"reference-count":55,"publisher":"MDPI AG","issue":"13","license":[{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"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":["42030806","42074120","42274093","42174167"],"award-info":[{"award-number":["42030806","42074120","42274093","42174167"]}],"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 study of the numerical simulation of seismoelectric effects is very helpful for understanding the theory and mechanism of seismoelectric activities. Quasi-static approximation is widely used in the numerical simulation of seismoelectric fields. However, numerical errors occur when the model domain is not within the near-field area of EM waves or the medium is of high salinity. To solve this problem, we propose a time-domain finite-element algorithm (FETD) based on the full-wave electromagnetic (EM) equation to simulate seismoelectric waves in 2D PSVTM mode. By decomposing the electrokinetic coupling equations into two independent ones, we can solve the seismoelectric waves separately. In our implementation, we focus our attention on the solution of EM waves based on vector\u2013scalar potentials, while using the open-source code SPECFEM2D to explicitly solve Biot\u2019s equations and obtain the relative fluid\u2013solid displacement, which is taken as the source for the complete Maxwell\u2019s equations. In the solution of EM wave fields, we use an unconditionally stable implicit method for time discretization. Computation efficiency can be improved by combining explicit and implicit recursions. After conducting the mathematical formulation, we first validate our method by comparing its results with the analytic solutions for a half-space and a two-layer model, as well as with a quasi-static approximation method. Moreover, we run numerical simulations and wavefield analyses on an elliptical hydrocarbon reservoir, and reveal that the interface responses are promising for the identification of underground interfaces and hydrocarbon reservoir exploration.<\/jats:p>","DOI":"10.3390\/rs15133321","type":"journal-article","created":{"date-parts":[[2023,6,30]],"date-time":"2023-06-30T01:02:41Z","timestamp":1688086961000},"page":"3321","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Simulation of Seismoelectric Waves Using Time-Domain Finite-Element Method in 2D PSVTM Mode"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5305-6169","authenticated-orcid":false,"given":"Jun","family":"Li","sequence":"first","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Changchun","family":"Yin","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3634-9832","authenticated-orcid":false,"given":"Yunhe","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}]},{"given":"Luyuan","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4326-5204","authenticated-orcid":false,"given":"Xinpeng","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Sciences and Technology, Jilin University, Changchun 130026, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"15678","DOI":"10.1103\/PhysRevB.50.15678","article-title":"Governing equations for the coupled electromagnetics and acoustics of porous media","volume":"50","author":"Pride","year":"1994","journal-title":"Phys. Rev. B Condens. Matter"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1190\/1.1444093","article-title":"Measurement of the seismoelectric response from a shallow boundary","volume":"61","author":"Butler","year":"1996","journal-title":"Geophysics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"28055","DOI":"10.1029\/2000JB900341","article-title":"Experimental studies of seismoelectric conversions in fluid-saturated porous media","volume":"105","author":"Zhu","year":"2000","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_4","first-page":"873","article-title":"Seismoelectromagnetic waves radiated by a double couple source in a saturated porous medium","volume":"181","author":"Gao","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1007\/s11589-009-0071-9","article-title":"A new numerical technique for simulating the coupled seismic and electromagnetic waves in layered porous media","volume":"23","author":"Ren","year":"2010","journal-title":"Earthq. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2460","DOI":"10.1002\/2015JB012381","article-title":"Seismo-electromagnetic thin-bed responses: Natural signal enhancements?","volume":"121","author":"Grobbe","year":"2016","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"24745","DOI":"10.1029\/97JB02936","article-title":"Electroseismic waves from point sources in layered media","volume":"102","author":"Haartsen","year":"1997","journal-title":"J. Geophys. Res. Atmos."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1190\/1.1436931","article-title":"Geophysical applications of electrokinetic conversion","volume":"12","author":"Thompson","year":"1993","journal-title":"Lead. Edge"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1093\/gji\/ggz249","article-title":"The effect of rock permeability and porosity on seismoelectric conversion: Experiment and analytical modelling","volume":"219","author":"Peng","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1093\/gji\/ggaa174","article-title":"Measurements of the seismoelectric responses in a synthetic porous rock","volume":"222","author":"Wang","year":"2020","journal-title":"Geophys. J. Int."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1121\/1.416018","article-title":"Electroseismic wave properties","volume":"100","author":"Pride","year":"1996","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"G9","DOI":"10.1190\/1.2428267","article-title":"Seismoelectric imaging of shallow targets","volume":"72","author":"Haines","year":"2007","journal-title":"Geophysics"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1111\/j.1365-246X.2008.03828.x","article-title":"Evidence of the theoretically predicted seismo-magnetic conversion","volume":"174","author":"Bordes","year":"2008","journal-title":"Geophys. J. Int."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"N29","DOI":"10.1190\/1.3592984","article-title":"Seismoelectric interface response: Experimental results and forward model","volume":"76","author":"Schakel","year":"2011","journal-title":"Geophysics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1093\/gji\/ggw144","article-title":"Numerical simulation of seismo-electromagnetic fields associated with a fault in a porous medium","volume":"206","author":"Ren","year":"2016","journal-title":"Geophys. J. Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"7190","DOI":"10.1002\/2016JB013703","article-title":"Seismoelectric responses to an explosive source in a fluid above a fluid-saturated porous medium","volume":"122","author":"Gao","year":"2017","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_17","first-page":"418","article-title":"Simulation of seismoelectric waves using finite-difference frequency-domain method: 2D SHTE mode","volume":"216","author":"Gao","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"N57","DOI":"10.1190\/1.2357789","article-title":"Seismoelectric numerical modeling on a grid","volume":"71","author":"Haines","year":"2006","journal-title":"Geophysics"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2136\/vzj2013.06.0106","article-title":"Seismoelectric Conversion for the Detection of Porous Medium Interfaces between Wetting and Nonwetting Fluids","volume":"13","author":"Smeulders","year":"2014","journal-title":"Vadose Zone J."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1093\/gji\/ggac444","article-title":"Estimation of fluid salinity using coseismic electric signal generated by an earthquake","volume":"233","author":"Ma","year":"2022","journal-title":"Geophys. J. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/jge\/gxac089","article-title":"Numerical investigation on seismoelectric wave fields in porous media: Porosity and permeability","volume":"20","author":"Peng","year":"2023","journal-title":"J. Geophys. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Grobbe, N., Revil, A., Zhu, Z., and Slob, E. (2020). Seismoelectric Exploration: Theory, Experiments, and Applications, John Wiley & Sons.","DOI":"10.1002\/9781119127383"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1016\/j.jcis.2006.06.051","article-title":"Chemico-electromechanical coupling in microporous media","volume":"302","author":"Revil","year":"2006","journal-title":"J. Colloid Interface Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1093\/gji\/ggt198","article-title":"Seismoelectric wave propagation numerical modelling in partially saturated materials","volume":"194","author":"Warden","year":"2013","journal-title":"Geophys. J. Int."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"918","DOI":"10.1093\/gji\/ggw431","article-title":"Dependence of shear wave seismoelectrics on soil textures: A numerical study in the vadose zone","volume":"208","author":"Zyserman","year":"2016","journal-title":"Geophys. J. Int."},{"key":"ref_26","unstructured":"Jougnot, D. New approach to up-scale the frequency-dependent effective excess charge density for seismoelectric modeling. Proceedings of the SEG Technical Program Expanded Abstracts."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"WB19","DOI":"10.1190\/geo2020-0524.1","article-title":"Predicting the frequency-dependent effective excess charge density: A new upscaling approach for seismoelectric modeling","volume":"86","author":"Jougnot","year":"2021","journal-title":"Geophysics"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1121\/1.1908239","article-title":"Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range","volume":"28","author":"Biot","year":"1956","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"F27","DOI":"10.1190\/geo2015-0337.1","article-title":"Seismoelectromagnetic homogeneous space Green\u2019s functions","volume":"81","author":"Slob","year":"2016","journal-title":"Geophysics"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"7958","DOI":"10.1029\/2010JB007958","article-title":"Electromagnetic field generated by a finite fault due to electrokinetic effect","volume":"116","author":"Hu","year":"2011","journal-title":"J. Geophys. Res."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"C53","DOI":"10.1190\/geo2022-0386.1","article-title":"Seismoelectric waves generated by a point source in horizontally stratified vertical transversely isotropic porous media","volume":"88","author":"Cheng","year":"2023","journal-title":"Geophysics"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.jappgeo.2010.07.004","article-title":"Finite element modeling of SHTE and PSVTM electroseismics","volume":"72","author":"Zyserman","year":"2010","journal-title":"J. Appl. Geophys."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.ijggc.2014.12.009","article-title":"Borehole seismoelectric logging using a shear-wave source: Possible application to CO2 disposal?","volume":"33","author":"Zyserman","year":"2015","journal-title":"Int. J. Greenh. Gas Control"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1111\/j.1365-246X.2005.02501.x","article-title":"A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling","volume":"160","author":"Pain","year":"2005","journal-title":"Geophys. J. Int."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1927","DOI":"10.1111\/1365-2478.12958","article-title":"Seismoelectric numerical simulation in 2D vertical transverse isotropic poroelastic medium","volume":"68","author":"Tohti","year":"2020","journal-title":"Geophys. Prospect."},{"key":"ref_36","first-page":"4471","article-title":"Numerical simulation of seismoelectric wavefields in 3D orthorhombic poroelastic medium","volume":"65","author":"Tohti","year":"2022","journal-title":"Chin. J. Geophys."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"T135","DOI":"10.1190\/geo2021-0235.1","article-title":"A high-order finite-difference scheme for time-domain modeling of time-varying seismoelectric waves","volume":"87","author":"Ji","year":"2022","journal-title":"Geophysics"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"8066","DOI":"10.1002\/2017JB014251","article-title":"Comparison of full and quasi-static seismoelectric analytically based modeling","volume":"122","author":"Gao","year":"2017","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1111\/j.1365-246X.2008.03907.x","article-title":"Spectral-element simulations of wave propagation in porous media","volume":"175","author":"Morency","year":"2008","journal-title":"Geophys. J. Int."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"N1","DOI":"10.1190\/1.2399458","article-title":"Field tests of electroseismic hydrocarbon detection","volume":"72","author":"Thompson","year":"2007","journal-title":"Geophysics"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1529","DOI":"10.1785\/BSSA0670061529","article-title":"Absorbing boundary conditions for acoustic and elastic wave equations","volume":"67","author":"Clayton","year":"1977","journal-title":"Bull. Seism. Soc. Am."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3919","DOI":"10.1063\/1.338584","article-title":"New vector finite elements for three-dimensional magnetic field computation","volume":"61","author":"Barton","year":"1987","journal-title":"J. Appl. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3145","DOI":"10.1109\/20.34388","article-title":"On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents","volume":"25","author":"Biro","year":"1989","journal-title":"IEEE Trans. Magn."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Allaire, G.S.M.K. (2008). Numerical Linear Algebra, Springer.","DOI":"10.1007\/978-0-387-68918-0"},{"key":"ref_45","unstructured":"Hughes, T.J.R. (1987). The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Courier Corporation."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1111\/j.1365-246X.2010.04536.x","article-title":"Stability of the high-order finite elements for acoustic or elastic wave propagation with high-order time stepping","volume":"181","author":"Sen","year":"2010","journal-title":"Geophys. J. Int."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1016\/j.parco.2005.07.004","article-title":"Hybrid scheduling for the parallel solution of linear systems","volume":"32","author":"Amestoy","year":"2006","journal-title":"Parallel Comput."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"ESE 5-1","DOI":"10.1029\/2001JB000316","article-title":"Full waveform numerical simulations of seismoelectromagnetic wave conversions in fluid-saturated stratified porous media","volume":"107","author":"Garambois","year":"2002","journal-title":"J. Geophys. Res. Solid Earth"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1093\/gji\/ggz010","article-title":"Quantifying interface responses with seismoelectric spectral ratios","volume":"217","author":"Dzieran","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1999","DOI":"10.1093\/gji\/ggy101","article-title":"An analytical solution to assess the SH seismoelectric response of the vadose zone","volume":"213","author":"Monachesi","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"108513","DOI":"10.1016\/j.petrol.2021.108513","article-title":"Electroseismic and seismoelectric responses at irregular interfaces: Possible application to reservoir exploration","volume":"202","author":"Wang","year":"2021","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Sheriff, R.E., and Geldart, L.P. (1995). Exploration Seismology, Cambridge University Press.","DOI":"10.1017\/CBO9781139168359"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1417","DOI":"10.1190\/1.1487087","article-title":"Seismoelectric wave conversions in porous media: Field measurements and transfer function analysis","volume":"66","author":"Garambois","year":"2001","journal-title":"Geophysics"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Crespy, A., Revil, A., Linde, N., Byrdina, S., Jardani, A., Bol\u00e8ve, A., and Henry, P. (2008). Detection and localization of hydromechanical disturbances in a sandbox using the self-potential method. J. Geophys. Res. Atmos., 113.","DOI":"10.1029\/2007JB005042"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"N19","DOI":"10.1190\/1.3279833","article-title":"Stochastic joint inversion of 2D seismic and seismoelectric signals in linear poroelastic materials: A numerical investigation","volume":"75","author":"Jardani","year":"2010","journal-title":"Geophysics"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/13\/3321\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:03:34Z","timestamp":1760126614000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/13\/3321"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,29]]},"references-count":55,"journal-issue":{"issue":"13","published-online":{"date-parts":[[2023,7]]}},"alternative-id":["rs15133321"],"URL":"https:\/\/doi.org\/10.3390\/rs15133321","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2023,6,29]]}}}