{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T14:23:36Z","timestamp":1760711016592,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T00:00:00Z","timestamp":1659916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences","award":["XDA14020102","42174150","YDZJ202102CXJD016"],"award-info":[{"award-number":["XDA14020102","42174150","YDZJ202102CXJD016"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["XDA14020102","42174150","YDZJ202102CXJD016"],"award-info":[{"award-number":["XDA14020102","42174150","YDZJ202102CXJD016"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Jilin Province Science and Technology Development Program","award":["XDA14020102","42174150","YDZJ202102CXJD016"],"award-info":[{"award-number":["XDA14020102","42174150","YDZJ202102CXJD016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>A new algorithm is developed to accurately compute the electromagnetic (EM) fields in the layered biaxial anisotropic media. We enclose the computational region in an infinitely long rectangular region by four vertical truncation planes and establish the corresponding algorithm to approximate the EM fields in the entire space. The EM fields in this region are expanded as a two-dimensional (2-D) Fourier series of the transverse variables. By using the spectral state variable method, the generalized reflection coefficient matrices and transmission matrices are then derived to determine the Fourier coefficients per layer. Therefore, we can obtain the spatial-domain EM fields by summing the 2-D Fourier series. To enhance the accuracy and efficiency of this algorithm, we apply the method of images to estimate the influence of the artificial boundaries on the EM fields at the observer. We then further develop a quantitative principle to choose the proper size of the region according to the desired error tolerance. With the proper choice, the summation of the series can achieve satisfactory accuracy. This algorithm is finally applied to simulate the responses of the triaxial logging tool in transversely isotropic and biaxial anisotropic media and is verified through comparisons to the other method.<\/jats:p>","DOI":"10.3390\/rs14153836","type":"journal-article","created":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T04:16:55Z","timestamp":1660018615000},"page":"3836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Finite-Region Approximation of EM Fields in Layered Biaxial Anisotropic Media"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5804-8600","authenticated-orcid":false,"given":"Zhuangzhuang","family":"Kang","sequence":"first","affiliation":[{"name":"International Center for Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1035-4123","authenticated-orcid":false,"given":"Hongnian","family":"Wang","sequence":"additional","affiliation":[{"name":"International Center for Computational Method and Software, College of Physics, Jilin University, Changchun 130012, China"}]},{"given":"Changchun","family":"Yin","sequence":"additional","affiliation":[{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130012, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1190\/1.1441529","article-title":"Review of elastic and electromagnetic wave propagation in horizontally layered media","volume":"48","author":"Ursin","year":"1983","journal-title":"Geophysics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1109\/TAP.2013.2286835","article-title":"Electromagnetic response of anisotropic laminates to distributed sources","volume":"62","author":"Zhong","year":"2014","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"G115","DOI":"10.1190\/1.2197492","article-title":"MMT forward modeling for a layered earth with arbitrary anisotropy","volume":"71","author":"Yin","year":"2006","journal-title":"Geophysics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1376","DOI":"10.1109\/8.898770","article-title":"Petrophysics of magnetic dipole fields in an anisotropic earth","volume":"48","author":"Howard","year":"2000","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1109\/TAP.2021.3098522","article-title":"3-D finite volume modeling for LWD azimuthal propagation resistivity tool with multiple annular antenna recesses using coupled potentials on cylindrical grids","volume":"70","author":"Yu","year":"2022","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1109\/LGRS.2018.2813972","article-title":"Accelerated computation of triaxial induction tool response for arbitrarily deviated wells in planar-stratified transversely isotropic formations","volume":"15","author":"Li","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1863","DOI":"10.1109\/TAP.2018.2803210","article-title":"Computation of tensor Green\u2019s functions in uniaxial planar-stratified media with a rescaled equivalent boundary approach","volume":"66","author":"Xing","year":"2018","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_8","first-page":"1811","article-title":"A hybrid algorithm for LWD azimuthal electromagnetic responses with annular grooved drill collar","volume":"64","author":"Wang","year":"2021","journal-title":"Chin. J. Geophys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1109\/TGRS.2006.888139","article-title":"Cylindrical FDTD analysis of LWD tools through anisotropic dipping-layered earth media","volume":"45","author":"Lee","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1109\/LAWP.2003.820697","article-title":"Response of a point source embedded in a layered medium","volume":"2","author":"Chew","year":"2003","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3107","DOI":"10.1109\/TGRS.2013.2269714","article-title":"Characteristics of the sum of cross-components of triaxial induction logging tool in layered anisotropic formation","volume":"52","author":"Hong","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1109\/8.558666","article-title":"Multilayered media Green\u2019s functions in integral equation formulations","volume":"45","author":"Michalski","year":"1997","journal-title":"IEEE Trans. Antennas Propagat."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1109\/TMTT.2005.860304","article-title":"Singularity subtraction for evaluation of Green\u2019s functions for multilayer media","volume":"54","author":"Simsek","year":"2006","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_14","unstructured":"Chew, W.C. (1995). Waves and Fields in Inhomogenous Media, Wiley-IEEE Press."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1111\/j.1365-246X.2007.03390.x","article-title":"Electromagnetic fields in planarly layered anisotropic media","volume":"170","author":"Ursin","year":"2007","journal-title":"Geophys. J. Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1109\/TAP.1987.1144069","article-title":"Electromagnetic scattering by stratified inhomogeneous anisotropic media","volume":"35","author":"Morgan","year":"1987","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/8.558667","article-title":"A spectral recursive transformation method for electromagnetic waves in generalized anisotropic layered media","volume":"45","author":"Yang","year":"1997","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9120","DOI":"10.1109\/TGRS.2020.3040193","article-title":"An analytic algorithm for dipole electromagnetic field in fully anisotropic planar-stratified media","volume":"59","author":"Hong","year":"2021","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2071","DOI":"10.1109\/TGRS.2019.2952952","article-title":"Electromagnetic logging response in multilayered formation with arbitrary uniaxially electrical anisotropy","volume":"58","author":"Hu","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"053303","DOI":"10.1103\/PhysRevE.89.053303","article-title":"Tensor Green\u2019s function evaluation in arbitrarily anisotropic layered media using complex-plane Gauss-Laguerre quadrature","volume":"89","author":"Sainath","year":"2014","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5758","DOI":"10.1109\/TGRS.2018.2825430","article-title":"Electromagnetic waves in multilayered generalized anisotropic media","volume":"56","author":"Hu","year":"2018","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1644","DOI":"10.1109\/TGRS.2019.2947279","article-title":"An analytic algorithm for electromagnetic field in planar-stratified biaxial anisotropic formation","volume":"58","author":"Li","year":"2020","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"D71","DOI":"10.1190\/geo2015-0105.1","article-title":"A semianalytic solution to the response of a triaxial induction logging tool in a layered biaxial anisotropic formation","volume":"81","author":"He","year":"2016","journal-title":"Geophysics"},{"key":"ref_24","first-page":"4277","article-title":"Study of multi-component induction logging in layered crossbedding formations by using propagation matrix method","volume":"63","author":"Kang","year":"2020","journal-title":"Chin. J. Geophys."},{"key":"ref_25","first-page":"3026","article-title":"Study on the responses of multi-component induction logging tool in layered orthorhombic anisotropy formations by using propagator matrix method","volume":"53","author":"Yao","year":"2010","journal-title":"Chin. J. Geophys."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3383","DOI":"10.1109\/TGRS.2012.2183135","article-title":"Efficient and reliable simulation of multicomponent induction logging response in horizontally stratified inhomogeneous TI formations by numerical mode matching method","volume":"50","author":"Wang","year":"2012","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"D31","DOI":"10.1190\/geo2015-0610.1","article-title":"Fast inversion of triaxial induction data in dipping crossbedded formations","volume":"82","author":"Wang","year":"2017","journal-title":"Geophysics"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4483","DOI":"10.1109\/TGRS.2011.2142187","article-title":"Adaptive regularization iterative inversion of array multicomponent induction well logging datum in a horizontally stratified inhomogeneous TI formation","volume":"49","author":"Wang","year":"2011","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_29","first-page":"1","article-title":"Fourier series approximation of tensor Green\u2019s function in biaxial anisotropic media","volume":"19","author":"Kang","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6911","DOI":"10.1109\/TGRS.2014.2305669","article-title":"An efficient algorithm of both Fr\u00e9chet derivative and inversion of MCIL data in a deviated well in a horizontally layered TI formation based on TLM modeling","volume":"52","author":"Yang","year":"2014","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_31","unstructured":"Kong, J.A. (2000). Electromagnetic Waves Theory, EMW Publishing."},{"key":"ref_32","first-page":"588","article-title":"Foundation of the tensor induction well logging","volume":"42","author":"Zhdanov","year":"2001","journal-title":"Petrophysics"}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3836\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:05:57Z","timestamp":1760141157000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/14\/15\/3836"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,8]]},"references-count":32,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2022,8]]}},"alternative-id":["rs14153836"],"URL":"https:\/\/doi.org\/10.3390\/rs14153836","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2022,8,8]]}}}