{"title":"MT 的三维轴向各向异性响应研究","authors":"Xiao Liu, Qi-Ji Sun","doi":"10.3389/feart.2024.1454962","DOIUrl":null,"url":null,"abstract":"Electrical anisotropy has a significant impact on the observation data of the magnetotelluric (MT) method; therefore, it is necessary to develop forward and inverse methods in electrical anisotropic media. Based on the axis anisotropic electric field control equations, forming a large linear equation through staggered finite difference approximation, adding boundary conditions, and using the quasi-minimum residual method to solve the equation, this study obtained MT forward modeling results in axis anisotropic media. The correctness of the algorithm was verified by comparing it with the 2D quasi-analytic solution. By designing several sets of axis anisotropic 3D models, the characteristics of the apparent resistivity tensor and tipper were analyzed. The results indicated that the <jats:inline-formula><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula>, <jats:inline-formula><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula> and <jats:inline-formula><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></jats:inline-formula> are sensitive to changes in resistivity in the X direction of the anomalous body, whereas the <jats:inline-formula><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula>, <jats:inline-formula><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula> and <jats:inline-formula><mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></jats:inline-formula> are sensitive to changes in resistivity in the Y direction. The apparent resistivity tensor and tipper are insensitive to changes in resistivity in the Z direction of the anomalous body. For exploration of anisotropic media, the apparent resistivity tensor and tipper of MT can identify the changes in resistivity in two horizontal axes directions and the boundaries of the anomalous body, which has the advantages for exploration.","PeriodicalId":12359,"journal":{"name":"Frontiers in Earth Science","volume":"2672 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A study of 3D axis anisotropic response of MT\",\"authors\":\"Xiao Liu, Qi-Ji Sun\",\"doi\":\"10.3389/feart.2024.1454962\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Electrical anisotropy has a significant impact on the observation data of the magnetotelluric (MT) method; therefore, it is necessary to develop forward and inverse methods in electrical anisotropic media. Based on the axis anisotropic electric field control equations, forming a large linear equation through staggered finite difference approximation, adding boundary conditions, and using the quasi-minimum residual method to solve the equation, this study obtained MT forward modeling results in axis anisotropic media. The correctness of the algorithm was verified by comparing it with the 2D quasi-analytic solution. By designing several sets of axis anisotropic 3D models, the characteristics of the apparent resistivity tensor and tipper were analyzed. The results indicated that the <jats:inline-formula><mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula>, <jats:inline-formula><mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mi>y</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula> and <jats:inline-formula><mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>y</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></jats:inline-formula> are sensitive to changes in resistivity in the X direction of the anomalous body, whereas the <jats:inline-formula><mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>y</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula>, <jats:inline-formula><mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"><mml:mrow><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>x</mml:mi><mml:mi>x</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msubsup></mml:mrow></mml:math></jats:inline-formula> and <jats:inline-formula><mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>z</mml:mi><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></jats:inline-formula> are sensitive to changes in resistivity in the Y direction. The apparent resistivity tensor and tipper are insensitive to changes in resistivity in the Z direction of the anomalous body. For exploration of anisotropic media, the apparent resistivity tensor and tipper of MT can identify the changes in resistivity in two horizontal axes directions and the boundaries of the anomalous body, which has the advantages for exploration.\",\"PeriodicalId\":12359,\"journal\":{\"name\":\"Frontiers in Earth Science\",\"volume\":\"2672 1\",\"pages\":\"\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Frontiers in Earth Science\",\"FirstCategoryId\":\"89\",\"ListUrlMain\":\"https://doi.org/10.3389/feart.2024.1454962\",\"RegionNum\":3,\"RegionCategory\":\"地球科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"GEOSCIENCES, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Frontiers in Earth Science","FirstCategoryId":"89","ListUrlMain":"https://doi.org/10.3389/feart.2024.1454962","RegionNum":3,"RegionCategory":"地球科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"GEOSCIENCES, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
电各向异性对磁测（MT）方法的观测数据有很大影响，因此有必要发展电各向异性介质中的正演和反演方法。本研究以轴各向异性电场控制方程为基础，通过交错有限差分近似形成大线性方程，加入边界条件，利用准最小残差法求解方程，得到了轴各向异性介质中的 MT 正演建模结果。通过与二维准解析解的比较，验证了算法的正确性。通过设计几组轴向各向异性三维模型，分析了视电阻率张量和翻板的特征。结果表明，ρxya、ρyya 和 Tzy 对异常体 X 方向的电阻率变化敏感，而 ρyxa、ρxaa 和 Tzx 对 Y 方向的电阻率变化敏感。视电阻率张量和翻板对异常体 Z 方向的电阻率变化不敏感。在勘探各向异性介质时，MT 的视电阻率张量和倾角可以识别两个水平轴方向的电阻率变化和异常体的边界，具有勘探优势。
Electrical anisotropy has a significant impact on the observation data of the magnetotelluric (MT) method; therefore, it is necessary to develop forward and inverse methods in electrical anisotropic media. Based on the axis anisotropic electric field control equations, forming a large linear equation through staggered finite difference approximation, adding boundary conditions, and using the quasi-minimum residual method to solve the equation, this study obtained MT forward modeling results in axis anisotropic media. The correctness of the algorithm was verified by comparing it with the 2D quasi-analytic solution. By designing several sets of axis anisotropic 3D models, the characteristics of the apparent resistivity tensor and tipper were analyzed. The results indicated that the ρxya, ρyya and Tzy are sensitive to changes in resistivity in the X direction of the anomalous body, whereas the ρyxa, ρxxa and Tzx are sensitive to changes in resistivity in the Y direction. The apparent resistivity tensor and tipper are insensitive to changes in resistivity in the Z direction of the anomalous body. For exploration of anisotropic media, the apparent resistivity tensor and tipper of MT can identify the changes in resistivity in two horizontal axes directions and the boundaries of the anomalous body, which has the advantages for exploration.
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