Геофизикийн тоон загварчлал. I. Төгсгөлөг ялгаврын аргад суурилсан цахилгаан соронзон индукцийн тэгшитгэлийн 2-D гаргалгаа
DOI:
https://doi.org/10.22353/physics.v40i646.11046Keywords:
Цахилгаан соронзон индукц, Магнетотеллурик, Төгсгөлөг ялгаврын арга, 2-D шууд бодлогоAbstract
Геофизикийн цахилгаан соронзон индукцийн арга нь Дэлхийн царцдас болон мантийн цахилгаан дамжуулах чадварын тогтцыг судлах физик тодорхойлолт юм. Энэхүү судалгаанд хоёр хэмжээст цахилгаан соронзон орны тоон загварчлалын үндсэн тэгшитгэлүүдийг Максвеллийн тэгшитгэлээс гарган авч, тэдгээрийг төгсгөлөг ялгаврын аргын хүрээнд томьёоллоо. Геофизикийн судалгаанд хэрэглэгддэг давтамжийн мужид тохиромжтой квазистатик дөхөлтийг ашиглан давтамжийн муж дахь хосолсон цахилгаан соронзон системийг загварчилсан. Хоёр хэмжээст Дэлхийн загварыг авч үзсэнээр бодлогыг хөндлөн цахилгаан болон хөндлөн соронзон горимуудад задлан, тус бүрийг скаляр Гельмгольцийн хэлбэрийн тэгшитгэлээр илэрхийлэв. Эдгээр тэгшитгэлийг бүтэцлэгдсэн торон дээр төвийн төгсгөлөг ялгаврын схемээр дискретчилж, тоон хэрэгжилтэд тохиромжтой шугаман алгебрийн тэгшитгэлийн систем болгон хувиргав. Ийнхүү боловсруулсан томьёолол нь цахилгаан соронзон хариу үйлдлийн шууд загварчлал, ялангуяа магнетотеллурикийн хэрэглээнд зориулсан онолын суурийг бүрдүүлж байна. Энэхүү ажил нь цаашдын тоон хэрэгжилт, торон байгууламжийн оновчлол, мөн нийлмэл гео-цахилгаан бүтэцтэй орчны урвуу бодлогын хүрээг хөгжүүлэх үндэс болно.
[English abstract]
Electromagnetic induction provides a fundamental physical basis for imaging the electrical conductivity structure of the Earth’s crust and mantle. In this study, we derive the governing equations for two-dimensional electromagnetic field modelling from Maxwell’s equations and formulate them within the finite difference method. Under the quasi-static approximation, appropriate for geophysical frequencies, the displacement current is neglected, simplifying the coupled electromagnetic system in the frequency domain. Assuming a 2-D Earth, the problem is decomposed into transverse electric and transverse magnetic modes, each governed by a scalar
Helmholtz-type equation. These equations are subsequently discretized on a structured grid using central finite difference schemes, resulting in a system of linear algebraic equations suitable for numerical implementation. The presented formulation establishes a rigorous theoretical foundation for forward modelling of electromagnetic responses, particularly in magnetotelluric (MT) applications. This work serves as a basis for subsequent developments in numerical implementation, mesh design, and inversion frameworks for complex geo-electrical structures.
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