Earthquake Research Institute, The University of Tokyo
抄録
When applying electromagnetic sounding methods, such as the magnetotelluric method, studies are usually carried out by: (1) treating the inducing field as spatially uniform and (2) treating the Earth as a semi-infinite conductor with a plane surface. These assumptions are both approximations of electro-magnetic induction caused by the incidence of a laterally non-uniform inducing field into the conducting spherical Earth. Although the basic theoretical concept was established many decades ago, the physical conditions for these two approximations are not fully and systematically understood, and some confusion appears in the literature. Therefore, the basic formulation of electromagnetic induction in both spherical and Cartesian coordinate systems is re-examined and the conditions for systematically deriving the two approximations are clarified. The results reveal that the solutions for the two coordinate systems are consistent with each other at an appropriate limit and that the two approximations result in neither indefinite nor non-unique problems, as suggested by some previous studies, if appropriate approximation conditions are applied.
通常マグネトテルリク法をはじめとする電磁誘導法では，（1）地球を半無限導体とみなし，平坦な地表より上方から与えられる（2）空間的に一様な電磁場変動が起こす電磁誘導を扱うことが多い．（1）と（2）はそれぞれ，空間的に非一様な電磁場変動が，球体の地球内部に生じる電磁誘導の近似的取り扱いである．電磁誘導法の理論的枠組みが確立してから長い年月が経過しているが，この 2つの近似の成り立つ物理的条件は系統的に理解されているとは言いがたく，文献には混乱も見られる．小論では，球座標系および直交座標系における電磁誘導問題の基本式を再吟味することにより，2つの近似の条件がどのように導かれているのかを明らかにすることを目指す．得られた結果は，それぞれの座標系での解には適切な極限において必ず整合性があることを示した．すなわち，近似の条件を適切に与えさえすれば，過去の文献で指摘されたような「不定性」や「非一意性」などの問題は生じないことがわかった．
雑誌名
東京大学地震研究所彙報 = Bulletin of the Earthquake Research Institute, University of Tokyo
巻
93
号
1
ページ
1 - 14
発行年
2018
ISSN
00408972
書誌レコードID
AN00162258
著者版フラグ
publisher
出版者
東京大学地震研究所
出版者別名
Earthquake Research Institute, University of Tokyo
Plane-wave and Flat Earth Approximations in Natural-source Electromagnetic Induction Studies
IHO93101.pdf
(200.24KB)
