二維平面分層媒質(zhì)中的數(shù)值模式匹配算子矩陣理論及計算方法的應用
THE NUMERICAL MODE MATCHING METHOD ON 2-D STRATIFIED MEDIA-MATRIX THEORY AND COMPUTATION METHOD FOR APPLICATION
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摘要: 本文在直角坐標系中針對任意二維非均勻媒質(zhì)中的電磁場問題,研究并推廣了數(shù)值模式匹配的算子矩陣理論。提出了更為一般和實用的公式表達,導出了統(tǒng)一的任意激勵源展開公式。所導出的公式更便于邊界的匹配得到快收斂的數(shù)值解答,并且可普遍適用于未正交歸一化的基函數(shù)和特征函數(shù)以及存在簡并模式的情況。另外,文中還著重討論了建立在以上理論基礎上的一般數(shù)值計算方法。論述了選擇分域三角基的優(yōu)越性。討論了確定格點的原則,給出了格點坐標的公式,介紹了數(shù)值模式匹配法在電磁波傳播測井(EPT)中的應用及其數(shù)值計算的實現(xiàn)途徑;比較了用不同途徑的計算結(jié)果。所得數(shù)值結(jié)果與文獻報道一致。Abstract: By studying the arbitrary two dimensional problems of EMF in Cartesian coordinates with the numerical mode matching method, this paper presents a series of more general and applicable formulation, including the unified matrix expanding formula suitable for any source excitation. In discussing the computation method, triangular bases are chosen and its advantages are pointed out. A formula of determining grid points is prsented. As an example, a typical problem in the Electromagnetic Propagation Tool (EPT) is solved in different ways by using the proposed theory and methods. The present results agree with the ones in the literature.
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Chew W C, et al. Geophys., 1984, 49(18): 1586-1595.[2]Chew W C. IEEE Trans. on AP, 1985, AP-33(6): 649-654.[3]Chew W C. IEEE Trans. on GE, 1988, GE-26(4):388-398.[4]Chew WC, Nie Z, Liu Q, Anderson B. IEEE Trans. on GE, 1991, GE-29(2):308-313.[5]聶在平,等.地球物理學報,1992,35(4): 479-489.[6]Chew W C, Liu Q. IEEE Trans. on AP, 1990, AP-38(4):498-506.[7]Chew W C. IEEE Trans. on GE, 1988, GE-26(4): 382-387.[8]Liu Q, et al. Modelling Study of Electromagnetic Propagation Tool in Complicated Bore-[9]hole Environments. Electromagnetics Lab., Univ. of Illinoes, Techn. Report, 1990. -
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