二维各向异性地电断面大地电磁场的有限元法解法
SOLUTION OF MAGNETOTELLURIC FIELD EQUATIONS FOR A TWO-DIMENSIONAL, ANISOTROPIC GEOELECTRIC SECTION BY THE FINITE ELEMENT METHOD
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摘要: 假定各向异性主轴之一与层面垂直,另一主轴与构造走向平行,本文给出这种条件下,二维各向异性地电断面的大地电磁场的变分方程。用有限单元法解变分方程。对区域进行三角单元剖分,在单元内进行二次函数插值,将变分方程转变为线性代数方程组。解方程组得各节点的场值,并可计算场的导数。由这些值可计算地表的视电阻率。 算例表明,对于Hx型波(x平行构造走向),各向异性体与各向同性体的大地电磁场有很大区别。Abstract: We assume that one of the principal axes of anisotropy is coincident with the direction perpendicular to the stratification, the another is parallel to the structural strike. Under these conditions, a variation equation of the magnetotelluric field for a two-dimensional anisotropic geoelectric section is given in this paper. We solve the variation equation by means of the finite element method: Dividing the entire region into many triangular elements and interpolating with a quadratic function in each element the variation equation is converted into a system of linear algebric equations. By solving the equation system we can obtain the field values on the nodes and calculate the derivatives of the field. Prom these values the apparent resistivity on the ground surface can be calculated.The calculation example shows that the magnetotelluric field in the case of aniso-tropy is obviously different from that of isotropy for wave Hx (x parallel to the structural strike).
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[1] Reddy, I. K., D. Rankin, Magntotelluric response of lsterally inhomogeneous and anisotropic media Geophysics, 40, 6, 1035—1045, 1975.
[2] 赵生凯、徐世浙,有限单元法计算良导嵌入体二维模型的大地电磁测深曲线,物化探电子计算技术,1, 14—21,1983. -
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