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本文讨论了有关有限元法在大地电磁测深二维正演中的应用问题,论述了现有文献中采用的网格剖分方案。矩形网格具有易于使公式规则化和便于进行计算的优点,但失去对界面几何形状较好的适应能力;再有,由于在矩形单元上采用双线性插值公式,因而场相对z的偏导数仅是y的(线性)函数,而沿z方向是常数,这就影响确定辅助场值的准确程度。基于这种考虑,作者采用三角形—矩形单元综合剖分方案,即在地面和界面(特别是倾斜界面)处,以对角线将矩形划分为两个直角三角形,然后采用拉格朗日二次插值公式,计算泛函,再按矩形单元构成组合的刚度矩阵,最后合成总刚度矩阵。这样,既可较好地适应各种几何形状的界面,又可提高计算界面附近场值及地面处辅助场值的准确程度。这时,辅助场值的表达式是y、z的线性函数,并可表示成插值点处函数值的简单的线性组合,即J=a~TV。这在反演计算中会带来很大的方便。文中给出了相应的计算公式。
This paper discusses the application of finite element method in the 2D forward modeling of the magnetotelluric sounding in the earth and discusses the meshing scheme used in the existing literature. Rectangular grids have the advantage of being easy to formulate and facilitate the calculation, but lose their ability to adapt to the interface geometry. Furthermore, the partial derivative of the field relative to z due to the bilinear interpolation formula on rectangular units Only the (linear) function of y, which is constant along the z direction, affects the accuracy of the determination of the auxiliary field values. Based on this consideration, the author uses a triangular-rectangular unit synthetic subdivision scheme, that is, at the ground and the interface (especially the inclined interface), diagonally divide the rectangle into two right-angled triangles, and then use the Lagrange second Interpolation formula, computing functional, and then by the combination of rectangular elements constitute the stiffness matrix, the final synthesis of the total stiffness matrix. In this way, the interface of various geometric shapes can be well adapted and the accuracy of field values and the auxiliary field values at the ground surface can be increased. At this time, the expression of the auxiliary field value is a linear function of y, z and can be expressed as a simple linear combination of function values at the interpolation point, that is, J = a ~ TV. This will bring great convenience in inversion calculation. The paper gives the corresponding calculation formula.