自适应有限元法的大地电磁二维各向异性正反演

电性各向异性广泛存在于地壳和上地幔范围内，对观测电磁场有不可忽视的影响。大地电磁法能够探测大范围深部电性结构并反映其各向异性特征，但目前关于该方法各向异性二维正反演的研究还有待加深。利用基于非结构网格的自适应有限元法求解对角各向异性情况下大地电磁正演控制方程，既有利于起伏地形和复杂地质构造的建模，又便于模拟包含多种尺寸结构的地电模型；网格的自动细化可避免人为网格划分导致的计算误差并可提高计算效率。反演算法则采取了经典模型空间Occam策略，使得模型的搜索过程非常稳定，能在较少迭代次数内获得合理的反演结果。对经典四层层状模型和二维各向异性块体模型进行了正演模拟试算，并分别与一维准解析解、二维有限差分数值解结果进行对比，验证了正演算法的准确性；最后对一复杂海底起伏各向异性模型进行了反演试算，反演结果准确反映了各向异性异常体的存在，并成功地还原了真实模型的主要电性特征。

Forward and inverse modeling of the magnetotelluric field in 2D anisotropic media with an adaptive finite element method

Electrical anisotropy, which widely exists in the crust and upper mantle, has shown great influence on the observation of the electromagnetic field in earth. This electrical anisotropy will affect on magnetotellurics sounding (MT), an electromagnetic geophysical method for inferring the earth subsurface electrical resistivity from measurements of natural geomagnetic and geoelectric field variation at the earth surface. We propose in the paper forward and inverse modeling of magnetotelluric fields in 2D anisotropic media. MT governing equations of electromagnetic field in 2D medium with tri-axial anisotropy are derived, and solved with an adaptive finite element method based on unstructured grids. The unstructured triangle grids can easily simulate general models with not only bathymetry and topography, but also large-range scales and complex structures. The anisotropic inversion strategy employs the classical model space Occam method, so that the model searching is very stable and the reasonable inversion results can be achieved with a few iteration steps. This proposed method is tested on two models, a four-layer 1D model and a 2D anisotropic block model, which are respectively compared with the standard quasi-analytic solution and the standard finite difference solution. A complex 2D anisotropic seafloor model with bathymetry is also designed to test the inversion method. All the test results demonstrate the validity of the proposed algorithms.