基于第三类边界条件的大地电磁三维矢量有限元任意各向异性正演

3D vector finite element modeling of magnetotelluric in general anisotropic media with the third type boundary condition

地球内部介质的各向异性对地球物理场解译有很大影响,研究各向异性介质中大地电磁响应具有重要的意义.边界条件是影响电磁场正演精度的一个关键因素,其中第一类边界条件需要将底面边界设置在离异常体足够远的地方,面临着计算规模大、求解速度慢的问题.相比第一类边界条件,第三类边界条件具有计算规模更小、计算精度更高的优点,在三维各向同性正演中被广泛使用.然而,各向异性使得第三类边界条件理论变得更为复杂,目前尚未见到采用第三类边界条件的大地电磁三维各向异性正演.本文推导出各向异性介质中三维矢量有限元底界面的第三类边界条件,通过模型计算对算法的可靠性和精度进行了验证.结果表明,当精度相同时,第三类边界条件的计算规模可以更小;而当底界面离异常体较近时,第三类边界条件有着更高的精度.

The anisotropy of the earth's internal medium has a great influence on the geophysical exploration.Therefore,it is important to study the responses of magnetotelluric(MT)method in anisotropic media.The boundary conditions play an important role in the accuracy of electromagnetic modeling.The first type boundary condition requires the bottom boundary to be set far enough away from the anomalies,which leads to a larger computational domain and longer computational time.The third type boundary condition has smaller computational scale and higher computational accuracy than the first type boundary condition,which is widely used in the modeling of 3D isotropic media.However,the theory of the third type boundary condition is more complex in anisotropic media.At present,there are no published papers that achieved 3D MT modeling with the third type boundary condition in general anisotropic media.In this paper,for 3D vector finite element the third type boundary condition of the bottom interface in anisotropic media is derived.The reliability and accuracy of the algorithm are verified by several models.The results show that the computational domain with the third type boundary condition can be smaller when the accuracy is the same;and the third type boundary condition has a higher accuracy when the bottom boundary is closer to the anomaly.