基于自适应有限元正演的大地电磁法三维反演算法研究

Three-dimensional inversion of magnetotelluric based on adaptive finite element method

目前大地电磁法三维反演大多基于有限差分正演.反演使用规则六面体网格无法有效模拟复杂地形,同时正反演网格同套存在严重影响反演可靠性的问题.针对上述两个问题,本文利用自适应有限元算法,开发了基于非规则六面体的高精度大地电磁三维正演方法;反演中,使用独立的反演网格和正演网格来提高正演计算精度和反演可靠性.这一思路既保证了正演响应和灵敏度矩阵计算的精确性,又降低了因反演参数过多造成的不唯一性.最后,通过算例验证了正演算法的精确性和反演算法对地形处理的有效性.

At present,most of the 3D inversion of magnetotelluric method are based on finite difference forward modeling.The regular hexahedral mesh used in inversion cannot effectively simulate complex terrain,and using the same mesh in forward modeling and inversion has the problem that seriously affect the reliability of inversion.In response to the above two problems,this paper uses the adaptive finite element algorithm to develop a high-accuracy three dimensional magnetotelluric forward modeling method based on irregular hexahedrons;in the inversion,independent inversion mesh and forward mesh are used to improve the accuracy of forward modeling and reliability of inversion.This idea not only ensures the accuracy of forward response and sensitivity matrix calculation,but also reduces the non-uniqueness caused by too many inversion parameters.Finally,numerical examples are used to verify the accuracy of the forward modeling algorithm and the effectiveness of the inversion algorithm for terrain processing.