耦合PML边界条件的三维大地电磁二次场有限差分法

Three-dimensional finite difference method for the magnetotelluric secondary field with coupled PML boundary conditions

本文将大地电磁场分解为一次场和二次场,应用交错网格有限差分法模拟计算大地电磁二次场,并引入各向异性最佳匹配层(PML)吸收边界条件作为二次场边界条件,实现了耦合PML吸收边界条件的三维大地电磁二次场有限差分正演模拟.为了确保正演的稳定性和效率,QMR求解器和磁感应矢量散度校正技术被用于PML吸收边界条件下系数矩阵的快速求解.三维模型正演响应表明,基于二次场的三维大地电磁有限差分算法具有较高的计算精度和可靠性.通过计算分析不同PML吸收因子条件的大地电磁正演结果,显示在适当的吸收因子下,PML吸收边界条件可较大幅度的减小外边界距离,从而有效的压缩模型求解空间,最终提高三维大地电磁正演模拟的效率.

A new staggered-grid finite difference algorithm has been developed for computing the magnetotelluric responses of three-dimensional （3D） models using the secondary field method. The use of the secondary field allows us to apply the anisotropic Perfectly Matched Layer （PML） absorbing boundary conditions based on absorbing factors. To ensure the stability and efficiency, the quasi-minimum residual （QMR） method and divergence correction of magnetic induction vector are used to solve the linear system of equations. Two different 3D models are simulated to validate the effectiveness of this algorithm. The modelling responses are in a good agreement with the solutions from other methods. The comparison of different absorbing factors shows that the PML absorbing boundary conditions can reduce the outer boundaries and improve the efficiency of magnetotelluric forward modeling.