大地电磁三维交错网格有限差分数值模拟中的散度校正方法研究

散度校正对加快大地电磁三维正演速度、提高计算精度均具有重要意义.本文基于交错网格有限差分开展了三维大地电磁正演模拟,从Maxwell方程中磁场散度为零的特征出发,提出了三种散度校正方法:直接磁场散度校正(DDCM)、磁场散度残差复校正(RPCM)、磁场散度残差实校正(RRCM),并将上述校正方法用于垂直接触带、典型低阻异常体和国际标准地电模型的正演计算.结果表明:相对于其他两种散度校正和不做散度校正求解方案,磁场散度残差复校正具有计算时间短,收敛速度更快,计算结果更精确的优点.此外,不同网格剖分下的磁场散度残差实校正方案计算结果显示出该校正方案具有良好的稳定性和适用性.

Study on divergence correction method in three-dimensional magnetotelluric modeling with staggered-grid finite difference method

Divergence correction is significant both in accelerating three-dimension magnetotelluric modeling and in improving calculation precision. Based on three-dimensional magnetotelluric modeling with staggered-grid finite difference method, three different methods of divergence correction were presented by utilizing the characteristic that magnetic divergence in Maxwell equations was equal to zero. They include the direct divergence correction of magnetic field(DDCM), complex residual divergence correction of magnetic field(RPCM), and real residual divergence correction of magnetic field(RRCM). In order to compare the effect of the three different methods, we tested with three geo-electrical models: abutting quarter spaces, typical low resistivity and international standard model. The results indicate that, compared with the other two divergence correction methods and no divergence correction, RRCM has the advantages of shorter computation time,faster convergence and higher precision. In addition, it shows good stability and adaptability for different mesh generation schemes.