大地电磁交错采样有限差分二维正反演研究

Two-dimensional magnetotelluric forward and inverse analysis of the finite-difference method with staggered sampling

交错采样网格能自动保证电磁场分布遵守能量守恒定律。本文基于交错采样网格,推导了大地电磁二维有限差分正演过程,实现了二维正演程序;通过与一维解析解对比,验证了算法的正确性且具有较高的计算精度。随后利用有限内存拟牛顿最优化算法,实现了交错采样有限差分二维反演;通过理论模型反演,验证了反演算法的稳定性,揭示有限内存拟牛顿反演计算效率明显优于非线性共轭梯度法。最后,通过对宕昌县官鹅沟大地电磁资料反演解释,查明了测区深部构造特征,表明算法具有较强实用性。

The staggered sampling grid can automatically ensure that the electromagnetic field distribution obeys the law of energy conservation.Based on the staggered sampling grid,the authors deduced the two-dimensional finite difference forward process of magnetotelluric survey,and realized the two-dimensional forward program.Compared with one-dimensional analytical solution,the algorithm is proved to be correct and has high accuracy.Then,using the finite memory quasi Newton optimization algorithm,the authors realized the staggered sampling grid finite difference two-dimensional inversion.The correctness of the inversion algorithm was verified by theoretical model inversion,which shows that the efficiency of quasi Newton inversion with finite memory is better than that of nonlinear conjugate gradient.Finally,the deep structure of the survey area was found through the inversion and interpretation of the magnetotelluric data from Guanegou in Dangchang County,which shows that the algorithm has strong practicability.