三维频率域航空电磁反演研究

航空电磁数据的三维解释由于数据量大需要有高效的反演算法作为支撑.本文利用两种目前主流的数值优化技术（非线性共轭梯度和有限内存的BFGS法）实现了三维频率域航空电磁反演，并进一步比较了两种方法的有效性和运算效率.在反演过程中，为了更好地反演异常体的空间位置，模型方差矩阵中的光滑系数在反演起始阶段取值较大；当数据拟合差下降趋于平缓时，再利用较小的光滑因子约束反演过程来实现聚焦和获得精确的反演结果.理论数据反演表明这两种优化策略具有相似的内存需求，但是有限内存的BFGS技术比非线性共轭梯度法在计算时间和模型反演分辨率上具有一定的优越性，因此有限内存BFGS法更适合于求解大规模三维反演问题. 模型试验进一步表明目前主流的迭代法求解技术不适合大规模航空电磁数据反演，未来移动平台多源电磁数据快速正反演可通过引入矩阵分解技术来实现.

3D inversion for frequency-domain HEM data

In order to find an efficient inversion algorithm for 3D helicopter-borne electromagnetic (HEM) data interpretation, we present in this paper two popular nonlinear optimization algorithms-non-linear conjugate gradients (NLCG) and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) and compare their effectiveness and efficiency. For better recovering the depth of anomalous targets, large smoothing parameters in the model covariance matrix are employed at the beginning of inversion process. When the misfit decrement becomes very slow, small smoothing parameters are used to obtain focusing and accurate results. Numerical results show that these two methods have similar memory requirements, but L-BFGS method performs better than NLCG in terms of time-cost and the model resolution, making the L-BFGS method more suitable for large scale optimization problems. Further model experiments show that the current iterative algorithms may not suit for the inversion of large HEM datasets, technologies like the matrix factorization may be needed in the future for the fast modeling and inversion for airborne EM platform.