3D LBFGS inversion of controlled source extremely low frequency electromagnetic data

人工源极低频电磁法三维LBFGS反演（英文）

The controlled source extremely low frequency （CSELF） electromagnetic method is characterized by extremely long and powerful sources and a huge measurement range. Its electromagnetic field can therefore be affected by the ionosphere and displacement current. Research on 3D forward modeling and inversion of CSELF electromagnetic data is currently in its infancy. This paper makes exploratory attempts to firstly calculate the 1D extremely low frequency electromagnetic field under ionosphere-air-earth coupling circumstances, and secondly analyze the propagation characteristics of the background electromagnetic field. The 3D staggered-grid finite difference scheme for solving for the secondary electric field is adopted and incorporated with the 1D modeling algorithm to complete 3D forward modeling. Considering that surveys can be carried out in the near field and transition zone for lower frequencies, the 3D Limited-memory Broyden-Fletcher-Goldfarb-Shanno （LBFGS） inversion of CSELF electromagnetic data is presented （in which the sources, or primary fields, are included）, with the aim of directly inverting the impedance data, regardless of where it is acquired. Derivation of the objective functional gradient is the core component in the inversion. Synthetic tests indicate that the well-chosen approximation to the Hessian can significantly speed up the inversion. The model responses corresponding to the coexistence of conductive and resistive blocks show that the off-diagonal components of tensor impedance are much more sensitive to the resistivity variation than the diagonal components. In comparison with conventional scalar inversion, tensor inversion is superior in the recoveries of electric anomalies and background resistivity.

人工源极低频电磁法因其具有场源长度大,观测范围广的特点,使得极低频电磁波的传播会受到电离层和位移电流的影响。现阶段针对该方法的三维正反演研究尚处于起步阶段。作为一项探索性的尝试,本文首先给出了电离层、空气以及地下介质耦合情况下一维极低频背景电磁场的计算方案,并对电离层影响下背景电磁波的传播特征进行了分析、总结。通过将之与求解二次电场的交错网格有限差分数值模拟算法整合,实现了人工源极低频电磁法的三维正演。针对人工源极低频探测中可能遇到的近区、过渡区数据反演问题,本文进而采用针对该方法的三维有限内存Broyden-Fletcher-GoldfarbShanno(Limited-memory BFGS,LBFGS)带源反演算法,实现了对全区张量阻抗数据的直接反演。文中详细介绍了目标函数梯度计算这一LBFGS反演中的核心问题。合成数据反演算例结果表明在LBFGS反演中,选择恰当的近似Hessian矩阵能够有效提高反演效率。高低阻异常同时存在下的反演模型响应告诉我们张量阻抗反对角元素对恢复地下电性结构的贡献远大于主对角元素。与常规标量数据反演相比,张量数据反演在异常体的恢复和背景电阻率的控制方面具有明显的优势。