基于位移逆Krylov子空间的全波形航空瞬变电磁法三维数值模拟和响应特征

为了研究复杂地电模型的航空瞬变电磁法全波形响应特征，需要开发考虑发射波形的三维数值模拟算法。本研究基于非结构四面体网格和位移逆Krylov子空间(Shift-and-Invert Krylov,简称SAI Krylov)方法，采用基于电偶极子离散的场源处理方法模拟场源，在时间域进行计算实现了全波形航空瞬变电磁法矢量有限元三维数值模拟。使用均匀半空间模型在阶跃波、半正弦波、三角波和梯形波激发下的全波形解析解、VTEM实际激发波形的后推欧拉算法计算结果，检验了本研究开发的数值模拟算法的正确性。设计地表起伏异常体模型，计算和分析了航空瞬变电磁响应特征。开发的基于位移逆Krylov子空间的全波形航空瞬变电磁法三维数值模拟算法适合模拟复杂地电模型的响应，具有较高的计算精度。

Three-dimensional Full-time Airborne TEM Modeling with Shift-and-Invert Krylov Subspace Method and Response Characteristic Analysis

To study the fulltime response characteristics of airborne TEM with complex geoelectric models, it is necessary to develop a 3D forward algorithm with transmitted waveform consideration. Based on the unstructured tetrahedral mesh and the Shift-and-Invert Krylov subspace (SAI Krylov) method, we achieve the fulltime 3D edge finite-element simulation of airborne transient electromagnetic, by using the source processing technology-based dipole discretization technique. We simulate the shape of the transmitting loop by topography, and then the instantaneous current pulse technology is used to simulate the transmitting waveform. The numerical simulation algorithm developed here is verified by the analytical solutions of the uniform half-space model, under the excitation of step wave, half-sine wave, triangle wave, and trapezoidal wave, and by the calculation results of the 3D FETD algorithm of the VTEM actual transmitting waveform. The anomaly spherical model with uplifted terrain is designed, and the characteristics of airborne transient electromagnetic response are calculated and analyzed. The fulltime 3D numerical simulation algorithm of airborne TEM (based on SAI Krylov subspace) is suitable to calculate the response of complex geoelectric models, and is highly accurate.