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

doi:10.19657/j.geoscience.1000-8527.2022.075

摘要/Abstract

摘要：

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。

关键词: 航空瞬变电磁法, 三维正演, 全波形, 位移逆Krylov子空间, 矢量有限元

Abstract:

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.

Key words: airborne TEM, 3-D modeling, fulltime waveform, SAI Krylov subspace, edge finite-element

中图分类号:

P631

董岩, 谭捍东, 付兴. 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[J]. 现代地质, 2023, 37(01): 74-83.

DONG Yan, TAN Handong, FU Xing. Three-dimensional Full-time Airborne TEM Modeling with Shift-and-Invert Krylov Subspace Method and Response Characteristic Analysis[J]. Geoscience, 2023, 37(01): 74-83.

图/表 15

图1 任意发射波形示意图

Fig.1 Schematic diagram of the arbitrary transmitting waveform

图2 研究区域非结构网格剖分示意图

Fig.2 Schematic diagram of unstructured grid schematics in the study area

图3 四面体单元棱边电场分布图

Fig.3 Edge electric field distribution (of tetrahedral element) diagram

图4 有理Arnoldi近似

Fig.4 Rational Arnoldi approximation

图5 发射波形示意图

Fig.5 Schematic diagram of transmission waveforms

图6 均匀半空间模型

Fig.6 Homogenous half-space model

图7 阶跃波SAI Krylov数值模拟结果和解析解的比较 (a)dbz/dt响应;(b)相对误差

Fig.7 Comparison of SAI Krylov and analytic solution for step waveform model

图8 半正弦波、三角波SAI Krylov计算结果和解析解的比较 (a)半正弦波dbz/dt响应;(b)半正弦波相对误差;(c)三角波dbz/dt响应(d)三角波相对误差

Fig.8 Comparison of SAI Krylov and analytic solution for half-sine waveform model and triangle waveform model

图9 梯形波SAI Krylov结果和解析解的比较 (a)dbz/dt响应;(b)相对误差

Fig.9 Comparison of SAI Krylov and analytic solution for trapezoidal waveform model

图10 阶跃波、三角波、半正弦波、梯形波的off-time dbz/dt响应

Fig.10 ATEM dbz/dt response of step, triangular, half-sine and trapezoidal waves during off-time

图11 立方异常体模型

Fig.11 Model of cubic anomaly body

图12 VTEM实际发射波形及其ATEM响应 (a)VTEM实际发射波形;(b)SAI Krylov子空间方法和FETD计算的dbz/dt响应

Fig.12 Realistic transmitting waveform for VTEM system and its ATEM response

图13 隆起地形球体模型示意图

Fig.13 Schematic diagram of spherical model with upliftedterrain

图14 半正弦波off-time阶段不同时刻的dbz/dt剖面曲线

Fig.14 dbz/dt response of half-sine waveform model during off-time

图15 均匀半空间、水平地表球体、隆起地形球体断电后0.255 ms的dbz/dt响应

Fig.15 ATEM dbz/dt response at 0.255 ms for homogeneous half-space model, sphere model without terrain, and sphere model with uplifted terrain

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