Volume integral equation-based electromagnetic inversion of 3D complex resistivity bodies
Jianping Li1, Tongxiao Shang2, Yixiao Guan3
1State Key Laboratory of Mining Disaster Prevention and Control, Shandong University of Science and Technology, Qingdao, 266590, China
2Key Laboratory of Earth Fissures Geological Disaster of MLR, Nanjing, 210018, China
3Geological Survey of Jiangsu Province, Nanjing 210018, Jiangsu, China
This study proposed the volume integral equation method to invert the complex resistivity parameters of 3D bodies in homogeneous half space. The partial derivative matrix of 3D bodies to complex resistivity was obtained with the use of electromagnetic field partial derivatives to the real resistivity combined with the complex resistivity spectrum partial derivatives of the Cole–Cole model. The classical damped least squares inversion method was applied. Results show that with at least four frequency data points, true complex resistivity parameters, as well as geometric parameters, can be inverted. The four parameters in the Cole–Cole model are interdependent. Chargeability and time constant are highly correlated, such that either one of these factors should be fixed prior to inversion. Furthermore, the proposed inversion algorithm we proposed has high efficiency because it only works in a split unit.