Three-Dimensional Joint Inversion of the Resistivity Method and Time-Domain-Induced Polarization Based on the Cross-Gradient Constraints

The resistivity method and time-domain-induced polarization (TDIP) are two branches of electric exploration that are used to solve problems in mineral exploration, hydrogeology and engineering geology. In recent years, integrating different physical parameters for joint inversion to improve the accuracy of inversion results has been extensively examined; however, three-dimensional joint inversion of the two methods above has not been realized. To further address this issue, in this research, we used the limited-memory BFGS (L-BFGS) method to develop a three-dimensional joint inversion algorithm of the resistivity method and TDIP based on the cross-gradient constraints. In the new algorithm, the resistivity method and TDIP inversion were iteratively updated alternately to ensure that the inversion results can simultaneously meet the two conditions of obtaining minimum data misfits and finding structural similarity. The three-dimensional synthetic dataset inversion results showed that the models obtained by joint inversion are more accurate in the recovery of both the boundaries and the values of the anomalies. Especially in the background of high noise, joint inversion has higher resolution for the target body. The joint inversion algorithm was also successfully applied to a groundwater detection practice in Beijing, China, in which the practicability of the algorithm was confirmed.