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.

In the double carbon background, riding the wind of new energy vehicles and the battery high nickelization, nickel resources rise along with the trend. In recent years, due to the influence of geopolitical conflicts and emergencies, as well as the speculation and control of international capital with its advantages and rules, the world may face price and security supply risks to a certain extent. Therefore, to obtain the most objective trade redistribution strategy, this paper first constructs the nickel material trade network, identifies the core trading countries and the main trade relations of nickel material trade, and finds that the flow of nickel material mainly occurred between a few countries. On this basis, a trade redistribution model is constructed based on the maximum entropy principle. Taking Indonesia, the largest exporter, and the largest trade relationship (Indonesia exports to China) as examples, the nickel material redistribution between countries when different supply risks occur are simulated. The results can provide an important reference for national resource recovery after the risk of the nickel trade.

Many rocks exhibit electrical anisotropic characteristics, leading to artifacts in isotropic inversion of direct current resistivity data. To mitigate this issue, we employ the flexible unstructured finite element method for three-dimensional anisotropic forward modeling and anisotropic inversion for direct current resistivity data. Synthetic inversions further validate algorithm feasibility. The code not only replicates the inversion of principal axis resistivities accomplished by previous researchers but also reconstructs challenging all angle parameters. Comparative analysis of inversion using isotropic and arbitrary anisotropic assumptions reveals that anisotropic inversion accurately recovers the parameters. Models comprising conductive and resistive targets respectively are utilized to stimulate two realistic scenarios. The angle parameters of conductive target are challenging to recover compared to a conductive one with the same anisotropy. We conduct comprehensive experiments to assess the results across various data types. Borehole-generated data enhances the principal resistivities resolution, aligning with the direction of the lines connecting to the boreholes, rather than all ones, whereas conventional surface configurations are unable to accurately capture discrepancies between principal resistivities and Euler angles. Moreover, the investigations confirm the resolvability of each anisotropy component, especially angle parameters, which depends on borehole distribution. These experiments on data-acquisition configurations greatly enhance the practical possibility of successfully collecting data containing anisotropy information, achieving reconstruction of angular parameters, and obtaining better images of principal axis resistivity in practical applications. Even with the correct anisotropic assumption, unreasonable data-acquisition configurations produce inversion results with distortion. Testing with the model containing multiple anisotropic targets further confirms the algorithm’s effectiveness.

The resistivity method is widely used to address long-term monitoring challenges in fields such as environmental protection, ecological restoration, seawater intrusion, and geological hazard assessment. However, external environmental changes can influence monitoring data, resulting in inversion results that fail to accurately reflect subsurface variations. Furthermore, the data volume required for such monitoring is several times larger than that for conventional single-point observations, leading to excessively long inversion times and low computational efficiency. To address these issues, we develop a three-dimensional inversion algorithm for the resistivity method that incorporates time-lapse constraints. Additionally, MPI parallelization is integrated into the program to increase computational efficiency. Through the design of theoretical models and the synthesis of data to test the algorithm, the results show that, compared with those of separate inversion, the shapes and values of time-lapse inversion results at different time points are more consistent, maintaining temporal continuity, and the computational efficiency of MPI parallel inversion is greatly improved. Particularly in high-noise environments, time-lapse inversion effectively suppresses background noise interference, reduces false anomalies, and produces results that closely align with the true model, thus confirming the algorithm’s effectiveness and superiority.

The resistivity method is widely used to address long-term monitoring challenges in fields such as environmental protection, ecological restoration, seawater intrusion, and geological hazard assessment. However, external environmental changes can influence monitoring data, causing inversion results that fail to accurately reflect subsurface variations. Furthermore, the data volume required for such monitoring is several times larger than that for conventional single-point observations, leading to excessively long inversion times and low computational efficiency. To address these issues, we develop a three-dimensional inversion algorithm for the resistivity method incorporating time-lapse constraints. Additionally, MPI parallelization is integrated into the program to enhance computational efficiency. Through the design of theoretical models and the synthesis of data to test the algorithm, the results show that, compared to separate inversion, the shape and values of time-lapse inversion results at different time points are more consistent, maintaining temporal continuity, and the computational efficiency of MPI parallel inversion is greatly improved. Particularly in high-noise environments, time-lapse inversion effectively suppresses background noise interference, reduces false anomalies, and produces results that closely align with the true model, thus confirming the algorithm’s effectiveness and superiority.

The resistivity method and time-domain induced polarization (TDIP) method are two branches of electrical geophysical prospecting. In recent years, researchers have implemented time-lapse resistivity inversion and time-lapse TDIP inversion based on time-lapse constraint theory. Although time-lapse inversion ensures temporal continuity between inversion results obtained at distinct epochs, it may not only cause the results to deviate from the true subsurface conditions, but also result in significant structural discrepancies resistivity and TDIP inversion results, thereby reducing inversion accuracy. To address these issues, the joint inversion of time-lapse resistivity and TDIP data was implemented based on cross-gradient constraint theory and time-lapse constraint theory. Using synthetic data from the theoretical model, we conducted separate inversion, time-lapse inversion, and time-lapse joint inversion. Comparative analysis of the results from these inversion schemes reveals that, compared with separate inversion and time-lapse inversion, time-lapse joint inversion not only maintains the temporal continuity of inverted models across consecutive monitoring epochs but also enforces structural similarity among distinct physical property models. This approach significantly increases the accuracy of the inversion results and exhibits superior noise robustness. These findings confirm the stability, reliability, and superiority of the algorithm developed in this study, providing a novel approach for addressing geological monitoring challenges.