Airborne transient electromagnetic (ATEM) technology is a technique often used in mineral exploration and geological mapping. Due to inductive polarization (IP) phenomena, the ATEM response curve often shows a negative response or declines rapidly to the attenuation curve. Traditional resistivity inversion techniques do not explain the IP response of a signal well, so the negative response is usually removed during data processing, resulting in a reduced correctness and authenticity of the findings. In this paper, in the parameter inversion based on the Cole–Cole model, the Jacobian matrix chain analysis method is used to calculate, and the current waveform calculation is also considered in the inversion. The results show that compared with the perturbation method, the analysis technique can greatly reduce the calculation time and improve the inversion efficiency. In the single-point one-dimensional inversion and lateral constraint quasi-two-dimensional inversion, the Cole–Cole four-parameter forward response has strong inversion accuracy, which can successfully invert the actual exploration content and the Cole–Cole four-parameter response. Some measured sounding data in the Qingchengzi survey area of Liaoning Province, China have a negative response to IP, and the resistivity scheme cannot be used alone for inversion, but the real underground resistivity structure can be obtained through the method studied in this paper, and good exploration results can be obtained.

In geophysical inversion issues, the Jacobian matrix computation takes the greatest time, and it is the most significant factor limiting the inversion’s calculation speed. We think that the correctness of the inverse problem is determined by the difference between the inversion data and the real data, not the precision of the gradient solution in each iteration. Based on this, we present an approximate computation approach for the Jacobian matrix that may rapidly solve the inverse issue by estimating the gradient information. In this research, the approximate gradient information is solved in each iteration process, and the approximate gradient is utilized for computation; nevertheless, the poor fitting of the evaluation data is correctly evaluated, and the inversion model that fits the criteria is achieved. We employed this approach of estimating the Jacobian matrix to invert the 3D airborne transient electromagnetic method (ATEM) on synthetic data, and it was able to significantly minimize the time necessary for the inversion while maintaining inversion accuracy. When the model mesh is more precise, this technique outperforms the previous way of finding the exact Jacobian matrix in terms of acceleration.

Cooperative inversion is a powerful underground imaging technique that can overcome the limitations of a single detection method. However, due to the different grid divisions used by various geophysical methodologies, imposing structural constraints between grids of different scales is challenging. This paper proposes a new cooperative inversion strategy and applies it to the inversion of the quasi-two-dimensional aerial transient electromagnetic method (ATEM) with the induced polarization (IP) effect and the two-dimensional magnetic method to solve the problem of applying cross-gradient constraints under grids of different scales. The mesh mapping method is incorporated into the iterative process of cooperative inversion in this inversion strategy. The inversion of synthetic data shows that this technique can effectively employ data complementarity to increase the accuracy of the results for describing the medium boundary. The mesh mapping methodology may be applied to the cooperative inversion of geophysical methods under any grid division and successfully solves the problem of grid division mismatch in cooperative inversion.