Transient electromagnetic pseudo wavefield imaging based on the sweep-time preconditioned precise integration algorithm

The solution of the transient electromagnetic pseudo wavefield is a seriously ill-posed problem, and conventional methods do not facilitate a stable and high-precision solution. The precise integration method is a powerful method for solving ill-conditioned linear equations, since it converts the solution of highly ill-conditioned linear equations into an integral process, thereby overcoming the key challenge of solving transient electromagnetic pseudo wavefields. In this study, various norm functions are employed to preprocess the coefficient matrix based on this method. The study findings reveal that, when compared to the results obtained without preprocessing, the result obtained with 1-norm preprocessing is optimal. Then, following preprocessing, the condition number of the coefficient matrix improves, and the optimal solution can be reached in fewer iterations. In this paper, the corresponding relationship between the diffusion field time range and pseudo time range is then further studied, as are the selection criteria of discrete points of diffusion field time and pseudo time, and the selection basis of the integral step of the preconditioned precise integration method. The resolution can be further improved by introducing the sweep-time strategy. After verifying the stability and practicality of the proposed method, the effectiveness of the proposed method is validated using a complex 3D mineral model. The results reveal that the pseudo wavefield reflects the interface information of abnormal bodies. Finally, the study demonstrates the great developmental potential of the proposed method in engineering exploration employing field data.