Fast forward modeling of grounded electrical-source transient electromagnetic based on inverse Laplace transform adaptive hybrid algorithm

Frequency–time conversion is a crucial step in grounded electrical-source transient electromagnetic response calculation, and the performance of the algorithm is directly related to the overall accuracy and speed of forward modeling. In mainstream algorithms, algorithms with high accuracy often have slow computation speed while algorithms with high efficiency have unsatisfactory accuracy, especially when facing inversion problems that are difficult to meet requirements. This paper introduces three inverse Laplace transform algorithms for this problem: the Gaver–Stehfest algorithm, the Euler algorithm, and the Talbot algorithm. The performance of each algorithm in forward modeling was analyzed using half-space and layered models, and the optimal selection schemes for algorithm weight coefficients were provided. The numerical calculation results show that the Gaver–Stehfest algorithm has a unique advantage in computational efficiency, while the Talbot algorithm and Euler algorithm meet the accuracy requirements. After considering both accuracy and efficiency, the Talbot algorithm is selected to replace conventional algorithms for calculation of grounded electrical-source transient electromagnetic forward modeling. In addition, this paper combines the characteristics of the Gaver–Stehfest algorithm and the Talbot algorithm to implement an adaptive hybrid algorithm. This algorithm uses the Gaver–Stehfest algorithm for forward modeling in the early times and the Talbot algorithm to compensate for the decrease in accuracy in the later times. Through the comparison of forward modeling calculations, it can be seen that the hybrid algorithm proposed in this paper fully utilizes the advantages of both algorithms. The hybrid algorithm greatly improves computational speed while meeting accuracy requirements, and has significant advantages over conventional algorithms.