An innovative comparative study among three different global optimization methods (GOMs) to invert time domain electromagnetic data (TDEM), was applied in the 1.5D subsurface resistivity imaging. These stochastic methods allow the incorporation of different kinds of constraints in the objective function, due to the easiness of implementation in their algorithms and their computational efficiency. Nevertheless, global optimization methods, like any other based on swarm intelligence cost much computational time, including problems with a high number of unknown parameters and when the forward modeling involves time-consuming calculations such as Gaver-Stehfest inverse transforms, Hankel transforms, and others. To overcome this difficulty, we developed a parallel pure MPI version of each GOM, allowing the distribution of the computation among several cores of a cluster. The performances of the classic version of particle swarm optimization (PSO), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) using MPI parallelism for solving 1.5D TDEM inverse problems are compared here in a set of synthetic and real data. The principal outcomes show: (1) These GOMs reproduce quite well the distribution of subsurface resistivity either synthetic models or real data, (2) WOA and PSO exhibit better computational performances, converging first than GWO, (3) WOA provided better performance in the final value achieved of the cost function than PSO and GWO, and (4) pure MPI parallelism provided a 17x and 50x speedup in the computation time for both synthetic and real data, respectively. In a better way to classify this comparison, we analyzed the solutions using total variation (TV) and Global smoothness (GS) constraints, to identify smooth and sharp structures. Additionally, we have diminished the computational time execution with the parallel solution (MPI version of each stochastic traditional method) against the sequential processing.

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