1D regularization inversion combining particle swarm optimization and least squares method

For geophysical inversion problems, deterministic inversion methods can easily fall into local optimal solutions, while stochastic optimization methods can theoretically converge to global optimal solutions. These problems have always been a concern for researchers. Among many stochastic optimization methods, particle swarm optimization (PSO) has been applied to solve geophysical inversion problems due to its simple principle and the fact that only a few parameters require adjustment. To overcome the nonuniqueness of inversion, model constraints can be added to PSO optimization. However, using fixed regularization parameters in PSO iteration is equivalent to keeping the default model constraint at a certain level, yielding an inversion result that is considerably aff ected by the model constraint. This study proposes a hybrid method that combines the regularized least squares method(RLSM) with the PSO method. The RLSM is used to improve the global optimal particle and accelerate convergence, while the adaptive regularization strategy is used to update the regularization parameters to avoid the influence of model constraints on the inversion results. Further, the inversion results of the RLSM and hybrid algorithm are compared and analyzed by considering the audio magnetotelluric synthesis and field data as examples. Experiments show that the proposed hybrid method is superior to the RLSM. Furthermore, compared with the standard PSO algorithm, the hybrid algorithm needs a broader model space but a smaller particle swarm and fewer iteration steps, thus reducing the prior conditions and the computational cost used in the inversion.