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 (LS) with the PSO method. The regularized LS 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 regularized LS 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 regularized LS. 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.

对于地球物理反演问题，确定性反演方法容易陷入局部最优解，而随机优化方法理论上可以收敛到全局最优解。这些问题一直是研究人员关注的问题。在众多随机优化方法中，粒子群优化（PSO）由于其原理简单，只需调整很少的参数，已被应用于解决地球物理反演问题。为了克服反演的非唯一性，可以将模型约束添加到 PSO 优化中。然而，在 PSO 迭代中使用固定正则化参数相当于将默认模型约束保持在一定水平，从而产生受模型约束影响很大的反演结果。本研究提出了一种将正则化最小二乘法 (LS) 与 PSO 方法相结合的混合方法。正则化LS用于改进全局最优粒子并加速收敛，而自适应正则化策略用于更新正则化参数以避免模型约束对反演结果的影响。进一步以音频大地电磁合成和外场数据为例，对正则化LS和混合算法的反演结果进行了对比分析。实验表明，所提出的混合方法优于正则化 LS。此外，与标准 PSO 算法相比，混合算法需要更宽的模型空间，但需要更小的粒子群和更少的迭代步骤，