###### Abstract  
Semi-airborne transient electromagnetics (SATEM) is a geophysical survey tool known for its ability to perform three-dimensional (3D) observations and collect high-density data in large volumes. However, SATEM data processing is presently restricted to 3D model-driven inversion, which is not conducive to detailed surveys. This paper presents a new 3D model- and data-driven inversion algorithm using the particle swarm optimization (PSO) and gradient descent (GD) algorithms. PSO is used to suppress the multiplicity of solutions associated with inverse problems, and the GD algorithm is employed to accelerate the convergence of the inversion process. For the PSO-GD algorithm, a new model-updating equation is established and a cosine probability function is introduced as a weighting term for PSO and GD algorithms to ensure a smooth transition between the two algorithms in the iterative process. The \(\alpha\)-trimmed filter function is used as a regularization constraint to smooth the model. The stability and reliability of the PSO-GD algorithm are verified through numerical simulations. Finally, the new algorithm is applied to the processing of SATEM measurements of the Qinshui coal mine in Jincheng, Shanxi Province, China. semi-airborne transient electromagnetics; three-dimensional inversion; particle swarm optimization; gradient descent; trim filter function +
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method [23, 24]. All of these methods use the first- and second-order gradient directions or conjugate direction of the objective function as guidance to correct the model parameters, and these above algorithms have the characteristics of mature theories and high convergence rates. Deterministic inversion algorithms play an important role in 3D geophysical inversion [15, 16, 17, 18]. However, model-driven methods have notable deficiencies in two areas. On the one hand, the inversion result heavily relies on the selection of an initial model [25]. Consequently, these methods are susceptible to falling into certain local optimum solutions near the initial model and face difficulties in converging with global optimum solutions for nonlinear, ill-conditioned geophysical inverse problems [26]. On the other hand, the inversion result lacks an evaluation of the model parameters. These limitations have called into question the accuracy of model-driven inversion methods [27]. The other group is composed of data-driven inversion methods based on statistics or the theory of swarm evolution. Stochastic algorithms include the particle swarm optimization (PSO) algorithm, the simulated annealing algorithm, the genetic algorithm, the bee colony algorithm, neural networks, and the Bayesian algorithm, et cetera [28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39]. Using multiple models, stochastic algorithms can not only obtain the better-fitting model, but also estimate the uncertainty of the retrieved solution. Compared to model-driven inversion methods, data-driven inversion methods are more capable of escaping from local optimum solutions, can provide an uncertainty evaluation of the global convergence and inversion result independent of the initial model, and are particularly suitable for solving geophysical inverse problems without a priori information. However, data-driven inversion is often more computationally expansive than model-driven inversion by several orders of magnitude [40]. In recent years, the development of computer science has allowed for an increasing application of data-driven inversion methods for geophysical inverse problems. PSO is a typical data-driven inversion algorithm inspired by the optimization process involved in the search for food by bird or fish swarms in nature. Compared to other data-driven inversion algorithms, PSO requires fewer models and quickly converges during the optimization process; therefore, it has been extensively applied in many engineering fields.