A comprehensive probabilistic framework to solve geophysical inverse problems while accounting for multiple sources of uncertainty is provided by the Bayesian approach. However, widely used standard Markov chain Monte Carlo (MCMC) methods may fail to properly explore and approximate the posterior probability density function (PDF) of the parameters of interest in complex (e.g., non-linear, high-dimensional, multi-modal) scenarios. A recurrent challenge when tackling inverse problems using MCMC methods is to efficiently sample high-likelihood regions of the posterior within feasible computational times. In practice, Markov chains often get trapped sampling local solutions and fail to transition between distinct high-likelihood regions. Alternative methods based on tempering strategies address these difficulties by enhancing the freedom of exploration using an auxiliary variable in Bayes’ theorem that reduces the influence of the likelihood function. In particular, sequential Monte Carlo (SMC) methods build and sample a sequence of tempered distributions starting from the prior PDF and progressively increasing the likelihood influence until reaching the posterior PDF. Through successive importance sampling steps, the method gradually bridges the prior and posterior PDFs, reducing the risk of getting trapped in local solutions. On the other hand, a second major challenge in geophysical Bayesian inversions is the high computational cost associated with the iterative evaluation of expensive, high-fidelity forward solvers that simulate the underlying physics. In this work, we explore the use of surrogate solvers to reduce the computational times in geophysical inversions, and we demonstrate how they can be naturally embedded within sequential tempering schemes. Within this framework, the surrogate model is progressively refined throughout the inversion, becoming increasingly accurate as the influence of the likelihood function strengthens toward the posterior distribution. We test the proposed approach on a synthetic geophysical wave propagation problem. Our results suggest that the progressively improved surrogate solvers can efficiently reproduce the inversion results obtained with high-fidelity forward models in substantially lower times. The proposed importance-sampling-based sequential scheme offers a robust and flexible framework that allows transitions and adaptivity in both tempering and the refinement of surrogate models.