Inversion is a critical and challenging task in geophysical research. Geophysical inversion can be formulated as an optimization problem to find the best parameters whose forward synthesis data most fit the observed data. The inverse problems are usually highly non-linear, multi-modal as well as ill-posed, so conventional optimization algorithms cannot handle it very efficiently. In the past decades, genetic algorithm (GA) and its many variants are widely applied to inverse problems and achieve great success. Swarm intelligence algorithms are a family of global optimizers inspired by swarm phenomena in nature, and have shown better performance than GA for diverse optimization problems. However, swarm intelligence algorithms are not utilized for geophysical inversion problems until recently and only limited number of works are reported. In this paper, we try to apply two swarm intelligence algorithms, Particle Swarm Optimization (PSO) and Fireworks Algorithm (FWA), to the regional seismic waveform inversion. To explore the advantages and disadvantages of swarm intelligence algorithms over GA, synthetic experiments are conducted by using these two swarm intelligence algorithm and several GA variants as well as Differential Evolution (DE). The experimental results show that, both swarm intelligence algorithms outperform the widely used GA, DE, and the models estimated by swarm intelligence algorithms are closer to the true solution. The promising results imply that swarm intelligence algorithms are a potentially more powerful tool for inversion problems.