Comparison of deterministic and stochastic approaches to crosshole seismic travel-time inversions

The Bayesian inversion method is a stochastic approach based on the Bayesian theory. With the development of sampling algorithms and computer technologies, the Bayesian inversion method has been widely used in geophysical inversion problems. In this study, we conduct inversion experiments using crosshole seismic travel-time data to examine the characteristics and performance of the stochastic Bayesian inversion based on the Markov chain Monte Carlo sampling scheme and the traditional deterministic inversion with Tikhonov regularization. Velocity structures with two different spatial variations are considered, one with a chessboard pattern and the other with an interface mimicking the Mohorovičić discontinuity (Moho). Inversions are carried out with different scenarios of model discretization and source–receiver configurations. Results show that the Bayesian method yields more robust single-model estimations than the deterministic method, with smaller model errors. In addition, the Bayesian method provides the posterior probabilistic distribution function of the model space, which can help us evaluate the quality of the inversion result.