Bayesian geoacoustic inversion using mixture density network

Bayesian geoacoustic inversion problems are conventionally solved by Markov chain Monte Carlo methods or its variants, which are computationally expensive. This paper extends the classic Bayesian geoacoustic inversion framework using the mixture density network (MDN), which provides a much more efficient way to solve geoacoustic inversion problems in Bayesian inference framework. Some important geoacoustic statistics of Bayesian geoacoustic inversion are derived from the multidimensional posterior probability density (PPD) using the MDN theory. These statistics make it convenient to train the network directly on the whole parameter space and get the multidimensional PPD of model parameters. The network is trained on a simulated dataset of surface-wave dispersion curves with shear-wave velocities as labels. The results show that the network gives reliable predictions and has good generalization performance on unseen data. Once trained, the network can rapidly (within seconds) give a fully probabilistic solution which is comparable to Monte Carlo methods. It provides an promissing approach for real-time inversion.