  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 by
deriving important geoacoustic statistics of Bayesian geoacoustic inversion
from the multidimensional posterior probability density (PPD) using the mixture
density network (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 present approach provides a much more efficient way to
solve geoacoustic inversion problems in Bayesian inference framework. The
network is trained on a simulated dataset of surface-wave dispersion curves
with shear-wave velocities as labels and tested on both synthetic and real data
cases. 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 promising approach for
real-time inversion.
