Bayesian geoacoustic inversion using mixture density network

TL;DR

The paper tackles the computational burden of Bayesian geoacoustic inversion by introducing a mixture density network to learn the multidimensional posterior $P(\mathbf{m|d})$ directly from simulated data. It derives geoacoustic statistics (MAP, mean, marginal PDFs, covariance) from the MDN outputs, enabling efficient probabilistic inference without MCMC. The MDN is trained on a large synthetic dataset generated by forward modeling with a layered seabed and then validated on synthetic and real data cases, including Snorre field. Results show rapid (seconds) generation of fully probabilistic solutions with competitive accuracy to Monte Carlo methods, suggesting potential for real-time geoacoustic inversion.

Abstract

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.

Figures (12)

• Figure 1: Model parametrization. The bottom layer is a semi-infinite layer. Note that layers with different thickness do not keep the same scale for display purposes.
• Figure 2: The shear-wave velocity density distribution.
• Figure 3: Network structure. Dense layer is the regular deeply connected neural network layer.
• Figure 4: The modified ELU activation function.
• Figure 5: The loss as a function of epoch. (a) The loss of the training on noiseless data. (b) The loss of the training on noisy data.