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.

翻译：贝叶斯地声反演问题传统上采用马尔可夫链蒙特卡洛方法或其变体求解，计算成本高昂。本文通过混合密度网络理论，从多维后验概率密度中推导贝叶斯地声反演的重要地声统计量，从而扩展了经典贝叶斯地声反演框架。这些统计量使得能够直接在完整参数空间上训练网络，并获取模型参数的多维后验概率密度。本方法为贝叶斯推断框架下的地声反演问题提供了更高效的求解途径。网络以面波频散曲线模拟数据集进行训练（以横波速度为标签），并在合成数据与实测数据案例中进行测试。结果表明，该网络能给出可靠预测，并对未见数据具有良好的泛化性能。网络训练完成后，可在数秒内快速给出与蒙特卡洛方法相当的完全概率解，为实时反演提供了前景广阔的技术路径。