This paper introduces an infinite-dimensional Bayesian framework for acoustic seabed tomography, leveraging wave scattering to simultaneously estimate the seabed and its roughness. Tomography is considered an ill-posed problem where multiple seabed configurations can result in similar measurement patterns. We propose a novel approach focusing on the statistical isotropy of the seabed. Utilizing fractional differentiability to identify seabed roughness, the paper presents a robust numerical algorithm to estimate the seabed and quantify uncertainties. Extensive numerical experiments validate the effectiveness of this method, offering a promising avenue for large-scale seabed exploration.

翻译：本文提出了一种用于声学海底层析成像的无限维贝叶斯框架，利用波散射现象同步估计海底地形及其粗糙度。层析成像被视为一个不适定问题，多种海底构型可能导致相似的测量模式。我们提出了一种聚焦于海底统计各向同性的新方法。通过利用分数阶可微性识别海底粗糙度，本文提出了一种稳健的数值算法来估计海底地形并量化不确定性。大量数值实验验证了该方法的有效性，为大规模海底勘探提供了前景广阔的研究途径。