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床层析成像的无限维贝叶斯框架，利用波的散射同步估计海床及其粗糙度。层析成像被视为一个不适定问题，其中多种海床构型可能产生相似的测量模式。我们提出了一种新方法，聚焦于海床的统计各向同性。通过利用分数阶可微性识别海床粗糙度，本文给出了一个鲁棒的数值算法以估计海床并量化不确定性。大量数值实验验证了该方法的有效性，为大规模海床勘探提供了有前景的途径。