Ocean-depth measurement using shallow-water wave models

In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically, we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible, irrotational fluid from measurements of the free-surface deviation alone, within the context of dispersive shallow-water wave models. The need to consider the shallow-water regime arises from the ill-posed nature of the problem and is motivated by prior work. Assuming only a relatively inaccurate initial guess for the bottom-boundary, we design an algorithm to accurately deduce the fluid velocities and the true bottom-boundary profile. We achieve this by considering two separate inverse problems: one to deduce the bottom-boundary from velocities and the surface deviation, and another to recover the velocities from the surface deviation and an approximate bottom-boundary. The former is a classic inverse problem that requires the inversion of an ill-conditioned matrix, whereas the latter employs the observer framework. Combining the two inverse problems leads to our reconstruction algorithm. We emphasize the role played by model selection and its impact on algorithm design and the accuracy of the reconstruction.

Automated summary

This paper discusses an algorithm for inferring the bottom impermeable boundary of ocean basins from measurements of free-surface deviation, focusing on the reconstruction of bottom-boundary profile and fluid velocities. By considering two separate inverse problems, the algorithm accurately deduces the information needed. The role of model selection on algorithm design and reconstruction accuracy is emphasized.