Oceandepth measurement using shallowwater wave models
Abstract
In this paper, we consider a problem inspired by the realworld 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 freesurface deviation alone, within the context of dispersive shallowwater wave models. The need to consider the shallowwater regime arises from the illposed nature of the problem and is motivated by prior work. We design an algorithm using which, both fluid velocities and the bottomboundary profile, may be accurately recovered assuming an a priori relatively inaccurate guess for the bottom boundary. We achieve this by considering two separate inverse problems: one to deduce the bottomboundary from velocities and the surface deviation, and another to recover the velocities from the surface deviation and an approximate bottomboundary. The former is a classic inverse problem that requires the inversion of an illconditioned matrix while the latter employs the observer framework. Combining the two inverse problems leads to our reconstruction algorithm. We emphasise the role played by model selection and its impact on algorithm design and the accuracy of the reconstruction.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.00964
 arXiv:
 arXiv:2106.00964
 Bibcode:
 2021arXiv210600964V
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 35R30 (Primary);
 35Q35;
 76B15 (Secondary)