Terrine, Mr Raphael (2023) Identification des déformations du fond marin à l'aide de mesures sur la surface libre PFE - Project Graduation, ENSTA.
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Abstract
This report presents the basis for the study of the reconstruction of seabed deformations by measuring the level of the free surface using a method of regularizing the equations of the inverse problem, an innovation in the bathymetry literature. Classically, the resolution of such problems is considered in the literature from the point of view of optimization, within the framework of a flat-bottomed ocean. The method used here is a more direct method of variational formulation regularized by Tikhonov, with no assumptions on the ocean floor. As such, it allows us to to treat the problem in its generality without any assumption about the shape of the ocean floor. The shape of the seabed is deduced, by equations derived from oceanographic models, from noisy measurements on a surface. Two problems are successively addressed on the basis of this method: the linear tsunami detection problem and the more difficult bathymetry geometric inverse problem, aimed at detecting the ocean floor through agitation of the medium.\\ This work is only a first approach in terms of solving the general problem. It suffers from several limitations: frequency regime (whereas the real problem is one of temporal evolution), the 2D model and the use of linear models only. All the numerical simulations were carried out using the XLIFE++ library \cite{xlifepp} developed in the equip POEMS.
Item Type: | Thesis (PFE - Project Graduation) |
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Uncontrolled Keywords: | Bathymétrie |
Subjects: | Mathematics and Applications |
ID Code: | 9822 |
Deposited By: | Raphael Terrine |
Deposited On: | 11 oct. 2023 15:14 |
Dernière modification: | 11 oct. 2023 15:14 |
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