Date of Award
12-17-2024
Document Type
Thesis
Abstract
The problem of tsunami run-up has been extensively studied in the framework of the shallow water equations. Typically one assumes that the initial water displacement and the initial velocity are known, and then the run-up is computed using the Carrier-Greenspan transformation. The inverse problem consists of recovering the initial displacement and/or velocity from the shoreline oscillations. It has been previously demonstrated that the initial displacement can be recovered from shoreline oscillations under the assumption of zero initial velocity for the sloping plane beach. We show that this result can be generalised to arbitrary power-shaped bathymetries. Moreover, we show that for non-breaking waves, the contributions of velocity and displacement can be separated at the shoreline. This separation allows for the recovery of both the initial displacement and velocity from the shoreline oscillations.
Recommended Citation
Bobrovnikov, Oleksandr, "Inverse problems for shallow water equations and applications to tsunami modelling" (2024). Mathematics and Statistics . 66.
https://ualaska.researchcommons.org/uaf_grad_math_stats/66
Handle
http://hdl.handle.net/11122/15669