Tsunami propagation in Cartesian space over rigid & elastic seabeds, plus propagation on the sphere with rigid seabed

Williams, Byron 2024. Tsunami propagation in Cartesian space over rigid & elastic seabeds, plus propagation on the sphere with rigid seabed. PhD Thesis, Cardiff University. Item availability restricted.

Preview	PDF - Accepted Post-Print Version Download (20MB) | Preview
	PDF (Cardiff University Electronic Thesis and Dissertation Form) - Supplemental Material Restricted to Repository staff only Download (1MB)

Abstract

This work discusses the generation and propagation of tsunamis and their associated acoustic–gravity waves. Many studies of tsunamis have been carried out in the past, dating back decades, but here we aim to extend the results of two - relatively recent - key papers. In the process new results were found, which it is hoped, may help in the future development of tsunami early warning systems. The first extension takes the rigid seabed, purely acoustic, slender fault model as developed by Mei and Kadri and adds the restoring force of gravity. With this addition, it becomes possible to derive the equations governing the tsunami propagation as well as the acoustic-gravity waves. Since the underlying mathematical model is linear, we found more complex multi-fault clusters could be handled quite easily using superposition. Results were validated with numerical models. The next step aimed to address the more realistic scenario whereby the seabed is now regarded as an elastic medium. The inclusion of elasticity has some interesting consequences. Firstly the acoustic–gravity waves are found to terminate after a finite time, with the decay time most affected by seabed rigidity. Secondly, elasticity enables coupling of the acoustic–gravity waves to the seabed and propagation with the shear wave velocity. We derive improved estimates for these frequencies. Next, elasticity enables the propagation of a second surface wave of negligible amplitude which travels at the speed of sound - this is not seen in the rigid model. The cut-off frequency for this wave is derived. We also noted the acoustic-gravity wave signal carried information which depended on the time evolution and geometry of the rupture. We show that, with appropriate filtering, information on the fault’s geometry and dynamics can be retrieved. Finally we shift perspective from a local, Cartesian coordinate system to a global spherical coordinate system. By application of appropriate scales, the equations governing the defocusing and focusing of the tsunami amplitude due to the spherical geometry involved can be derived. The acoustic–gravity waves undergo a similar defocusing/focusing effect. A qualitative comparison is made with the Tonga eruption of 2022 which saw tsunami and acoustic–gravity wave propagation on a global scale.

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Date of First Compliant Deposit:	19 June 2024
Last Modified:	20 Jun 2024 13:50
URI:	https://orca.cardiff.ac.uk/id/eprint/169900

Actions (repository staff only)

Edit Item