Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 472575, 16 pages
Research Article

A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves

1Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan 609-735, Republic of Korea
2Maritime and Ocean Engineering Research Institute, Daejeon 305-343, Republic of Korea

Received 20 June 2011; Revised 17 September 2011; Accepted 8 October 2011

Academic Editor: Mohammad Younis

Copyright © 2012 T. S. Jang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents an inverse problem and its solution procedure, which are aimed at identifying a sudden underwater movement of the sea bottom. The identification is mathematically shown to work with a known snapshot data of generated water wave configurations. It is also proved that the problem has a unique solution. However, the inverse problem is involved in an integral equation of the first kind, resulting in an ill-posed problem in the sense of stability. That is, the problem lacks solution stability properties. To overcome the difficulty of solution instability, in this paper, a stabilization technique, called regularization, is incorporated in the present solution procedure for the identification of the sea bottom movement. A numerical experiment is presented to demonstrate that the proposed (numerical) solution procedure operates.