A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves. (12th January 2012) - Jang Jang, T. S. T. S.; Sung Sung, Hong Gun Hong Gun; Park Park, Jinsoo Jinsoo
Abstract : 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.