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

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  • T. S. Jang
  • Hong Gun Sung
  • Jinsoo Park

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.

Suggested Citation

  • T. S. Jang & Hong Gun Sung & Jinsoo Park, 2012. "A Determination of an Abrupt Motion of the Sea Bottom by Using Snapshot Data of Water Waves," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-16, January.
    • Handle: RePEc:hin:jnlmpe:472575
    DOI: 10.1155/2012/472575
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