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Mathematical Problems in Engineering
Volume 2013, Article ID 286247, 10 pages
Research Article

Reconstruction of Initial Wave Field of a Nonsteady-State Wave Propagation from Limited Measurements at a Specific Spatial Point Based on Stochastic Inversion

Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan

Received 1 August 2012; Revised 11 March 2013; Accepted 14 March 2013

Academic Editor: Fatih Yaman

Copyright © 2013 S. L. Han and Takeshi Kinoshita. 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 studies an inverse problem that can be used for reconstructing initial wave field of a nonsteady-state wave propagation. The inverse problem is ill posed in the sense that small changes in the input data can greatly affect the solution of the problem. To address the difficulty, the problem is formulated in the form of an inference problem in an appropriately constructed stochastic model. It is shown that the stochastic inverse model enables the initial surface disturbance to be reconstructed, including its confidence intervals given the noisy measurements. The reconstruction procedure is illustrated through applications to some simulated data for two- and three-dimensional problem.