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Title: The inverse tsunami problem for symmetric islands of simple shape
Authors: Knowles, Charles Ernest
Reid, Robert O.
Keywords: Ocean waves--Mathematical models
Publisher: Texas A & M University. College of Geosciences.
Texas A & M University. Department of Oceanography.
Coastal Engineering Research Center (U.S.)
Series/Report no.: [Texas. A & M University. Department of Oceanography] Project 471A, Reference;70-7T
Abstract: Abstract: The problem investigated in this paper is that of estimating the deep water signature of a tsunami based on an observed marigram in the immediate vicinity of an island. The basic assumption is made that the incident tsunami in deep water is represented by a plane wave but that its signature in time at a fixed point in deep water is unknown. This implies that the distance of the earthquake epicenter is large compared with the horizontal scale of the island at its base on the ocean floor. The present study is limited to the linear theory for long waves and accordingly its application requires that the observed water level signatures be at locations where non-linear effects and dispersion are minimal. The method is numerical. For a given direction of the input wave train in deep water and a given observation point (P) near the island, the solution of the problem as posed rest on the determination of the transfer function for the response at P due to the input. If the transfer function can be established from a known pair of input-output time sequences ·having a broad band spectrum, then presently being employed for the study of deep sea tides and could detect a tsunami (Miller, personal correspondence)), so what is known has been derived almost entirely from theory. Records obtained on small islands in the mid-Pacific have given the best information, but theoretical deductions imply that the waves can be significantly modified by the transformation that takes place when they interact with the island shoreline and surrounding sea-floor topography. Included in this interaction are modifications and amplifications due to linear and non-linear transformations related to shoaling, scattering, diffraction, refraction and possible resonance phenomena created when wave energy is trapped around the island by the bathymetry (see Longuet-Higgins, 1967). Studies of this transformation should take into account each of these factors.
Description: Contract Report
Rights: Approved for public release; distribution is unlimited.
Appears in Collections:Contract Report

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