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Abstract <p>A practical method has been developed for determining the region of space in which the dispersionless shallow-water approximation is capable of reproducing dispersive tsunami waves with a given accuracy. We propose to evaluate the accuracy by the degree of delay of the dispersive wave packet relative to the front of long waves. The degree of delay is calculated along the wave rays emitted from the center of the source at different azimuth angles. The calculation of rays is implemented on a spherical surface taking into account the bottom relief, which is smoothed to meet the conditions of applicability of the ray theory. The dominant period of tsunami waves is calculated based on the shape of the initial elevation of the water surface in the source taking into account the distribution of ocean depths along each of the rays. The degree of delay of the dispersing wave packet is calculated based on the dominant period and the depth profile along the ray. The operation of the method is demonstrated using the example of two tsunami events on the Central Kuril Islands (Simushir tsunamis of November 15, 2006, and January 13, 2007).</p>

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Assessment of the Area of Applicability of the Shallow-Water Approximation for Reproducing Dispersive Tsunami Waves

  • 期刊论文

  • 发表日期：

    2025年8月14日

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  • M. A. Nosov,
  • A. I. Zarubina,
  • S. V. Kolesov

摘要

Abstract

A practical method has been developed for determining the region of space in which the dispersionless shallow-water approximation is capable of reproducing dispersive tsunami waves with a given accuracy. We propose to evaluate the accuracy by the degree of delay of the dispersive wave packet relative to the front of long waves. The degree of delay is calculated along the wave rays emitted from the center of the source at different azimuth angles. The calculation of rays is implemented on a spherical surface taking into account the bottom relief, which is smoothed to meet the conditions of applicability of the ray theory. The dominant period of tsunami waves is calculated based on the shape of the initial elevation of the water surface in the source taking into account the distribution of ocean depths along each of the rays. The degree of delay of the dispersing wave packet is calculated based on the dominant period and the depth profile along the ray. The operation of the method is demonstrated using the example of two tsunami events on the Central Kuril Islands (Simushir tsunamis of November 15, 2006, and January 13, 2007).