Scholarlink

<p>We discuss the following inverse problem: given the run-up data of a tsunami wave, can we recover its initial shape? We study this problem within the framework of the non-linear shallow water equations, a model widely used to study tsunami propagation and inundation. Previously, we demonstrated that in the case of infinite sloping bathymetry, it is possible to recover the initial water displacement and velocity from shoreline readings (Rybkin et al. [<CitationRef CitationID="CR29">29</CitationRef>, <CitationRef CitationID="CR31">31</CitationRef>, <CitationRef CitationID="CR33">33</CitationRef>]). We consider a finite sloping bathymetry. We show that it is possible to recover boundary conditions (water displacement and velocity) on a virtual buoy from the shoreline data. Further, we discuss stitching together the shallow water equations and the Boussinesq equation in a more complex piece-wise sloping bathymetry in order to recover the initial conditions, while incorporating the dispersion into our model.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Reconstruction of the Non-linear Wave at a Buoy from Shoreline Data and Applications to the Tsunami Inverse Problem for Piece-Wise Sloping Bathymetry

  • 期刊论文

  • 发表日期：

    2026年2月3日

查看全文
  • Oleksandr Bobrovnikov,
  • Madison Jones,
  • Shriya Prasanna,
  • Josiah Smith,
  • Alexei Rybkin,
  • Efim Pelinovsky

摘要

We discuss the following inverse problem: given the run-up data of a tsunami wave, can we recover its initial shape? We study this problem within the framework of the non-linear shallow water equations, a model widely used to study tsunami propagation and inundation. Previously, we demonstrated that in the case of infinite sloping bathymetry, it is possible to recover the initial water displacement and velocity from shoreline readings (Rybkin et al. [29, 31, 33]). We consider a finite sloping bathymetry. We show that it is possible to recover boundary conditions (water displacement and velocity) on a virtual buoy from the shoreline data. Further, we discuss stitching together the shallow water equations and the Boussinesq equation in a more complex piece-wise sloping bathymetry in order to recover the initial conditions, while incorporating the dispersion into our model.