Abstract
Abstract. This paper deals with the application of the r-solution method to recover the initial tsunami waveform in a tsunami source area by remote water-level measurements. Wave propagation is considered within the scope of a linear shallow-water theory. An ill-posed inverse problem is regularized by means of least square inversion using a truncated SVD (singular value decomposition) approach. The method presented allows one to control instability of the numerical solution and to obtain an acceptable result in spite of ill-posedness of the problem. It is shown that the accuracy of tsunami source reconstruction strongly depends on the signal-to-noise ratio, the azimuthal coverage of recording stations with respect to the source area and bathymetric features along the wave path. The numerical experiments were carried out with synthetic data and various computational domains including a real bathymetry.
Highlights
All of us were witnesses of the terrible tsunami that occurred on 11 March 2011 off the coast of Japan
The developed numerical inversion technique based on least square inversion and truncated SVD approach is here described to reconstruct the initial tsunami waveform in a tsunami source area based on inversion of remote water-level measurements
We have applied an approach based on SVD and r-solution methods to recovering the initial tsunami waveform in a tsunami source area
Summary
All of us were witnesses of the terrible tsunami that occurred on 11 March 2011 off the coast of Japan. Among the recent studies dealing with the inverse tsunami source problem, it is necessary to cite an approach which is successfully applied and which is a method of direct sorting combined with the minimal residual method (Percival et al, 2011; Lavrentiev and Romanenko, 2014) This method determines the unknown coefficients of a set of the typical unit tsunamigenic sub-faults disposed at the subduction zone so that residuals between the calculating data from. The developed numerical inversion technique based on least square inversion and truncated SVD (singular value decomposition) approach is here described to reconstruct the initial tsunami waveform (tsunami source) in a tsunami source area based on inversion of remote water-level measurements (marigrams) This inversion method was first described in its fundamentals in the Russian scientific journals (Voronina and Tcheverda, 1998; Voronina, 2004, 2013). The results of the numerical simulations have shown a promising outlook of this approach
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