Articles | Volume 15, issue 6
Nat. Hazards Earth Syst. Sci., 15, 1251–1263, 2015

Special issue: Progress in tsunami science in light of the 2004 and 2011...

Nat. Hazards Earth Syst. Sci., 15, 1251–1263, 2015

Research article 16 Jun 2015

Research article | 16 Jun 2015

Inversion method for initial tsunami waveform reconstruction

V. V. Voronin1, T. A. Voronina2, and V. A. Tcheverda3,4 V. V. Voronin et al.
  • 1Novosibirsk State University, Novosibirsk, Russia
  • 2Institute of Computational Mathematics and Mathematical Geophysics of SB RAS, Novosibirsk, Russia
  • 3A.A.Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk, Russia
  • 4Kazakh-British Technical University, Almaty, Kazakhstan

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.

Short summary
The developed numerical inversion technique based on the least square inversion and a truncated SVD approach were applied to recovering the initial tsunami waveform. The method presented allows one to control the instability of the numerical solution. Analyzing the singular spectra of the matrix obtained during numerical calculations one can estimate the future inversion by a certain observational system that will allow offering more effective disposition for the registrators by precomputations.
Final-revised paper