Reconstruction of initial Tsunami waveforms by a truncated SVD method

Abstract

Abstract This paper proposes an approach to reconstructing initial tsunami waveforms in tsunami source areas based on the inversion of remote measurements of water-level data. This inverse problem is treated as an ill-posed problem of hydrodynamic inversion with tsunami tide gauge records. Tsunami wave propagation is considered within the scope of the linear shallow-water theory. The direct problem is approximated by a finite-difference technique. The ill-posed inverse problem of reconstructing initial tsunami waveforms is regularized by means of a least square inversion using the truncated SVD approach. A so-called r-solution is numerically obtained. The algorithm is verified with real bathymetry data of the Peru subduction zone and synthetic records. It is found that the accuracy of tsunami source reconstruction strongly depends on the signal-to-noise ratio, the azimuthal and temporal coverage of tide gauge stations relative to the target area and the bathymetric features along the wave path.