Abstract
Abstract. This paper deals with the application of 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 approach. The properties of obtained solution are determined to a large extent by the properties of an inverse operator, which were numerically investigated. 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. The method proposed allows us to make a preliminary prediction of the efficiency of the inversion with a given set of the recording stations and to find out the most informative part of the existing observation system. This essential property of the method can prove to be useful in designing a monitoring system for tsunamis.