The paper deals with the reconstruction of the original tsunami waveform in the source area records from the waves observed on a set of the coastal wave gauges. The wave propagation is described by the linearized shallow-water equations when depth depends on one variable. The direct problem is approximated by the explicit-implicit finite difference scheme. The ill-posed inverse problem of the reconstruction is regularized by means of the least square inversion using the truncated SVD approach, so r-solution is a result of the numerical process. Results of numerical experiments are presented.