The inverse problem to infer the initial water displacement is treated as an ill-posed problem of the hydrodynamic inversion of tsunami tide gauge records. To this end, we have developed a technique based on the least square inversion and a truncated SVD approach. The proposed filtering technique essentially improves the recover of a tsunami source. We have carried out a series of numerical experiments with synthetic data and a real bathymetry. The accuracy of the tsunami source recovery depends on the spatial distribution of an observation system, target areas and bathymetric features along the wave path. The validity of the approach proposed is confirmed by the numerical results obtained.