This paper highlights the influence of the model parametrization, including the sea level recorders localization and source discretization, on the tsunami source inversion. Modeling the initial water displacement in the tsunami source area is based on the least square inversion and a truncated singular value decomposition approach that makes possible to overcome the instability of a numerical solution and to obtain an acceptable result in spite of the ill-posedness of the problem. This paper discusses the importance of the consideration of the parameter r in conjunction with the source spatial discretization. The results obtained allow one to explain the appearance of the artifacts in the solution by the truncation effect. Moreover, the optimal choice of such parameters as the spatial discretization of a source, the arrangement of the sea level recorders and the parameter r leads to a profound improvement in recovering the initial tsunami waveform. The methodology proposed has been verified by the numerical simulation of the 16 September 2015 Chile tsunami source.