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Majority of devastating tsunami waves springs from strong bottom earthquakes. Co-seismic bottom deformation and associated displacement of water column from its equilibrium position is the main physical mechanism cause of tsunami generation. Thus, it is useful to establish simple general relationships between parameters of an earthquake and the subsequent tsunami. Such relationships are important for understanding the nature of tsunamis and other oceanic phenomena of seismotectonic origin. In practice, such relationships may support prompt assessment of characteristics of a seismogenic tsunami. In this study, in order to establish relationships between earthquake characteristics (moment magnitude and depth) and tsunami source parameters (double-amplitude of vertical bottom deformation, displaced water volume, and potential energy of initial elevation) we employ an empirical-analytical approach in combination with Monte-Carlo method. The approach is based on the Okada solution for a finite rectangular fault and empirical scaling laws for earthquake sources. As a result of Monte Carlo simulation we obtain synthetic distributions of the tsunami source parameters which allow us to determine their maximum and most probable values. Finally, we construct synthetic relationships which allow calculating maximum and most probable values of tsunami source parameters by a moment magnitude and a depth of an earthquake.