We study how the tsunami mode is generated by a scaled double-couple seismic source and how it propagates in realistic oceanic models. The method developed and used is the direct extension to tsunami waves, propagating in multilayered oceanic media, of the well-known Haskell method. The most intensive tsunamis may be expected from sources located in the deep-water parts of the ocean, within the crust. The extension to laterally heterogeneous structures, shows that if the thickness of the ocean liquid layer diminishes, the maximum amplitude of the tsunami wavetrain increases.