This paper presents an extension of the original Grim effective wave concept. The aim is to develop a basic tool that is able, with a reduced number of assumptions with respect to the original Grim effective wave, to simplify the problem of description of hydrostatic variations of roll restoring in irregular waves. The irregular sea surface is approximated by an "equivalent" (effective) regular wave having fixed wave length but variable mean value, amplitude and position of the crest. The characteristics of the effective wave are obtained from the irregular sea surface by means of linear transfer functions. The probabilistic properties of the obtained parameters of the substitute wave are analysed and examples of application of the developed concept are provided.
