A novel strong ground motion stochastic model is formulated in association with physically interpretable parameters that are capable of efficiently characterizing the complex evolutionary nature of the phenomenon. A multi-modal, analytical, fully non-stationary spectral version of the Kanai-Tajimi model is introduced achieving a realistic description of the evolutionary spectral energy distribution of the seismic ground motions. The functional forms describing the temporal evolution of the model parameters can effectively model complex highly non-stationary power spectral characteristics. The analysis space, where the analytical forms describing the evolution of the model parameters are established, is the energy domain instead of the typical use of the time domain. The Spectral Representation Method facilitates the simulation of sample model realizations.