Analytically and quantitatively we reveal that the GLE equation, based on a memory function approach, in which memory functions and information measures of statistical memory play fundamental role in determining the thin details of the stochastic behavior of seismic systems, naturally conduces to a description of seismic phenomena in terms of strong and weak memory. Due to a discreteness of seismic signals we use a finite - discrete form of GLE. Here we studied some cases of seismic activities of Earth ground motion in Turkey with consideration of complexity, nonergodicity and fractality of seismic signals.