The study of dynamic singularities of seismic signals by the generalized Langevin equation

Analytically and quantitatively we reveal that the generalized Langevin equation (GLE), based on a memory function approach, in which memory functions and information measures of statistical memory play a fundamental role in determining the thin details of the stochastic behavior of seismic systems, naturally leads 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 the GLE. Here we studied some cases of seismic activities of Earth ground motion in Turkey with consideration of the complexity, nonergodicity and fractality of seismic signals.