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

TL;DR

This paper investigates the dynamic singularities in seismic signals using a generalized Langevin equation framework, emphasizing the role of memory functions and statistical memory in understanding seismic phenomena's stochastic behavior.

Contribution

It introduces a finite-discrete form of the GLE to analyze seismic signals, incorporating complexity, nonergodicity, and fractality in seismic activity modeling.

Findings

Seismic signals exhibit strong and weak memory effects.

Memory functions are fundamental in describing seismic stochastic behavior.

The finite-discrete GLE effectively models complex seismic phenomena.

Abstract

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.