DECODING EARTH'S RUMBLES: UNVEILING SEISMIC SIGNATURES WITH SDFA ANALYSIS

Abstract

The Smoothed Detrended Fluctuation Analysis (SDFA), a method introduced by Linhares in 2016, has emerged as a valuable tool for unveiling long-range correlations within time series data. Rooted in the principles of Detrended Fluctuation Analysis (DFA) and the wavelet shrinkage procedure, SDFA employs varying window lengths (l) to compute statistical fluctuations measures denoted as F(l). Through a meticulous analysis of these measures across different window lengths, SDFA derives a scaling exponent, specifically the slope coefficient obtained through regression analysis of F(l) against ln(l), where l varies within a specific range determined by g(n).In a subsequent work in 2016, Linhares established an optimal choice for the function g(n), where g(n) is defined as ⌊(ln(n))⌋, with ⌊⋅⌋ representing the integer part function and n denoting the length of the time series. This abstract delves into the foundational concepts and procedural intricacies underlying the SDFA method, emphasizing its pivotal role in discerning and characterizing long-range correlations inherent in time series data