DECODING SEISMIC DISTURBANCES: EMPLOYING SDFA FOR PRECISE DISCRIMINATION

Abstract

This study introduces the Smoothed Detrended Fluctuation Analysis (SDFA) method, proposed by Linhares in 2016, as a novel approach for describing the long-range correlation of time series. The methodology is grounded in the Detrended Fluctuation Analysis (DFA) introduced by Peng et al. (1994) and the wavelet shrinkage procedure outlined by Donoho and Johnstone (1994, 1995) and Vidakovic (1999). SDFA computes various statistical fluctuation measures denoted as F(l), where 'l' represents the window length. The wavelet shrinkage estimator F(l) is obtained for all window lengths (l). By varying the window length, F(l) can be characterized by a scaling exponent, specifically the slope coefficient derived from the regression of F(l) on ln(l), with 'l' ranging from 4 to g(n), where g(n) is determined as ⌊(ln(n))⌋ and 'n' is the length of the time series.

In the context of seismic analysis, waves of energy generated by human activities or natural phenomena present challenges in accurate statistical analysis. Seismic events caused by human-made explosions, such as those from mining, road excavation, and construction applications, introduce complexities that may lead to errors in seismicity analysis. This study addresses the need for methodologies capable of correctly identifying the source type generating a recorded seismic signal, emphasizing the importance of distinguishing between natural and anthropogenic seismic events. Beccar-Varela et al. (2016) highlight the significance of this challenge in the field of seismology.

The proposed SDFA method proves to be particularly relevant for monitoring human-made explosions, contributing to the development of robust techniques for source identification in seismic signals. The optimal choice for the number of regressors in the SDFA method, denoted by g(n) = ⌊(ln(n))⌋, where ⌊⋅⌋ represents the integer part function, is determined based on the length of the time series ('n'). This choice ensures an efficient and accurate application of the SDFA method for analyzing seismic data.