The Multi-fractal Scaling Behavior of Seismograms Based on the Detrended Fluctuation Analysis

2015 ◽  
pp. 99-115
Author(s):  
Simanchal Padhy
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Scaling Behavior ◽  
Fluctuation Analysis ◽  
Fractal Scaling ◽  
Detrended Fluctuation

scholarly journals Fractal scaling analysis of groundwater dynamics in confined aquifers

2017 ◽  
Vol 8 (4) ◽  
pp. 931-949 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.

FLUCTUATION ANALYSIS OF MONTHLY RAINFALL TIME SERIES

2010 ◽  
Vol 09 (02) ◽  
pp. 219-228 ◽  
Author(s):  
JORGE O. PIERINI ◽  
LUCIANO TELESCA
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Scaling Behavior ◽  
Monthly Rainfall ◽  
Fluctuation Analysis ◽  
Rainfall Time Series ◽  
Scaling Exponents ◽  
Times Series ◽  
Detrended Fluctuation

The monthly rainfall time series, spanning more than a century, recorded in several sites in the middle Argentina were analyzed. The power spetral density (PSD) method reveals the presence of annual and semi-annual cyclic fluctuations. The detrended fluctuation analysis (DFA) performed on the residual times series (after removing the periodicities) shows a scaling behavior, characterized by DFA scaling exponents ranging between 0.54 and 0.58. These findings could contribute to a better understanding of rainfall dynamics.

scholarly journals Fractal Scaling Analysis of Groundwater Dynamics in Confined Aquifers

2017 ◽  
Author(s):  
Tongbi Tu ◽  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Time Series ◽  
Groundwater Level ◽  
Detrended Fluctuation Analysis ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Fractal Scaling ◽  
Groundwater Level Fluctuations ◽  
Groundwater Dynamics ◽  
Detrended Fluctuation ◽  
Infinite Moments

Abstract. Groundwater closely interacts with surface water and even climate systems in most hydro-climatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations of confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality; and Multifractal detrended fluctuation analysis (MF-DFA) and Multiscale Multifractal Analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics which may be fitted by the Lévy stable distribution or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes, which can model both the long-memory behavior as well as the Brownian finite-memory behavior.

Investigation scaling behavior of earthquake-related signals in magnetotelluric measurements, Northern Algeria

2021 ◽  
Author(s):  
Ahmed Seddik Kasdi ◽  
Abderrezak Bouzid ◽  
Mohamed Hamoudi ◽  
Abdslem Abtout
Keyword(s):  
Time Series ◽  
Detrended Fluctuation Analysis ◽  
Seismic Event ◽  
Scaling Behavior ◽  
Stationary Time Series ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Time Dynamics ◽  
Electromagnetic Signals ◽  
Detrended Fluctuation

<p>The north-central region of Algeria has been characterized by a swarm-type seismicity, after the strong Mw6.8 Boumerdès earthquake of May 21, 2003, culminating with the earthquake that occurred on July 17, 2013 of magnitude Mw=5. A magnetotelluric station was installed on December 2014 in the Medea region, 60 km south of the capital Algiers. We measured the five components of the telluric and magnetic field with a sampling frequency of 15 Hz. The seismic activity in the region provided the opportunity to observe and study the earthquake’s related electromagnetic signal. The scaling properties of the recorded electric and magnetic time series were investigated. On the basis of multifractal detrended fluctuation analysis, which is a powerful method for detecting scaling in non-stationary time series, deviations from the uniform scale of the power law were identified and quantified. We investigated the time dynamics of the earthquake related electromagnetic time series measured at the magnetotelluric station. The multifractal detrended fluctuation analysis showed the different multifractality properties of electromagnetic signals before, during and after the seismic event. The results of this work show an unstable scaling behavior in electromagnetic data during the occurrence of the seismic event. These first results could be useful in the framework of seismo-electromagnetic signals studies.</p>

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