Fractal and Chaos in Exploration Geophysics

Ouadfeul, Sid‐Ali; Aliouane, Leila; Boudella, Amar

doi:10.5772/53560

Cited by 4 publications

(4 citation statements)

References 26 publications

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“…Those studies have been mainly dealt with the characterization of fractality of spatial and temporal distributions revealing scaling, monofractal and multifractal features (see, for instance, the Iranian seismicity analysis by Zamani and Agh-Atabai [40], the Japanese microseismicity analysis by Hirata and Imoto [11], the Italian inter-event time distribution study by Telesca et al [27], Telesca and Lapenna [28], and the Mexican seismicity study by Flores-Marquez and Valverde-Esparza et al [9]). …”

Section: Introductionmentioning

confidence: 99%

Multifractal detrended fluctuation analysis of earthquake magnitude series of Mexican South Pacific Region

Márquez

Ramírez-Rojas

Telesca

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Multifractal detrended fluctuation analysis of earthquake magnitude series of Mexican South Pacific Region

Márquez

Ramírez-Rojas

Telesca

2015

Applied Mathematics and Computation

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“…From the 1980s onwards, chaos theory, in its various formulations, particularly fractal analysis, permeated many specific research areas, including geology, climatology, and neuroscience [59][60][61][62][63]. The attractors and equations of fractal analysis are capable mathematical formulations that explain chaotic and non-chaotic behavior in natural and sociotechnical systems.…”

Section: The Progress In the Systems Theories From The Mid-20th Centu...mentioning

confidence: 99%

Universal Complexity Science and Theory of Everything: Challenges and Prospects

Kesić

2024

Systems

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This article argues that complexity scientists have been searching for a universal complexity in the form of a “theory of everything” since some important theoretical breakthroughs such as Bertalanffy’s general systems theory, Wiener’s cybernetics, chaos theory, synergetics, self-organization, self-organized criticality and complex adaptive systems, which brought the study of complex systems into mainstream science. In this respect, much attention has been paid to the importance of a “reductionist complexity science” or a “reductionist theory of everything”. Alternatively, many scholars strongly argue for a holistic or emergentist “theory of everything”. The unifying characteristic of both attempts to account for complexity is an insistence on one robust explanatory framework to describe almost all natural and socio-technical phenomena. Nevertheless, researchers need to understand the conceptual historical background of “complexity science” in order to understand these longstanding efforts to develop a single all-inclusive theory. In this theoretical overview, I address this underappreciated problem and argue that both accounts of the “theory of everything” seem problematic, as they do not seem to be able to capture the whole of reality. This realization could mean that the idea of a single omnipotent theory falls flat. However, the prospects for a “holistic theory of everything” are much better than a “reductionist theory of everything”. Nonetheless, various forms of contemporary systems thinking and conceptual tools could make the path to the “theory of everything” much more accessible. These new advances in thinking about complexity, such as “Bohr’s complementarity”, Morin’s Complex thinking, and Cabrera’s DSRP theory, might allow the theorists to abandon the EITHER/OR logical operators and start thinking about BOTH/AND operators to seek reconciliation between reductionism and holism, which might lead them to a new “theory of everything”.

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Section: Introductionmentioning

confidence: 99%

“…A number of studies conducted in recent years have shown that many systems in nature generate time series with fractal behaviour [1][2][3][4][5][6]. Examples of such time series are: series of intervals between consecutive heartbeats [2,3,7], economic data on exchange rates [4], electricity prices [5], geophysical data on temperature, precipitation, tides [6,[8][9][10], etc. For the analysis of this type of processes, methods are applied that allow the determination of the global characteristics of the processes as well as the peculiarities of their local structures.…”

Section: Introductionmentioning

confidence: 99%

Methods for Mathematical Analysis of Simulated and Real Fractal Processes with Application in Cardiology

et al. 2022

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In the article, a comparative analysis is performed regarding the accuracy parameter in determining the degree of self-similarity of fractal processes between the following methods: Variance-Time plot, Rescaled Range (R/S), Wavelet-based, Detrended Fluctuation Analysis (DFA) and Multifractal Detrended Fluctuation Analysis (MFDFA). To evaluate the methods, fractal processes based of Fractional Gaussian Noise were simulated and the dependence between the length of the simulated process and the degree of self-similarity was investigated by calculating the Hurst exponent (H > 0.5). It was found that the Wavelet-based, DFA and MFDFA methods, with a process length greater than 214 points, have a relative error of the Hurst exponent is less than 1%. A methodology for the Wavelet-based method related to determining the size of the scale and the wavelet algorithm was proposed, and it was investigated in terms of the exact determination of the Hurst exponent of two algorithms: Haar and Daubechies with different number of coefficients and different values of the scale. Based on the analysis, it was determined that the Daubechies algorithm with 10 coefficients and scale (i = 2, j = 10) has a relative error of less than 0.5%. The three most accurate methods are applied to the study of real cardiac signals of two groups of people: healthy and unhealthy (arrhythmia) subjects. The results of the statistical analysis, using the t-test, show that the proposed methods can distinguish the two studied groups and can be used for diagnostic purposes.

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Fractal and Chaos in Exploration Geophysics

Cited by 4 publications

References 26 publications

Multifractal detrended fluctuation analysis of earthquake magnitude series of Mexican South Pacific Region

Multifractal detrended fluctuation analysis of earthquake magnitude series of Mexican South Pacific Region

Universal Complexity Science and Theory of Everything: Challenges and Prospects

Methods for Mathematical Analysis of Simulated and Real Fractal Processes with Application in Cardiology

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