Nonlinear and multifractal approaches of the geomagnetic field

Hongre, Lionel; Sailhac, Pascal; Alexandrescu, Mioara; Dubois, Jacques

doi:10.1016/s0031-9201(98)00133-2

Cited by 27 publications

(21 citation statements)

References 46 publications

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“…An m-dimensional dynamical system has m-Lyapunov exponents. Three conditions are necessary (but not sufficient) for the behaviour of a dynamical system to be compatible with the presence of chaos (Wolf et al, 1985;Rosenstein et al, 1993;Hongre et al, 1999). At least one Lyapunov exponent must be positive to explain the divergence of the trajectories, at least one must be negative to justify the folding up of the trajectories, and the sum of all the exponents must be negative to account for the dissipative nature of the system.…”

Section: Legends To the Figuresmentioning

confidence: 99%

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Wysocki

Fiamma

Straus

et al. 2006

Respiratory Physiology & Neurobiology

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The mammalian ventilatory behaviour exhibits nonlinear dynamics as reflected by certain nonlinearity or complexity indicators (e.g. correlation dimension, approximate entropy, Lyapunov exponents...) but this is not sufficient to determine its possible chaotic nature. To address this, we applied the noise titration technique, previously shown to discern and quantify chaos in short and noisy time series, to ventilatory flow recordings obtained in quietly breathing normal humans. Nine subjects (8 men and 1 woman, 24-42 yrs) were studied during 15-minute epochs of ventilatory steadystate (10.1±3.0 breaths/minute, tidal volume 0.63±0.2L). Noise titration applied to the unfiltered signals subsampled at 5 Hz detected nonlinearity in all cases (noise limit 20.2±12.5%). Noise limit values were weakly correlated to the correlation dimension and the largest Lyapunov exponent of the signals. This study shows that the noise titration approach evidences a chaotic dimension to the behavior of ventilatory flow over time in normal humans during tidal breathing.

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Section: Legends To the Figuresmentioning

confidence: 99%

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Wysocki

Fiamma

Straus

et al. 2006

Respiratory Physiology & Neurobiology

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“…Nonstationary time series of many physical systems, including the geomagnetic field (Hongre et al, 1999), exhibit different scaling properties which can be characterized by means of multi-fractal analysis. MFDFA is a useful tool to investigate the degree of multi-fractality of these time series.…”

Section: Discussionmentioning

confidence: 99%

On the multi-fractal characteristics of the ULF geomagnetic field before the 1993 Guam earthquake

Masci

2013

Nat. Hazards Earth Syst. Sci.

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Abstract. Ida et al. (2005) document significant changes in the multi-fractal parameters of the ULF geomagnetic field H component starting about one month before the 1993 Guam earthquake. According to the authors, these multi-fractal signatures can be considered as precursory signals of the Guam earthquake. As a consequence, they conclude that the multifractal analysis may have an important role in the development of short-term earthquake prediction capabilities. Since this and other similar reports have motivated the idea that earthquake prediction based on electromagnetic precursory signals may one day become a routine technique, the presumed precursors need to be validated through independent datasets. In this review the seismogenic origin of the multifractal magnetic signatures documented by Ida et al. (2005) before the 8 August 1993 Guam earthquake is seriously put into question. By means of the geomagnetic K p index, it is demonstrated that these multi-fractal parameter changes are normal signals induced by the variation of the global geomagnetic activity level.

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“…Therefore, it is an important issue to know whether the field is ergodic or not, since if this were true, many computations, usually undertaken with many difficulties in the phase space (e.g. Hongre et al, 1999), would be more easily made in the conventional time domain . In addition, ergodicity would be a further evidence for the strong spatio-temporal coupling among the contributions composing the dynamical system that produces and sustains the geomagnetic field (Hongre et al, 1999;De Santis et al, 2003).…”

Section: Introductionmentioning

confidence: 99%

“…Hongre et al, 1999), would be more easily made in the conventional time domain . In addition, ergodicity would be a further evidence for the strong spatio-temporal coupling among the contributions composing the dynamical system that produces and sustains the geomagnetic field (Hongre et al, 1999;De Santis et al, 2003). The strong coupling is typical of many spatio-temporal chaotic phenomena (e.g.…”

Section: Introductionmentioning

confidence: 99%

Ergodicity of the recent geomagnetic field

Santis

Qamili

Cianchini

2011

Physics of the Earth and Planetary Interiors

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Please cite this article as: De Santis, A., Qamili, E., Cianchini, G., Ergodicity of the recent geomagnetic field, Physics of the Earth and Planetary Interiors (2011), doi: 10.1016/j.pepi.2011 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThe geomagnetic field is a fundamental property of our planet: its study would allow us to understand those processes of Earth's interior, which act in its outer core and produce the main field. Knowledge of whether the field is ergodic, i.e., whether time averages correspond to phase space averages, is an important question since, if this were true, it would point out a strong spatiotemporal coupling among the components of the dynamical system behind the present geomagnetic field generation. Another consequence would be that many computations, usually undertaken with many difficulties in the phase space, can be made in the conventional time domain. We analyse the temporal behaviour of the deviation between predictive and definitive geomagnetic global models for successive intervals from 1965 to 2010, finding a similar exponential growth with time. Also going back in time (at around 1600 and 1900 by using the GUFM1 model) confirms the same findings. This result corroborates previous chaotic analyses made in a reconstructed phase space from geomagnetic observatory time series, confirming the chaotic character of the recent geomagnetic field with no reliable prediction after around 6 years from definitive values, and disclosing the potentiality of estimating important entropic quantities of the field by time averages.Although more tests will be necessary, some of our analyses confirm the efforts to improve the representation of the geomagnetic field with more detailed secular variation and acceleration.

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Nonlinear and multifractal approaches of the geomagnetic field

Cited by 27 publications

References 46 publications

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration

On the multi-fractal characteristics of the ULF geomagnetic field before the 1993 Guam earthquake

Ergodicity of the recent geomagnetic field

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