Ergodicity of the recent geomagnetic field

Santis, Angelo De; Qamili, Enkelejda; Cianchini, Gianfranco

doi:10.1016/j.pepi.2011.04.008

Cited by 10 publications

(18 citation statements)

References 35 publications

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“…As a chaotic system, the recent geomagnetic field is sensitive to initial conditions [ Barraclough and De Santis , ; De Santis et al ., ; De Santis et al ., ; De Santis and Qamili , ] and the average divergence ε( t ) of initially close trajectories in the phase space propagates exponentially with time t (the rigorous formula imposes a limit of t → 0; [ Barraclough and De Santis , ])

e (t) \approx {normale}_{0} {e^{K}}^{t}

where K is the Kolmogorov or K‐Entropy (with K > 0), which is a quantity that measures the degree of chaos in the dynamics of a system. Since the prediction error increases exponentially with time, this implies a strict limitation of time on which these systems can be predicted.…”

Section: Nonlinear Chaotic Analysis Of the Geomagnetic Fieldmentioning

confidence: 99%

“…Imposing the same initial value for both predicted (extrapolated) and definitive (actual) models, each exponential growth should have an offset equal to –ε 0 . In this case the error we actually calculate reduces to

ε ‵ (t) = ε (t) - ε_{0} = ε_{0} e \frac{t}{τ} - ε_{0} = ε_{0} (e, \frac{t}{τ}, -, 1)

where ε 0 is a constant that measures the initial difference between prediction and actual value, while τ is the characteristic time of growth that is related to K‐Entropy when the system under study is ergodic and chaotic [ De Santis et al ., ]. For our convenience, hereafter we call ε'( t ) simply as ε( t ), although it is estimated with equation .…”

Section: Nonlinear Forecasting Approach In the Time Domainmentioning

confidence: 99%

“…This technique is able to detect a possible exponential divergence of some prediction from the real signal in the phase space, which is reconstructed from the time delay of the original signal. An important parameter is the mean exponential characteristic time τ, after which no reliable prediction can be made [ Barraclough and De Santis , ; De Santis et al ., ].…”

Section: Introductionmentioning

confidence: 99%

“…Combining this technique with the most classical and widely used in geomagnetism, i.e., the spherical harmonic analysis, we can perform our analysis in the usual time domain by taking advantage of the geomagnetic field ergodicity [ De Santis et al ., ]. This study deals with the detection and, possibly, confirmation of the presence of geomagnetic jerks by means of NFA in time, to find those epochs when the geomagnetic field appears more chaotic, i.e., those less predictable periods that are characterized by smaller characteristic time τ.…”

Section: Introductionmentioning

confidence: 99%

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Geomagnetic jerks as chaotic fluctuations of the Earth's magnetic field

Qamili

Santis

Isac

et al. 2013

Geochem Geophys Geosyst

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[1] The geomagnetic field is chaotic and can be characterized by a mean exponential time scale < t > after which it is no longer predictable. It is also ergodic, so time analyses can substitute the more difficult phase space analyses. Taking advantage of these two properties of the Earth's magnetic field, a scheme of processing global geomagnetic models in time is presented, to estimate fluctuations of the time scale t. Here considering that the capability to predict the geomagnetic field is reduced over periods of geomagnetic jerks, we propose a method to detect these events over a long time span. This approach considers that epochs characterized by relative minima of fluctuations in time scale t, i.e., those periods when a geomagnetic field is less predictable, are possible jerk occurrence dates. We analyze the last 400 years of the geomagnetic field (covered by the Gufm1 model) to detect minima of fluctuations, i.e., epochs characterized by low values of the time scale. Most of the well known jerks are confirmed through this method and a few others have been suggested. Finally, we also identify some short periods when the field is less chaotic (more predictable) than usual, naming these periods as steady state geomagnetic regime, to underline their opposite behavior with respect to jerks.

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e (t) \approx {normale}_{0} {e^{K}}^{t}

Section: Nonlinear Chaotic Analysis Of the Geomagnetic Fieldmentioning

confidence: 99%

ε ‵ (t) = ε (t) - ε_{0} = ε_{0} e \frac{t}{τ} - ε_{0} = ε_{0} (e, \frac{t}{τ}, -, 1)

Section: Nonlinear Forecasting Approach In the Time Domainmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Geomagnetic jerks as chaotic fluctuations of the Earth's magnetic field

Qamili

Santis

Isac

et al. 2013

Geochem Geophys Geosyst

Self Cite

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“…After we found these sets of parameter values, we extended the time series covering the near future. We do not pretend to give a prediction of the future behavior of the geomagnetic field because it has chaotic nature (Barraclough and De Santis, 1997;De Santis et al, 2011). Instead we aim to find if the period of low intensity dipolar field, like the one we are experiencing, is potentially the precursor of a reversal.…”

Section: Introductionmentioning

confidence: 99%

Insights into pre-reversal paleosecular variation from stochastic models

2015

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To provide insights on the paleosecular variation of the geomagnetic field and the mechanism of reversals, long time series of the dipolar magnetic moment are generated by two different stochastic models, known as the "domino" model and the inhomogeneous Lebovitz disk dynamo model, with initial values taken from the paleomagnetic data. The former model considers mutual interactions of N macrospins embedded in a uniformly rotating medium, where random forcing and dissipation act on each macrospin. With an appropriate set of the model's parameter values, the series generated by this model have similar statistical behavior to the time series of the SHA.DIF.14K model. The latter model is an extension of the classical two-disk Rikitake model, considering N dynamo elements with appropriate interactions between them. We varied the parameters set of both models aiming at generating suitable time series with behavior similar to the long time series of recent secular variation (SV). Such series are then extended to the near future, obtaining reversals in both cases of models. The analysis of the time series generated by simulating both the models show that the reversals appear after a persistent period of low intensity geomagnetic field.

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Transformative resonant moderation of geomagnetic polarity and strata

Omerbashich

2021

Preprint

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Claims of paleodata periodicity are many and controversial so that, for example, superimposing Phanerozoic (0-541 My) massextinction periods renders life on Earth impossible. This period hunt coincided with the modernization of geochronology which now ties geological timescales to orbital frequencies. Such tuneup simplifies energy-band (variance-) stratification of information contents, enabling separation of astronomical signal from any harmonics. Variance-based spectral analysis techniques can achieve this, such as the Gauss-Vaníček method favored by astronomers for resilience with even extreme data gaps. I thus show on diverse data (geomagnetic polarity, cratering, extinction episodes) that many-body subharmonic entrainment causes the Earth to respond to its astronomical forcing resonantly, so that the 2π-phase-shifted axial precession p=26 ky, and its Pi=2πp/i; i=1,…,n harmonics, are resonantly responsible for virtually all paleodata periods. This resonantly quasiperiodic nature of strata is shown co-triggered by the p'/4-lockstep to the p'=41-ky obliquity (also 2π-phase-shifted, to P'=3.5-My superperiod). For verification, residuals analysis after suppressing 2πp (and thus Pi, too) in the current polarity-reversals GPTS-95 timescale's calibration extending to end-Campanian (0-83 My) successfully detected weak signals of Earth-Mars planetary resonances, reported previously from older epochs. The only significant residual signal is intrinsic 26.5-My Rampino period -carrier wave of crushing deflections which, during Transformative Resonant Events (TRE), decimate strata to quasiperiodicity, co-responsible for polarity reversals and whose detection confirms geomagnetism overall ergodicity. The (2πp, Pi) resonant response of the Earth to orbital forcing is the longsought, energy-transfer mechanism of the Milankovitch theory -now a special case applicable to the current episode of Earth-Moon-Sun system resonant dynamics springing from the 1-40 My very long band. Fundamental system properties -2π-phaseshift, ¼ lockstep to a forcer, and discrete time translation symmetry (multiplied or halved periods) -previously were thought typical of a discrete time crystal, which here then appears unremarkable.

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Ergodicity of the recent geomagnetic field

Cited by 10 publications

References 35 publications

Geomagnetic jerks as chaotic fluctuations of the Earth's magnetic field

Geomagnetic jerks as chaotic fluctuations of the Earth's magnetic field

Insights into pre-reversal paleosecular variation from stochastic models

Transformative resonant moderation of geomagnetic polarity and strata

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