Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

Jonkers, Art R. T.

doi:10.1111/j.1365-246x.2007.03352.x

Cited by 5 publications

(11 citation statements)

References 44 publications

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“…The Cantor set is, however, artificial, in consisting of stratae only. By contrast, natural phenomena, being affected by noise and external processes, exhibit intermediate sizes (or durations) everywhere along the observed modulation (see Jonkers 2007, Fig. 5, for an example of Cantor synthetics with added noise).…”

Section: Methodsmentioning

confidence: 97%

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Discrete scale invariance connects geodynamo timescales

Jonkers

2007

Geophysical Journal International

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S U M M A R YThe geodynamo exhibits a bewildering gamut of time-dependent fluctuations, on timescales from years to at least hundreds of millions of years. No framework yet exists that comprises all and relates each to all others in a quantitative sense. The technique of bootstrapped discrete scale invariance quantifies characteristic timescales of a process, based upon log-periodic fits of modulated power-law scaling of size-ranked event durations. Four independent geomagnetic data sets are analysed therewith, each spanning different timescales: the sequence of 332 known dipole reversal intervals (0-161 Ma); dipole intensity fluctuations (0-2 Ma); archeomagnetic secular variation (5000 B.C.-1950 A.D.); and historical secular variation (1590-1990 A.D.).Six major characteristic timescales are empirically attested: circa 1.43 Ma, 56 Ka, and 763, 106, 21 and 3 yr. Moreover, all detected wavelengths and phases of the detected scaling signatures are highly similar, suggesting that a single process underlies all. This hypothesis is reinforced by extrapolating the log-periodic scaling signal of any particular data set to higher timescales than observed, through which predictions are obtained for characteristic scales attested elsewhere. Not only do many confirm one another, they also predict the typical duration of superchrons and geomagnetic jerks. A universal scaling bridge describes the complete range of geodynamo fluctuation timescales with a single power law.

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Section: Methodsmentioning

confidence: 97%

“…For an extensive introduction to DSI theory and many application examples in physics, see Sornette (1998). A detailed account of the method developed for the geomagnetic case (‘bootstrapped DSI analysis’) is given in a separate paper (Jonkers 2007); here only a brief outline is sketched.…”

Section: Methodsmentioning

confidence: 99%

Discrete scale invariance connects geodynamo timescales

Jonkers

2007

Geophysical Journal International

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“…At the longest wavelengths in the log PSD plot, the spectrum decays in a first approximation by a downward-trending straight line with slope ≈ −4π · h (Parker & O'Brien 1997) and depth h to the magnetic source. For the reversal timescale, there are indications for a weaker form of scale invariance describing only parts as self-similar (Jonkers 2007). For the reversal timescale, there are indications for a weaker form of scale invariance describing only parts as self-similar (Jonkers 2007).…”

Section: Auto Spectramentioning

confidence: 99%

A new towed marine vector magnetometer: methods and results from a Central Pacific cruise

Engels¹,

Barckhausen²,

Gee

2008

Geophysical Journal International

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SUMMARY This paper focuses on new instrumental and methodological aspects of the acquisition, processing and interpretation of marine magnetic data. Between two Overhauser sensors towed as a longitudinal gradiometer, a new fluxgate vector magnetometer was employed. A second independent vector magnetometer system operated simultaneously. This equipment was used during research cruise SO‐180 of R/V SONNE in the Central Pacific at about 120°W just south of the equator. The survey area on the Pacific Plate is the mirror image to the currently subducting Cocos plate off Central America. The oceanic crust was formed around 23 Ma at the East Pacific Rise when the Farallon plate broke up into the Cocos and Nazca plates. The magnetic seafloor anomalies in the survey area strike approximately north–south almost parallel to the main field, resulting in very low anomaly amplitudes which had hindered detailed anomaly identification so far. A new processing scheme was applied to the data which identifies the weak anomalies in the total field and those in the vertical component that, as a consequence of the source body geometry, have about doubled amplitude. The vertical component constrains 2‐D modelling much better than the total field alone. Processed fluxgate total field data are practically identical to the Overhauser reference and even provide a reliable gradient when combined with one Overhauser. Although towed vector magnetometers typically provide no independent estimate of yaw, we illustrate that a numerical yaw (bandpass filtered magnetic heading) can provide reasonable estimates of the horizontal field components. These component data open additional analysis tools: the strike direction of magnetic lineations can be estimated from single profiles by either magnetic boundary strike ellipses in the space domain or by coherences between vertical and horizontal components in the wavenumber domain. Auto power spectra of the total field provide an approximate depth to the anomaly source or, if in obvious contradiction to the bathymetric depth, allow the detection of distortions, for example, by external temporal geomagnetic variations.

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“…This statistically stationary signature of preferred scales expresses itself as a log-periodic modulation superposed on a power law probability Sornette (1998) and Jonkers (2007) for the mathematical underpinnings. Unless one is aware of DSI's features, it is easy to misinterpret it as a 'noisy' power law distribution.…”

Section: Discrete Scale Invariance Quantifies Characteristic Scalesmentioning

confidence: 99%

“…We applied a bootstrap technique (Jonkers 2007) to the model-generated sequences of outbreak sizes to quantify their associated recurrence times. This latter quantity expresses the number of outbreaks that on average pass before an epidemic of selected size (or larger) occurs.…”

Section: Discrete Scale Invariance Quantifies Characteristic Scalesmentioning

confidence: 99%

Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales

Jonkers

Sharkey

Christley

2009

J. R. Soc. Interface.

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Epidemics are frequently simulated on redundantly wired contact networks, which have many more links between sites than are minimally required to connect all. Consequently, the modelled pathogen can travel numerous alternative routes, complicating effective containment strategies. These networks have moreover been found to exhibit 'scale-free' properties and percolation, suggesting resilience to damage. However, realistic H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales. These system-preferred scales constitute small areas within an observed power law distribution that exhibit a lesser slope than the power law itself, indicating a slightly increased relative likelihood. These characteristic scales are here produced by a networkpervading intranet of so-called hotspot sites that propagate large epidemics below the percolation threshold. This intranet is, however, extremely vulnerable; targeted inoculation of a mere 3 -6% (depending on incorporated biosecurity measures) of the British poultry industry network prevents large and moderate H5N1 outbreaks completely, offering an order of magnitude improvement over previously advocated strategies affecting the most highly connected 'hub' sites. In other words, hotspots and hubs are separate functional entities that do not necessarily coincide, and hotspots can make more effective inoculation targets. Given the ubiquity and relevance of networks (epidemics, Internet, power grids, protein interaction), recognition of this spreading regime elsewhere would suggest a similar disproportionate sensitivity to such surgical interventions.

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Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

Cited by 5 publications

References 44 publications

Discrete scale invariance connects geodynamo timescales

Discrete scale invariance connects geodynamo timescales

A new towed marine vector magnetometer: methods and results from a Central Pacific cruise

Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales

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