Discrete scale invariance connects geodynamo timescales

Abstract

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.

GEOMAGIA50.v3: 1. general structure and modifications to the archeological and volcanic database

“…As global field models are constructed to recreate the field at the core-mantle boundary, they have the potential to be used to understand the geodynamo and have been used to investigate core flow (Dumberry and Finlay 2007;Wardinski and Korte 2008;Livermore et al 2014), with possible implications for length of day variations on millennial time scales (Dumberry and Bloxham 2006); the behavior of high latitude flux patches (Korte and Holme 2010;Amit et al 2011); hemispheric field asymmetries related to archeomagnetic jerks (Gallet et al 2009); discrete scale invariance across geodynamo time scales (Jonkers 2007); and similarities with the characteristics of dynamo simulations (Christensen et al 2011;Heimpel and Evans 2013;Davies and Constable 2014). Calculations of dipole eccentricity using CALS3k.4b and CALS10k.1b , coupled with observations of hemispherical variations in seismic velocity at the top of the Earth's inner core, motivated Olson and Deguen (2012) to investigate persistent eccentricity in numerical dynamo simulations and they suggested lopsided solidification within the inner core.…”

Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

“…This hypothesis would imply that all perceived types of geodynamo fluctuations are merely differently scaled surface expressions of the same scale‐invariant process, and that a single suite of constraints affects all. This notion is further explored in Jonkers (2007).…”

“…In a recent paper (Jonkers 2007), evidence is presented supporting the presence of power laws in geomagnetic fluctuations over a range of timescales, from years to millions of years. In addition, it is shown there that the power‐law residuals exhibit a statistically significant modulation, resulting in log‐periodic scaling stratae in the probability distribution function (near‐horizontal levels along the power‐law slope), representing preferred temporal scales of the system.…”

Geomagnetic and mineral magnetic characterization of the Anthropocene

“…The internal geomagnetic field is generated by convection in the liquid outer core, which causes magnetic induction and significant temporal variations at the Earth's surface over timescales longer than a few months (Jonkers 2007). However, due to the recording mechanism in Earth materials (and dating uncertainties), only changes that take place over longer than decadal timescales are likely to be reconstructed using traditional palaeomagnetic methods.…”