Discrete scale invariance connects geodynamo timescales

The 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.     

On the age calibration of the geomagnetic polarity timescale

Knowledge of the age of undated events is not null if a time-order relationship can be found among these events. The knowledge of such a time-ordered sequence can be formalized by using non-informative (uniform) prior probability densities for the ages of undated events and Bayes' theorem to introduce the time-order relationship condition. We show that the conditional probability densities of the ages of events of unknown age are given by various forms of Euler's beta distribution. These distributions yield an estimate of the probability for an undated event to occur in a given age interval.
  We use this method to propose appropriate probabilistic representations of our actual knowledge of the dating of the magnetic polarity reversals during the Cenozoic. These representations take into account the uncertainties arising from irregularities in accretion process and from the quality of a few calibration points. Both types of uncertainties generate large ambiguities in the age of magnetic reversals, which should be taken into consideration when the geomagnetic polarity timescale is used for dating purposes. We propose to use the entropy function to quantify these ambiguities.     

A Late Holocene geomagnetic secular variation record from Erhai Lake, southwest China

A secular variation record of the geomagnetic field direction for the last 6.5  kyr has been obtained from the magnetization of sediment cores from Erhai Lake, southwest China. In order to make a comparison with this record, secular variation in east-central China was investigated by combining available magnetic field data from historical records and archaeomagnetic measurements since about 350 bc . The secular variation in Erhai Lake shows features consistent with the combined record, except for the oldest three observed declination swings in Sian from 720 to 900 ad . Many features of declination and inclination in China also occur in Japan. From 500 to 1000 ad , declination was westerly ranging from about −20° to −5° in Erhai Lake, east-central China, and Japan.     

Observed geomagnetic field intensity in London since 1820

Our main purpose is to collect all magnetic intensity data observed in the vicinity of London and to adjust these to a common site (Greenwich) to complement the 400-year series of declination ( D ) and inclination ( I ) data of Malin & Bullard (1981 ). The present series is necessarily shorter, since a method for the measurement of intensity in absolute units was not devised until 1832. We have also supplemented the D and I series of Malin & Bullard with recently acquired data.
We have also made observations of D , I and total intensity ( F ) at a number of the sites, partly to bring the series up to date and partly to check on the site differences. With the increasing urbanization of London it is necessary to seek data from remoter sites. It is shown that the site differences change significantly with time, but that allowance can be made for this.
We present curves of our best estimates of the variation of D , I , F and the horizontal intensity ( H ) that define the complete geomagnetic vector at Greenwich for the interval 1820–1998. Frequency analysis shows little support for a 60-year line in the power spectrum. Within the uncertainty of their determinations, there is good continuity between archaeomagnetic intensity measures and the present results. The moving eddy hypothesis of Malin & Bullard is found to be untenable.     

Maximum entropy regularization of time-dependent geomagnetic field models

We incorporate a maximum entropy image reconstruction technique into the process of modelling the time-dependent geomagnetic field at the core–mantle boundary (CMB). In order to deal with unconstrained small lengthscales in the process of inverting the data, some core field models are regularized using a priori quadratic norms in both space and time. This artificial damping leads to the underestimation of power at large wavenumbers, and to a loss of contrast in the reconstructed picture of the field at the CMB. The entropy norm, recently introduced to regularize magnetic field maps, provides models with better contrast, and involves a minimum of a priori information about the field structure. However, this technique was developed to build only snapshots of the magnetic field. Previously described in the spatial domain, we show here how to implement this technique in the spherical harmonic domain, and we extend it to the time-dependent problem where both spatial and temporal regularizations are required. We apply our method to model the field over the interval 1840–1990 from a compilation of historical observations. Applying the maximum entropy method in space—for a fit to the data similar to that obtained with a quadratic regularization—effectively reorganizes the magnetic field lines in order to have a map with better contrast. This is associated with a less rapidly decaying spectrum at large wavenumbers. Applying the maximum entropy method in time permits us to model sharper temporal changes, associated with larger spatial gradients in the secular variation, without producing spurious fluctuations on short timescales. This method avoids the smearing back in time of field features that are not constrained by the data. Perspectives concerning future applications of the method are also discussed.     

Preliminary palaeomagnetic results of an Archaean dolerite dyke of west Greenland: geomagnetic field intensity at 2.8 Ga

The geomagnetic field intensity during Archaean times is evaluated from a palaeomagnetic and chronological study of a dolerite dyke intruded into the 3000 Ma Nuuk Gneisses at Nuuk (64.2°N, 51.7°W), west Greenland. Plagioclase from the dolerite dyke yields a mean K-Ar age of 2752 Ma. Palaeomagnetic directions after thermal demagnetization of the dyke and the gneiss reveal a positive baked-contact test, indicating that the high-temperature-component magnetization of the dyke is primary. Thellier experiments on 12 dyke specimens yield a palaeointensity value of 13.5±4.4 μT. The virtual dipole moment at ca. 2.8 Ga is 1.9±0.6 × 10²² Am², which is about one-quarter of the present value. The present study and other available data imply that the Earth's magnetic field at 2.7 ∼ 2.8 Ga was characterized by a weak dipole moment and that a fairly strong geomagnetic field similar to the present intensity followed the weak field after ca. 2.6 Ga.     

Control of smoothness in non-linear filtering of geomagnetic data by a one-pass method with a piecewise cubic polynomial

A smoother realized by a one-pass method with a piecewise cubic polynomial and a modified Powell criterion is termed a PCP filter. Since its action is data-adaptive, the PCP filter is non-linear. Furthermore, this filler is also non-causal and in practice causes little phase shift in the output and/or residual data as long as the input data has no dominant components with frequencies within its transition band. An average amplitude response of the PCP filter for sinusoidal inputs is determined numerically for each value of the parameter μ, which appears in the modified Powell criterion and controls the smoothness in output of the filter. An objective criterion for the selection of μ in the practical application of the PCP filter is then obtained from this response. Furthermore, the cut-off frequency of the PCP filter is defined as the first frequency at which the attenuation of the average amplitude response becomes 3 dB. It is found that the cut-off frequency is a good measure of the smoothness in output of the PCP filter. This frequency decreases with increasing μ, meaning that the output of the PCP filter becomes smoother and the oscillations with longer periods can be separated as residuals as μ grows large. As μ increases, the average number of sample points between two adjacent knots becomes larger and the computational cost increases for data processing by the PCP filter.     

Microwave palaeointensity from the R3–N3 geomagnetic field reversal

The microwave palaeointensity technique has been used to determine palaeointensity during the R3–N3 geomagnetic field reversal, using lavas from the Esja region of southwestern Iceland. The resulting intensity determinations have been compared to two previous studies which used the Shaw and Thellier techniques. Both reported low field intensities during the reversal except for four flows that produced high values (20.4–36.8 μT) using the Shaw technique compared to a single maximum intermediate value of 15.9 μT using the Thellier method. In this paper, an average microwave transitional palaeointensity of 6.95 ± 2.07 μT is found for samples used in the Shaw technique study, and of 7.80 ± 1.61 μT for samples used in the Thellier study, demonstrating that there is no evidence for strong fields during this reversal.