Motions at the core surface derived from SV data

Summary. Examples of core motions which generate the observed secular variation field – as given by various models for 1970 and 1980 – from the main field have been computed in the frozen flux approximation, assuming that the spectrum of the motion is of low degree and decreases with wave-number. No mode of degree > 4 in the expansion of the motion can be derived with any degree of confidence. Among the low degree modes, some appear to be stable (they come out with the same magnitude whatever the inversion scheme used). The flow made of these stable modes is then examined. An outstanding feature of the flow is the body westward drift. But it seems necessary, if one looks for such a regular flow, to consider both toroïdal and poloïdal components, which would imply upwelling and down-welling in the upper layers of the core. The toroïdal part of the flow appears to be enhanced by the 1969 impulse, although its geometry is nearly unchanged. On the contrary the geometry of the computed poloïdal part is different in 1980 and in 1970;     

Maximum entropy regularization of the geomagnetic core field inverse problem

The maximum entropy technique is an accepted method of image reconstruction when the image is made up of pixels of unknown positive intensity (e.g. a grey-scale image). The problem of reconstructing the magnetic field at the core–mantle boundary from surface data is a problem where the target image, the value of the radial field B_r , can be of either sign. We adopt a known extension of the usual maximum entropy method that can be applied to images consisting of pixels of unconstrained sign. We find that we are able to construct images which have high dynamic ranges, but which still have very simple structure. In the spherical harmonic domain they have smoothly decreasing power spectra. It is also noteworthy that these models have far less complex null flux curve topology (lines on which the radial field vanishes) than do models which are quadratically regularized. Problems such as the one addressed are ubiquitous in geophysics, and it is suggested that the applications of the method could be much more widespread than is currently the case.     

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.