Independent records of relative magnetic palaeointensity from sediment cores in different areas of the world can be stacked together to extract the evolution of the geomagnetic dipole moment and thus provide information regarding the processes governing the geodynamo. So far, this procedure has been limited to the past 800,000 years (800 kyr; ref. 3), which does not include any geomagnetic reversals. Here we present a composite curve that shows the evolution of the dipole moment during the past two million years. This reconstruction is in good agreement with the absolute dipole moments derived from volcanic lavas, which were used for calibration. We show that, at least during this period, the time-averaged field was higher during periods without reversals but the amplitude of the short-term oscillations remained the same. As a consequence, few intervals of very low intensity, and thus fewer instabilities, are expected during periods with a strong average dipole moment, whereas more excursions and reversals are expected during periods of weak field intensity. We also observe that the axial dipole begins to decay 60-80 kyr before reversals, but rebuilds itself in the opposite direction in only a few thousand years.

letters to nature NATURE | VOL 399 | 20 MAY 1999 | www.nature.com 249 structure factor S(q). However, for q → 0, a peak develops and grows with decreasing T, again demonstrating the presence of increasing long-range behaviour for G u (r, Dt ‫ء‬ ). No such growing peak at q ¼ 0 appears in S(q) (Fig. 4, inset). By analogy with conventional critical phenomena, we have attempted to fit S u (q, Dt ‫ء‬ ) by an Ornstein-Zernike form, S u ðqÞ ϰ 1=ð1 þ y 2 q 2 Þ, where y is the correlation length 16 . This form fits well at the highest T, but fails on approaching T c , possibly because of finite size effects. Larger simulations may be required to determine accurately the correct functional form for S u at small q. Nevertheless, the data show unambiguously that as T → T c , spatial correlations between the displacement of monomers become increasingly long-ranged.Our simulations reveal a dynamical length scale relevant both to the mode-coupling dynamical transition and the glass transition. In this way we provide a bridge between the phenomenon of dynamical heterogeneity and current theories of supercooled liquids and vitrification. Remarkably, our findings are qualitatively identical to new results for simulated Ni 80 P 20 , a model metallic glassformer 14 , showing that the correlated monomer motion above T c is neither due to nor strongly affected by chain connectivity. Instead, the striking similarity between Ni 80 P 20 and the present polymer melt suggests that correlated motion is a universal feature of (at least fragile 1 ) glass-forming liquids. Furthermore, we have identified a fluctuating dynamical variable U in this polymer melt whose fluctuations become long-ranged and appear to diverge at T c , and which thus behaves much like a static order parameter on approaching a second-order phase transition-albeit one that is not obviously accessible to traditional scattering experiments, but may be measurable in optical microscopy experiments on colloidal suspensions. Our findings suggest that substantial shifts in T c could be observed by confining glass-forming liquids and melts, thereby limiting the divergence that can occur. Whether this could also explain the confinement-induced shifts of T g observed experimentally 22-26 needs to be investigated. Our results indicate that it may be possible to obtain further insight into the nature of supercooled, glass-forming liquids using an extension to dynamically defined quantities of the framework of ordinary critical phenomena. Ⅺ Continental crust forms from, and thus chemically depletes, the Earth's mantle. Evidence that the Earth's mantle was already chemically depleted by melting before the formation of today's oldest surviving crust has been presented in the form of Sm-Nd isotope studies of 3.8-4.0 billion years old rocks from Greenland 1-5 and Canada 5-7 . But this interpretation has been questioned because of the possibility that subsequent perturbations may have re-equilibrated the neodymium-isotope compositions of these rocks 8 . Independent and more robust evidenc...

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[1] After many years spent by paleomagnetists studying the directional behavior of the Earth's magnetic field at all possible timescales, detailed measurements of field intensity are now needed to document the variations of the entire vector and to analyze the time evolution of the field components. A significant step has been achieved by combining intensity records derived from archeological materials and from lava flows in order to extract the global field changes over the past 12 kyr. A second significant step was due to the emergence of coherent records of relative paleointensity using the remanent magnetization of sediments to retrace the evolution of the dipole field. A third step was the juxtaposition of these signals with those derived from cosmogenic isotopes. Contemporaneous with the acquisition of records, new techniques have been developed to constrain the geomagnetic origin of the signals. Much activity has also been devoted to improving the quality of determinations of absolute paleointensity from volcanic rocks with new materials, proper selection of samples, and investigations of complex changes in magnetization during laboratory experiments. Altogether these developments brought us from a situation where the field changes were restricted to the past 40 kyr to the emergence of a coherent picture of the changes in the geomagnetic dipole moment for at least the past 1 Myr. On longer timescales the field variability and its average behavior is relatively well documented for the past 400 Myr. Section 3 gives a summary of most methods and techniques that are presently used to track the field intensity changes in the past. In each case, current limits and potential promises are discussed. The section 4 describes the field variations measured so far over various timescales covered by the archeomagnetic and the paleomagnetic records. Preference has always been given to composite records and databases in order to extract and discuss major and global geomagnetic features. Special attention has been devoted to discussing the degree of confidence to be put in the data by considering the integration of multiple data sets involving different techniques and/or materials.