Palaeosecular variation in Central Mexico over the last 30 000 years: the record from lavas

13 lava flows of known age (ages from ¹⁴C dating), which have been erupted in the last 30 000 years, have been studied to determine the palaeosecular variation of the geomagnetic field in Central Mexico. Samples were taken from two different monogenetic volcanic fields: the Michoacan-Guanajuato volcanic field (six sites) and the Chichinautzin Formation (seven sites), both part of the Transmexican Volcanic Belt. The lavas were studied in detail using rock magnetic methods (magnetic susceptibility at room temperature, low-temperature susceptibility behaviour, hysteresis loops, Curie temperatures), combined with reflected light microscopy, in order to deduce their magnetic mineralogy and the domain states of the magnetic minerals. The magnetic carriers are titanomagnetites, which show differing degrees of high-temperature deuteric oxidation, and seem to be predominantly pseudo-single domain (PSD), though in many cases are probably a mixture of domain states. Mean palaeomagnetic directions and palaeointensity values using Shaw and Thellier techniques were obtained using several specimens from each flow. Our data seem to indicate a sharp easterly swing in declination about 5000 years ago, which is also observed in lake sediments from Central Mexico. The calculated values of the virtual dipole moment (VDM) range from 3.1 to 14.9 × 10²² A m². Our data indicate that the virtual dipole moment seems to have increased gradually in magnitude over the last 30 kyr, with a peak at about 9000 years BP. These are features that have been observed in other parts of the globe and are probably caused by variations in the dipole part of the geomagnetic field.     

The geomagnetic field over the past 5 million years

The modern geomagnetic field is usually expressed as a spherical harmonic expansion. Although the palaeomagnetic record is very incomplete in both space and time, sufficient data are available from a span of ages to generate time-averaged spherical harmonic field models with many degrees of freedom. Here three data sets are considered: directional measurements from lavas, inclination measurements from ocean sediments, and intensity measurements from lavas. Individual data are analysed, as well as site-averages, using the same methods that have been developed for the modern field, to give models for the past 5 Myr. The normal-polarity field model has an axial-dipole intensity similar to that of the modern-day field, whilst the equatorial-dipole component is very much smaller. The field is not axisymmetric, but shows flux concentrations at the core's surface under Canada and Siberia similar to those observed in the field over historical timescales. Tests on synthetic data show that it is unlikely that these similarities result from the overprinting of the palaeomagnetic field due to inadequate cleaning of the samples. The reverse-polarity field model does not show such obvious features, but this may be due to the sparsity of the data.
The patterns observed in the normal-polarity field, with persistent features in the northern hemisphere and a smooth southern hemisphere, could be explained if the present pattern of secular variation is typical of the past several million years. This would reveal itself as large variations over time in the direction of the magnetic vector in regions of high secular variation, with relatively little change over quieter regions. However, we have been unable to find any evidence for a geographical pattern of secular variation in the data.     

Variations in the geomagnetic dipole moment over the last 12 000 years

An analysis has been made of archaeointensity data for the past 12 000 years. There are 3243 results from different areas of the world covering the past 12 000 years. Of these, 2203 are from the European region and 1040 are from the rest of the world. The archaeointensity data set analysed in the present study is almost three times larger than that used by McElhinny & Senanayake (1982 ). Although there is no major difference between our global data and the earlier data, the data for the non-European region have been improved and we now have a data set for Asia.     

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.     

Rotation of the geomagnetic field about an optimum pole

Since 1693, when Halley proposed that secular change was the result of the westward drift of the main field, his simple model has undergone many refinements. These include different drift rates for dipole and non-dipole parts; separation into drifting and standing parts; latitudinal dependence of drift rate; northward drift of the dipole; and non-longitudinal rotations of the individual harmonics of the geomagnetic field. Here we re-examine the model of Malin and Saunders, in which the main field is rotated about an optimum pole which does not necessarily coincide with the geographical pole. The optimum pole and rotation angle are those that bring the main field for epoch T ₁ closest to that for T ₂ , as indicated by the coefficients of correlation between the spherical harmonic coefficients for the two epochs, after rotation. Malin and Saunders examined the pole positions and rates of rotation using data from 1910 to 1965, and noticed a number of trends. We show that these trends are confirmed by recent IGRF models, spanning the interval 1900–2000 and to degree and order 10. We also show that the effect of the level of truncation is small.     

Geomagnetic field analysis—IV. Testing the frozen-flux hypothesis

Summary. We present a model of the magnetic field at the core–mantle boundary, for epoch 1959.5, based on a large set of observatory and survey measurements. Formal error estimates for the radial field at the core are 50 μT, compared with 30 and 40 μT for our previous MAGSAT (1980) and POGO (1970) models.
Current work on the determination of the velocity of the core fluid relies on the assumption that the core behaves as a perfect conductor, so that the field lines remain frozen to the fluid at the core surface. This frozen-flux condition requires that the integrated flux over patches of the core surface bounded by contours of zero radial field remain constant in time. A new method is presented for constructing core fields that satisfy these frozen-flux constraints. The constraints are non-linear when applied to main field data, unlike the case of secular variation which was considered in an earlier paper. The method is applied to datasets from epochs 1969.5 and 1959.5 to produce fields with the same flux integrals as the 1980 model.
The frozen-flux hypothesis is tested by comparing the changes in the flux integrals between 1980/1969.5, 1969.5/1959.5 and 1980/1959.5 with their errors. We find that the hypothesis can be rejected with 95 per cent confidence. The main evidence for flux diffusion is in the South Atlantic region, where a new null flux curve appears between 1960 and 1970, and continues to grow at a rapid rate from 1970 to 1980. However, the statistical result depends critically on our error estimates for the field at the core surface, which are difficult to assess with any certainty; indeed, doubling the error estimates negates the statistical argument. The conclusion is therefore, at this stage, tentative, and requires further evidence, either from older data, if good enough, or from future satellite measurements.