The kinematic dynamo action of spiralling convective flows

We consider the kinematic production of magnetic fields in a sphere by velocity fields dominated by differential rotation and spiralling convective cells. The high magnetic Reynolds number limit of Braginsky (1964) is considered and formulae are derived allowing an α-effect parametrization of such flows to be easily calculated. This permits an axisymmetric system to be investigated in parallel with the direct 3-D numerical computations. Good agreement between the asymptotic and 3-D calculations is found. The 'spiralling' property typical of convective motion in rotating spheres is important in terms of dynamo action; the differential rotation coexisting with this feature is also vital. Indeed, it is the presence of both features which allows the analysis of Braginsky to be employed. With flows approximating the columnar form anticipated for rapidly rotating convection, dynamo action is relatively easily achieved for all azimuthal wavenumbers; modes of differing wavenumbers interact almost by a simple superposition. With flows of more complex latitudinal form, the mutual interactions between modes become more complicated. For columnar-type flows, dipole magnetic fields are favoured when the sense of outward spiralling is prograde and the zonal flow is eastwards, as is physically preferred.     

Bootstrapped discrete scale invariance analysis of geomagnetic dipole intensity

The technique of bootstrapped discrete scale invariance allows multiple time-series of different observables to be normalized in terms of observed and predicted characteristic timescales. A case study is presented using the SINT2000 time-series of virtual axial dipole moment, which spans the past 2 Myr. It is shown that this sequence not only bears a clear signature of a preferred timescale of about 55.6 Ka, but additionally predicts similar features (of shorter and longer duration) that are actually observed on the timescales of historical secular variation and dipole reversals, respectively. In turn, the latter two empirical sources both predict the characteristic timescale found in the dipole intensity sequence. These communal scaling characteristics suggest that a single underlying process could be driving dynamo fluctuations across all three observed timescales, from years to millions of years.     

Magnetic and viscous coupling at the core–mantle boundary: inferences from observations of the Earth's nutations

Dissipative core–mantle coupling is evident in observations of the Earth's nutations, although the source of this coupling is uncertain. Magnetic coupling occurs when conducting materials on either side of the boundary move through a magnetic field. In order to explain the nutation observations with magnetic coupling, we must assume a high (metallic) conductivity on the mantle side of the boundary and a rms radial field of 0.69 mT. Much of this field occurs at short wavelengths, which cannot be observed directly at the surface. High levels of short-wavelength field impose demands on the power needed to regenerate the field through dynamo action in the core. We use a numerical dynamo model from the study of Christensen & Aubert (2006) to assess whether the required short-wavelength field is physically plausible. By scaling the numerical solution to a model with sufficient short-wavelength field, we obtain a total ohmic dissipation of 0.7–1 TW, which is within current uncertainties. Viscous coupling is another possible explanation for the nutation observations, although the effective viscosity required for this is 0.03 m² s⁻¹ or higher. Such high viscosities are commonly interpreted as an eddy viscosity. However, physical considerations and laboratory experiments limit the eddy viscosity to 10⁻⁴ m² s⁻¹, which suggests that viscous coupling can only explain a few percent of the dissipative torque between the core and the mantle.     

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.     

Equation for the field lines of an axisymmetric magnetic multipole

Summary. An exact equation is derived for the magnetic field lines of the general axisymmetric magnetic multipole of arbitrary degree ( n ). This new result has important applications in studies of the possible nature of solarterrestrial physics during geomagnetic polarity reversals. In the limiting case of a magnetic dipole ( n=1 ), the equation for the magnetic field lines of the general axisymmetric magnetic multipole simplifies correctly to the well-known dipolar form, which is used extensively in geomagnetism, magnetospheric physics and cosmic-ray physics as a first-order approximation to the actual configuration of the geomagnetic field.
It is also shown theoretically that suites of similar magnetic field lines of the general axisymmetric multipole attain their maximum radial distances from the origin on a set of circular conical surfaces, with coincident vertices at the centre of the Earth; this set includes the equatorial plane if the degree ( n ) of the multipole is odd. The magnetic field is horizontal everywhere on all these surfaces.
Palaeomagnetic studies have suggested that during some polarity reversals the magnetic field in the inner magnetosphere can be represented approximately either by a single, non-dipolar, low-degree (2 < n < 4), axisymmetric magnetic multipole or by a linear combination of such multipoles. In this situation, the equation for the field lines of an axisymmetric magnetic multipole of low degree (2 < n < 4) would be as fundamental to a proper understanding of magnetospheric, ionospheric and cosmic-ray physics during polarity reversals as is the equation for dipolar field lines in the case of the contemporary geomagnetic field.     

Palaeomagnetism of some Indian Rocks

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Hitherto, no palaeomagnetic data for India are available earlier than the Jurassic, 130 M.y. The remanent magnetic directions of oriented samples from one Jurassic and four pre-Cambrian rock formations in India have now been determined. One pre-Cambrian formation gave very scattered direction: the other four formations gave well-defined directions and their magnetic stability was demonstrated by a.c. and thermal demagnetization. The three pre-Cambrian results enable values of the ancient latitude and orientation of India to be estimated at 500, 600 and 750 M.y., assuming the ancient field to have been an axial dipole.
By making use of these new results, together with similar data by other workers for Australia, North America and Europe, it can be shown that, as far as the scanty data goes, the rate of drift in latitudes and orientation of the four continents has been of roughly the same magnitude throughout the period since 750 M.y.     

Geomagnetic secular variation since 1901

Summary. All available annual means, from the world-wide network of magnetic observatories, of north intensity ( X ), east intensity ( Y ) and vertical intensity (Z) from 1901 to 1977 are subjected to spherical harmonic analysis to obtain 38 models of the Earth's geomagnetic field at two-year intervals. These models are differenced to give 37 models of secular variation at two-year intervals from 1903.5 to 1975.5. The results show the decreasing trend of the dipole moment and are analysed for possible information on the westward drift of the magnetic field.     

A model for energy dissipation at the mantle—core boundary

Summary. An existing experimentally verified model for energy dissipation in a processing spherical cavity filled with liquid assumed to be in a semirigidized state except for a viscous Ekman boundary layer is applied to the Earth's liquid core to assess energy dissipation magnitudes. Application of the model to the best available Earth data occurs at the derived energy dissipation maximum for the model. Other existing research showing that the Earth's atmosphere appears to adjust to a state of maximum dissipation led to generic models for systems of maximum dissipation. The maximum dissipation mantle—core model with core motion driven by Earth precession alone, coupled to the mantle only by viscous shear stresses, and with a spherical mantle—core boundary leads to energy dissipation rates on the order of 10⁴ times those necessary for an Earth dynamo. The maximum dissipation model also leads to excessive magnetic field drift rates and to excessive retardation of the Earth's rotation rate. Effects of the mantle—core ellipticity and of magnetic field coupling are briefly discussed and are used to help develop a less than maximum dissipation model also driven by precession alone but using the additional coupling to yield a model more consistent with observed phenomena.     

The Palaeomagnetism of the Great Dyke of Southern Rhodesia

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Oriented cores have been secured from fourteen sites in the Great Rhodesian Dyke, by means of a portable sampling drill. The natural remanent magnetizations showed high dispersion at all sites except one. After demagnetization in alternating magnetic fields, nine sites gave well grouped directions of primary magnetization. These sites include five rock types distributed among three Complexes of the Great Dyke and two satellite dykes, over 200 miles of the length of the Dyke and through several thousand feet in depth as the rocks were originally intruded. The nine site mean directions of primary magnetization are closely grouped and are believed to represent directions of thermo-remanent magnetization at the date of intrusion of the Great Dyke. It is suggested that the dates of magnetization at the sites must cover a sufficient time interval to give a mean pole position close to the axial geocentric dipole freed from secular variation. On the assumption of a geocentric dipole field, the position of the mean South magnetic pole is 211/2 °N, 611/2 °E, with radius of 95 per cent confidence 9°. This pole position is close to positions of North magnetic poles given by studies of the palaeo-magnetism of the Pilansberg Dykes and Bushveld gabbro.     

Late Mesozoic and Cenozoic palaeomagnetism of Australia–II. Implications for geomagnetism and true polar wander

Summary. New palaeomagnetic results from Australia indicate that throughout the Cenozoic era the continent lay further south than suggested by hot-spot data. Moreover, while hot spots give a uniform rate of drift during most of the Cenozoic, the drift rate obtained from apparent polar wander varies considerably.
The discrepancies between the palaeomagnetic and hot-spot results are analysed by comparing the Australian data with those of Europe and the central Pacific. The analysis suggests that the discrepancies are due to: (1) departures of the Earth's magnetic field from the geocentric axial dipole model, and (2), either true polar wander or a non-axial inclined dipole component. It is found that since the mid-Tertiary the dominant non-dipole component has been a quadrupole, and that during this period both the quadrupolar field and the true polar displacement/non-axial dipole component decreased progressively. During the Quaternary, and also at the earliest Tertiary, the non-dipole components appear to have been moderate or small.
The comparison of data sets demonstrates that considerable errors may be incurred when Cenozoic, and presumably earlier, poles from one geographic region are used to derive those of another, widely separated, region. The results also imply that absolute plate velocities estimated from palaeomagnetic data can contain substantial errors, and that hot-spot data may need significant adjustments for true polar wander to yield correct palaeolatitudes.
Finally, the new early Tertiary pole for Australia is used in conjunction with updated early Tertiary poles from other lithospheric plates to reapply the McKenzie test for true polar wander. The results indicate a small true polar displacement since the beginning of the Tertiary. The amount and direction of the displacement, however, differ from those generally obtained from hot-spot data.     

A comparative study on the ionospheric current systems in the Antarctic and Arctic regions

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Electric field at the seafloor due to a two-dimensional ionospheric current

The relation between the seafloor electric field and the surface magnetic field is studied. It is assumed that the fields are created by a 2-D ionospheric current distribution resulting in the E-polarization. The layered earth below the sea water is characterized by a surface impedance. The electric field at the seafloor can be expressed either as an inverse Fourier transform integral over the wavenumber or as a spatial convolution integral. In both integrals the surface magnetic field is multiplied by a function that depends on the depth and conductivity of the sea water and on the properties of the basement. The fact that surface magnetic data are usually available on land, not at the sea surface, is also considered. Test computations demonstrate that the numerical inaccuracies involved in the convolution method are negligible. The theoretical equations are applied to calculate the seafloor electric fields due to an ionospheric line current or associated with real magnetic data collected by the IMAGE magnetometer array in northern Europe. Two different sea depths are considered: 100 m (the continental shelf) and 5 km (the deep ocean). It is seen that the dependence of the electric field on the oscillation period is weaker in the 5 km case than for 100 m.     

Quadrupole and octupole parameters of Jupiter's main magnetic field

Summary. The classical theory of multipoles is used to calculate the true quadrupole and octupole parameters for six different models of Jupiter's main magnetic field. These six magnetic-field models, which are based on measurements made by the Pioneer 10 and Pioneer 11 spacecraft, are specified in terms of the fifteen spherical harmonic coefficients required to define the Jovian dipole (3), quadrupole (5) and octupole (7). The set of five equations for the quadrupole parameters and the set of seven equations for the octupole parameters are each solved iteratively to give the corresponding true multipole moment and the directions of the associated multipole axes. It is found that the five quadrupole parameters are defined reasonably accurately by the Pioneer measurements, as are the three dipole parameters, but it is concluded that there are appreciable uncertainties in each of the seven octupole parameters. The true quadrupole and octupole magnetic moments are typically 14 and 5 per cent, respectively, of the dipole moment. These percentages are significantly different from the corresponding percentages for the pseudo-magnetic moments, namely 24 and 21 per cent, which are usually quoted in discussions of the higher multipoles of the Jovian magnetic field. Both the true and pseudo-multipole moments are larger for Jupiter than for the Earth. It is suggested finally that a proper multipole expansion of Jupiter's main magnetic field may have important applications in quantitative studies of several problems involving the Jovian magnetosphere, such as the decimetric and decametric radio emissions from Jupiter.     

Simulation of braided river flow using a new cellular routing scheme

Results are presented from a numerical simulation of two-dimensional flow patterns in a braided river using a simple cellular routing scheme. The results of the routing scheme are compared with field measurements of discharge per unit width obtained within the study reach at low flow and, for higher flows, with the predictions of a more sophisticated hydraulic model that solves the two-dimensional shallow water form of the Navier–Stokes equations. An assessment is made of the sensitivity of the routing scheme to variations in the values of its main parameters, and appropriate values are determined based on the physical characteristics of the study site and available flow measurements. It is shown that despite the simple approach adopted by the cellular routing scheme to simulate processes of water redistribution, it is able to replicate accurately both the field data and the results of the more sophisticated hydraulic model. These results indicate that the routing scheme outlined here is able to overcome some of the limitations of previous simple cellular automata models and may be suitable for use in modelling bedload transport and channel change in complex fluvial environments. As such this research represents a small and ongoing contribution to the field of numerical simulation of braided river processes.     

Interpretation of long-offset transient electromagnetic data from the Odenwald area, Germany, using two-dimensional modelling

The standard 1-D inversion approach for the interpretation of transient electromagnetic (TEM) data usually fails in the presence of near-surface conductivity anomalies. Since multidimensional inversion codes are not routinely available, the only alternative to discarding the data may be trial-and-error forward modelling. We interpret data from a long-offset transient electromagnetic (LOTEM) survey which was carried out in 1995 in the Odenwald area, using 2-D finite-difference modelling. We focus on a subsegment of the LOTEM profile, which was shot with two different electric dipole transmitters. A model is found which consistently explains the electric and magnetic field data at eight locations for both transmitters. First, we introduce a conductive dyke under the receiver spread to explain sign reversals in the magnetic field transients. A conductive slab under one of the transmitters is required to obtain a reasonable quantitative fit for that transmitter. Consideration of the electric field data then requires a modification of the layered earth background. Finally, we study the response of a crustal conductor, which was the original target of the survey. The data are sensitive to the conductor, and for the investigated subset of the data the fits are slightly better without the conductive layer.     

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.     

Transient electromagnetic fields about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space

Summary. Laplace and Bessel Transforms are used to solve for the transient behaviour of the electromagnetic fields after switching off a steady current in a grounded infinitesimal horizontal dipole on the surface of a uniformly conducting half-space. Simple analytic expressions, which are valid for times sufficiently long after the switch that displacement terms can be ignored, are obtained on the surface of the half-space for the electric field and the time derivative of the magnetic field. At the instant of switching an infinitesimally long image becomes established directly under the source dipole. It is the diffusion of this image which gives the vertical magnetic field and horizontal electric fields their transient behaviour. During the transient, there is also a decaying charge distribution on the surface.     

Street‐based topological representations and analyses for predicting traffic flow in GIS

It is well received in the space syntax community that traffic flow is significantly correlated to a morphological property of streets, which are represented by axial lines, forming a so called axial map. The correlation co‐efficient (R ²) approaches 0.8 and even a higher value according to the space syntax literature. In this paper, we study the same issue using the Hong Kong street network and the Hong Kong Annual Average Daily Traffic datasets, and find surprisingly that street‐based topological representations (or street–street topologies) tend to be better representations than the axial map. In other words, vehicle flow is correlated to a morphological property of streets better than that of axial lines. Based on the finding, we suggest the street‐based topological representations as an alternative GIS representation, and the topological analyses as a new analytical means for geographic knowledge discovery.     

THE PALAEOMAGNETISM OF THE KAINOZOIC BASALTS OF VICTORIA

Summary. The average geomagnetic pole position consistent with the magnetization of the Newer Volcanics of Victoria, which are for the most part of Pleistocene age, coincides with the present geographic pole just as do all pole determinations from Miocene and later rock formations from the Northern Hemisphere. During this time it appears that the Earth's magnetic field has approximated, on average, to that of a geocentric axial dipole and that the land masses concerned have maintained their present positions. In contrast, the pole determined from Lower Tertiary Volcanics of Victoria does not agree with the geographic pole nor with equivalent determinations from the Northern Hemisphere, suggesting that the relative positions of the continents may have been different in the past.     

Multivectorial magnetization in late Palaeozoic volcanics from North Sardinia; partial remagnetization and rotation

Summary . Detailed thermal demagnetization results combined with vector analysis and study of the convergence point of remagnetization circles reveal that the late Palaeozoic ignimbrites of North Sardinia possess a multi component remanence in addition to having experienced a tectonic rotation. The degree of palaeomagnetic complexity increases with increasing degree of oxidation of the magnetic mineralogy. It is concluded that the rocks were laid down in late Permian time just before the close of the reversed Kiaman geomagnetic epoch. Subsequent oxidation and partial remagnetization basically occurred in late Permian—Triassic time, during a period characterized by alternating field polarity. In the majority of the sites this remagnetization cycle brought about fairly erratic and relatively stable resultant magnetizations which are generally smeared out towards easterly directions. At a later date Sardinia was subject to an anticlockwise rotation of about 45 degrees, after which a minor chemical magnetization, aligned along the direction of the present axial dipole field, seems to have been acquired by some specimens.