Tracking a non-dipole geomagnetic anomaly using new archaeointensity results from north-east China

A collection of ceramics and samples, collected from north-east China with ages ranging from 1000 to 7000 years, have been investigated using a modified version of the Shaw palaeointensity techniques (Shaw 1974; Rolph & Shaw 1985) in which only partial NRMs and TRMs (PNRMs and PTRMs) with blocking temperatures (T_b) above 300 C are used after pre-selection of samples by mineral magnetic analysis. A secular variation curve obtained from this study is quite consistent with previous results from other areas of China (Wei et al. 1987; Tang et al. 1991), as well as with the global model of McElhinny & Senanayake (1982). Comparison of the Chinese results with contemporaneous results from Greece (Aitken et al. 1989) has allowed us to track the movement of a large non-dipole anomaly as it drifts westwards.     

Robust estimation of geomagnetic transfer functions

Summary. We show, through an examination of residuals, that all of the statistical assumptions usually used in estimating transfer functions for geomagnetic induction data fail at periods from 5 min to several hours at geomagnetic mid-latitudes. This failure can be traced to the finite spatial scale of many sources. In the past, workers have tried to deal with this problem by hand selecting data segments thought to be free of source effects. We propose an automatic robust analysis scheme which accounts for the systematic increase of errors with increasing power and which automatically downweights source contaminated outliers. We demonstrate that, in contrast to ordinary least squares, this automatic procedure consistently yields reliable transfer function estimates with realistic errors.     

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.     

A six-parameter statistical model of the Earth's magnetic field

A six-parameter statistical model of the non-dipole geomagnetic field is fitted to 2597 harmonic coefficients determined by Cain, Holter & Sandee (1990) from MAGSAT data. The model includes sources in the core, sources in the crust, and instrument errors. External fields are included with instrument errors. The core and instrument statistics are invariant under rotation about the centre of the Earth, and one of the six parameters describes the deviation of the crustal statistics from rotational invariance. The model treats the harmonic coefficients as independent random samples drawn from a Gaussian distribution. The statistical model of the core field has a correlation length of about 500 km at the core-mantle boundary, too long to be attributed to a white noise source just below the boundary layers at the top of the core. The estimate of instrument errors obtained from the statistical model is in good agreement with an independent estimate based on tests of the instruments (Langel, Ousley & Berbert 1982).     

Electrical anisotropy and conductivity distribution functions of fractal random networks and of the crust: the scale effect of connectivity

All explanations of the high-conductivity layers (HCL) found by magnetotellurics in the middle or lower crust incorporate a mixture of a low-conductivity rock matrix and a highly conductive phase, for example graphite or saline fluids. In most cases the bulk conductivity of the mixture does not depend on the conductivity of the rock matrix but rather (1) on the amount of high-conductivity material and, in particular, (2) on its geometry. The latter is quantitatively described by the parameter 'electrical connectivity'. Decomposition of the observed bulk conductivity of the mixture into these two parameters results in an ill-posed problem. Even if anisotropy occurs in the HCL, three output parameters (highly conductive phase fraction, connectivity with respect to the X direction, connectivity with respect to the Y direction) have to be estimated from the two bulk conductivities of the anisotropic HCL. The additional information required for solving this problem is provided if instead of single-site data the conductivities from many field sites are evaluated: a sample distribution of the conductivity can then be obtained. Ensembles of random networks are used to create theoretical distribution functions which match the empirical distribution functions to some extent. The use of random resistor networks is discussed in the context of other established techniques for the treatment of two-phase systems, such as percolation theory and the renormalization group approach. Models of embedded networks explain the discrepancy between 'small' anisotropy (2-3) on the laboratory scale and large anisotropy (10-100) found in electromagnetic field surveys encompassing volumes of several cubic kilometres. Strong anisotropy can indicate low electrical connectivity, and a possible explanation is that a network stays close to the percolation threshold.     

Spectral-finite-element approach to two-dimensional electromagnetic induction in a spherical earth

We present a spectral-finite-element approach to the 2-D forward problem for electromagnetic induction in a spherical earth. It represents an alternative to a variety of numerical methods for 2-D global electromagnetic modelling introduced recently (e.g. the perturbation expansion approach, the finite difference scheme). It may be used to estimate the effect of a possible axisymmetric structure of electrical conductivity of the mantle on surface observations, or it may serve as a tool for testing methods and codes for 3-D global electromagnetic modelling. The ultimate goal of these electromagnetic studies is to learn about the Earth's 3-D electrical structure.
Since the spectral-finite-element approach comes from the variational formulation, we formulate the 2-D electromagnetic induction problem in a variational sense. The boundary data used in this formulation consist of the horizontal components of the total magnetic intensity measured on the Earth's surface. In this the variational approach differs from other methods, which usually use spherical harmonic coefficients of external magnetic sources as input data. We verify the assumptions of the Lax-Milgram theorem and show that the variational solution exists and is unique. The spectral-finite-element approach then means that the problem is parametrized by spherical harmonics in the angular direction, whereas finite elements span the radial direction. The solution is searched for by the Galerkin method, which leads to the solving of a system of linear algebraic equations. The method and code have been tested for Everett & Schultz's (1995) model of two eccentrically nested spheres, and good agreement has been obtained.     

Periodicity of magnetic intensities in magnetic anomaly profiles: the Cenozoic of the South Atlantic

Spectral analyses of several published magnetic anomaly profiles from Candé & Kent (1992a) were undertaken prior to analysing, in the same way, raw magnetic anomaly data from similar parts of the South Atlantic. It was found that similar and distinct medium and short wavelengths were present in both the published and raw data. When these are converted into the time domain using the average rate of spreading for each profile, these periodicities appear similar, possibly identical, to those expected from the long-term eccentricity orbital parameters (Fischer, DeBoer & Premoli Silva 1990). While such correlations are not necessarily causative, they suggest that magnetohydro-dynamical processes near the core-mantle boundary may be affected by gravitational changes due to planetary orbital perturbations.